U.S. DEPARTMENT

, < - MERGE

ational ^ Bureau

ot

I 19*71 idards

The Menzel

Symposium

on Solar Physics,

Atomic Spectra,

and Gaseous

Nebulae

tflONAL BUREAU OF olAMJAKk>*

OCT 6 1971 UNITED STATES DEPARTMENT COMMERCE • Maurice EL Stans, Secretary

NATIONAL BUREAU OF STANDARDS • Lewis M. Branscomb, Din; tor

The Menzel Symposium

on

Solar Physics, Atomic Spectra,

and

Gaseous Nebulae

in Honor of the Contributions

Made by Donald H. Menzel

Proceedings of a Symposium held

at the Harvard College Observatory,

Cambridge, Massachusetts

April 8-9, 1971

Edited by

Katharine B. Gebbie

Joint Institute for Laboratory Astrophysics

Institute for Basic Standards

National Bureau of Standards Boulder, Colorado 80302

National Bureau of Standards Special Publication 353

Nat. Bur. Stand.( U.S.), Spec. Publ. 353, 213 pages (Aug. 1971) CODEN: XNBSA

Issued August 1971

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington, D.C. 20402 (Order by SD Catalog No. C13. 10:353) Price $1.75.
ABSTRACT

A symposium in honor of Donald H. Menzel 1 s contributions to astrophysics was held on his 70th birthday

at the Harvard College Observatory, Cambridge, Massachusetts, 8-9 April 19 71. Menzel and his school have

made distinguished contributions to the theory of atomic physics, solar physics, and gaseous nebulae. The

work on planetary nebulae represented the first investi

gations of non-equilibrium thermodynamic conditions in

astronomy; the solar work extended these investigations

to stellar atmospheres. The applied atomic physics

laid the basis for what we now call laboratory astrophysics and, together with work on non-equilibrium ther

modynamics, inspired the founding of the Joint Institute for Laboratory Astrophysics. Menzel has served as

a distinguished consultant to the National Bureau of

Standards, and publication of this volume represents a grateful acknowledgment of his service to the Bureau.

The papers summarize the current status of work in the

three fields he pioneered.

Key words: atomic energy levels, transition probabilities, solar physics, gaseous nebulae, non-LTE thermodynamics .
THE MENZEL SYMPOSIUM

ON

SOLAR PHYSICS, ATOMIC SPECTRA

AND GASEOUS NEBULAE

CONTENTS

Preface vii

Foreword ix

PART I ATOMIC ENERGY LEVELS AND TRANSITION

PROBABILITIES 1 W. R. S. Garton

Experimental Studies of Atomic Spectra

and Transition Probabilities 3 David Layzer

Towards an Elementary Theory of

the Periodic Table 20

Hugh P. Kelly

Many-body Calculations of Energies and

Transition Probabilities 37

Alexander Dalgarno

Radioactive Transitions in the Helium

Isoelectronic Sequence 47

PART II SOLAR ASTRONOMY 59

John W. Evans

Solar Instrumentation (Part I) 61

Richard B. Dunn

Solar Instrumentation (Part II) 71

Richard N, Thomas and Katharine B. Gebbie

e Solar Chromosphere and the General Structure

of a Stellar Atmosphere 84

J. 3. Zirker

The Corona 112

George L. Withbroe

The Chemical Composition of the

Photosphere and the Corona 127

v
PART III

GASEOUS NEBULAE 149

S. J. Czyzak and T. K, Krueger

Optical Line Spectrum 151

Lawrence H. Alter

Chemical Composition of Typical

Planetary Nebulae 161

Leo Goldberg

Radio Recombination Lines 169

William Liller

Internal Motions and Kinematics

of Planetary Nebulae 182

Donald H. Menzel

Filamentary Structure of

Planetary Nebulae 190

vi
PREFACE

The papers in these proceedings were presented at

a symposium in honor of Donald H. Menzel on the occasion of his 70th birthday at the Harvard College Observatory, Cambridge, Massachusetts, 8 and 9 April 19 71.

The symposium was supported in part by the National

Science Foundation. The formal Organizing Committee

was composed of Leo Goldberg, Lawrence Aller, David

Layzer, and Richard Thomas. Robert 0. Doyle of Harvard

College Observatory did a great deal of organizational

work and I wish to thank him and the secretarial staff

of Harvard College Observatory, particularly Mrs. Nicki

Vance

.

To Alice Levine, my production editor, goes the

entire credit and responsibility for supervising the

production of these proceedings. Working with her is

always a joy; for her professional competence and sus- tained good spirits I am deeply grateful. Judy Schlepp

has not only prepared the typescript and assisted in

the production but also attended to a myriad of details.

Many authors will be grateful to her for the persistence

with which she checked their references.

I am indebted to the publications office of the

National Bureau of Standards, and in particular to W. R.

Tilley and Betty L. Oberholtzer, for the publication of

this volume.

Katharine B. Gebbie

July 19 71

Boulder, Colorado

vii
DONALD H. MENZ EL
FOREWORD

Some two hundred friends and admirers of Professor

Donald H. Menzel assembled at Harvard last April for a two-day symposium on progress in the interpretation of

atomic spectra, in solar physics, and in the theory of

gaseous nebulae, in recognition of Menzel' s second

retirement. He had retired once in 1966 as Director of

Harvard College Observatory, a post he had held from

1954, and on this occasion was retiring from his position on the staff of the Smithsonian Astrophysical

Observatory'. This volume records the papers that were

presented on this occasion.

A two-day symposium was necessarily inadequate

even to touch on the many other interests that Menzel

has followed in his life with competence and gusto and verve. Not covered was his emphasis on the study of

solar-terrestrial relationships, in particular the way

changing solar conditions manifest themselves in the

terrestrial ionosphere, with consequent enormous

changes in the conditions of long-distance radio wave

propagation. Menzel was one of the first in this country to recognize the great importance of knowing about

these effects in detail, and of organizing the observations in a way that would facilitate the making of predictions of radio communication links at all frequencies and over all paths. This subject was his principal occupation during his service as a naval officer

during World War II.

At the end of the war he was a leader in the group

that set up the Central Radio Propagation Laboratory in

the National Bureau of Standards to provide this essential service for civilian and military communications.

This happened during the period (19 45-51) when I was Director of NBS , and it provided the opportunity for

deepening a personal friendship that had begun in prewar days in the study of atomic spectra. I am happy

that this volume can be included in the NBS publications in recognition of Menzel 's scientific and administrative contributions to the establishment of CRPL.

Another area of Menzel 1 s interests that deserves

mention is the serious effort he devoted to the study

of "flying saucers" on which he wrote two books.* Here

he devoted a great deal of effort to providing rational

explanations, often in terms of little-known or poorly

i ix
understood phenomena of atmospheric optics, for many of

the reports which the true believers were uncritically

accepting in support of their fantasies about the

Earth's being visited by spacecraft from other civilizations. This brought about another happy period (1966-

69) of collaboration between us, when he served as a consultant on the U. S. Air Force sponsored project, of

which I was Director. This project led to the preparation of Scientific Study of Unidentified Flying

Objects .

Menzel was born in Florence, Colorado and raised

in Leadville, one of the great mining camps of the

Rockies; he still has strong roots here. It was he who

introduced me to this area in 19 49, on a momentous

visit that led to the choice of Boulder as the location for the NBS laboratories for the study of radio

propagation.

E. U. Condon

July 1971

Boulder, Colorado

*Donald H. Menzel, Flying Saucers (Cambridge, Mass.:

Harvard University Press) , 19 53; and Donald H. Menzel

and Lyle G. Boyd, The World of Flying Saucers (New York:

Doubleday) , 196 3.

+(New York: Bantam, Dutton) 1969.

x
J.C. Pecker

I ATOMIC ENERGY LEVELS AND TRANSITION PROBABILITIES

Chairman: David Layzer

Harvard College Observatory

There are many paths to astronomy,

and I probably followed the most

violent one of all.

Donald H. Menzel

EXPERIMENTAL STUDIES OF ATOMIC SPECTRA

AND TRANSITION PROBABILITIES

W. R. S. Garton

Imperial College of Science

and Technology 3 London

Some special sentiments may be expected from a contributor to the Menzel Symposium who happens to be

based at Imperial College, London, because of the long

relation between that institution and the centre of

astrophysical excellence at Harvard College Observatory.

This reflection relates to the close community of

interest and a good deal of collaboration and correspondence that occurred years ago between two pioneers

in the field of astrophysics: E. C. Pickering - Dr.

Menzel' s predecessor but one (1877-1919) as Director at

Harvard College Observatory - and his counterpart in

what ultimately became Imperial College, Sir Norman

Lockyer. The closely related activities of these two

pioneer investigators can be illustrated by quoting the

opening words from the celebrated paper of Saha (19 21) , written about the time he was working in Imperial

College with Lockyer ' s successor, Alfred Fowler: "The

present paper embodies an attempt towards a physical

explanation of the ordered gradation in the spectra of

stars — a subject in which pioneering work was done by

the late Sir Norman Lockyer, but which was worked up

with systematic thoroughness at the Harvard College

Observatory, under the lead of the late Professor E. C.

Pickering and Miss A. J. Cannon." This historical

background gives, understandably, an added flavor to

the satisfaction within both institutes that the con- nections have now been powerfully renewed. From about

1960 there have been close collaborative efforts

founded on observational work by rocket- and satelliteborne instrumentation and supporting laboratory astrophysics at Harvard, and on research, mainly on vacuumultraviolet and soft X-ray spectra, at the Imperial

College Laboratory. A recent spectacular success of

this cooperation - in this case involving also the

Astrophysics Research Unit, Culham, and the Centre for

3
Figure 1. Flash and coronal spectra at the March 7,

1970 solar eclipse: (a) before second contact; (b) and

(c) near second contact; (d) at totality.

Research in Experimental Space Science at York University, Toronto - has been the set of spectra of chromosphere and corona in the vacuum ultraviolet, obtained

with a rocket-borne spectrograph at Wallops Island

during the total eclipse in March 1970 (Speer et al.

19 70) . A time sequence of fifty stigmatic spectra from

before and through totality were registered in the

region 850 - 2100 A; Figure 1 shows sample spectra at

several phases of the eclipse. Photometric reduction

of the spectra, now completed on the excellent densitometer at Harvard, has produced a wealth of material for

interpretation by solar physicists.

The concern of the Menzel Symposium and the present volume is to pay tribute to the significant work

done over a period of nearly fifty years, roughly half

a century after the pioneering days of Pickering and

Lockyer. Menzel' s scientific contributions began in

4
the mid-1920 's, when he was among those exploiting the

advances in atomic physics of the second and third

; decades of the twentieth century, which generated the

' quantum formulation of the structure and mechanics of

i atoms and molecules. .An early comprehensive paper

(Menzel 1931), "A Study of the Solar Chromosphere",

! sets out and applies the theory of spectral line formaj tion and radiative transfer. This contribution inevitably depended on speculative estimates of most of the

atomic parameters involved, e.g. f -values of astrophysically important lines of other than H-like ions, linebroadening parameters, and photoionization cross sections of cosmically abundant metals. Because of the

decline in laboratory and theoretical work in atomic

physics, which began in the early 1930 's, Menzel 's work

I on the chromosphere would have had little advantage

twenty years later. Such neglect of richly rewarding

! fields terminated in the 1950 's with the emergence of

space astrophysics, aeronomy, and plasma physics. The

present article sketches some of the results from this

period in laboratory astrophysics. This short article

deals with a narrow selection of material, much of

which is drawn from work done in the author's laboratory or in collaboration with associated institutions,

notably the Harvard Observatory, the Argonne National

Laboratory, the National Bureau of Standards, and York

University, Toronto.

A great deal has been accomplished towards a systematic determination of atomic and molecular f-values

and the associated problems of reliable diagnostic

methods for the measurement of temperature and particle

densities in astrophysical and/or laboratory plasmas.

Important and continuing programs were started in the

early 1950 's by Lochte-Holtgreven (1958) and Maecker

I (1951, 1955) in Kiel, based on development of several

forms of stabilized arc discharge. The many significant experiments in laboratory astrophysics that

emerged from this program have been continued in the

capable hands of Wiese (1970a, b) , at the National

Bureau of Standards, on oscillator strengths, and of

Griem (1964, 1968) , at Maryland, more particularly

towards elucidating the mechanisms of spectral line

broadening. In the latter field, recent useful contributions have been made by Cooper (1969) at Boulder and

(by D. D. Burgess (1970, 1971) at Imperial College and

1 Harvard. In spite of strenuous efforts by theorists, a unified explanation of line broadening, valid for both

wings and line centers, has yet to be formulated. For

many years we have relied on the statistical (micro-

: field) approach to account for the details of line

5
wings and on the impact approximation for the line centers. It is hardly surprising that the intermediate

region, where neither approach is fully satisfactory

and where effects of the correlated motions of the perturbers are most significant, is of the greatest

interest to astronomers. Another area, not yet seriously explored, concerns the effects of the cooperation

of plasma waves, separated by the plasma frequency or

an harmonic or two (Baranger and Mozer 1961) . These

can be responsible for strongly oscillating electric

fields and hence for the production of satellites to

spectral lines. Burgess and collaborators (unpublished

have recently observed lines in C IV that are probably

satellites such as these; these results are illustrated

in Figure 2. It is interesting to speculate on the

presence of such satellites in the spectra of flares or

of the solar transition layer. Mention should also be J made of recent (unpublished) experiments by D. D.

Burgess in collaboration with Parkinson and Reeves at

Harvard; the object is to study spectral line broadening in cosmically important light elements and metal

Figure 2. Plasma-wave-induced satellite features in C I.

6
atoms in atmospheres of hot but neutral atomic hydrogen

The experiments use a large "piston-compressor" tube,

n which hydrogen can be heated adiabatically and dissociated - but only slightly ionized - at pressures and

[temperatures comparable with those in the upper photosphere; line broadening in the spectra of chosen additives can be investigated. The first successful

Results (Burgess and Grindley 19 70) concerned the

broadening of the Na-D line in atmospheres of neutral

pelium, and current experiments aim at substituting

(hydrogen for helium.

Work oh the determination of atomic f-values of

astrophysically important transitions is currently in

^progress by Huber, Parkinson, and Reeves at Harvard,

"rhey have applied both equivalent width techniques and

measurements of anomalous dispersion ("hook method") to

plasmas produced in shock tubes. Until the start of

the Harvard experiments, use of the "hook method" was

confined almost entirely to the group under Penkin

(1964) in Leningrad. This valuable Russian work, which

has been in progress for many years, has been

restricted chiefly to measurements of f-values of transitions involving the ground state or low excitation

states of an atom. The Harvard work has included a wider wavelength range towards the ultraviolet and has

extended the technique , by means of shock tubes , to

transitions between fairly highly excited states and to

ionic species. Examples of some important results are

fto be found in Huber and Tobey (196 8) and Grasdalen

It al. (1969) on Fe I and II, Cr I and II, and in

Garton et al. (1964) on an autoionizing doublet of Al I near 1930 A. The special significance of this Al I doublet for solar physics has been emphasized by

Soldberg (1966) and by Withbroe (1966).

The Harvard laboratory program has determined

molecular f-values - for example, the vibrational transition probabilities of the CO fourth positive system - by measurement of equivalent widths (Rich 196 8) . At

Imperial College, application of the hook method

(Anketell and Pery-Thorne 1967; Pery-Thorne and

Banfield 1970) has yielded improved f-values for ultraviolet bands of the important radicals OH and NO. At

,York University, Toronto, a variety of emission and

[absorption techniques have been applied (e.g. Nicholls

|1969; Drake et al. 1967) including the hook method, for

many molecules of astrophysical and/or aeronomical significance.

Space allows only passing mention of the large and

important programs to measure lifetimes of excited

^states by means of the relatively new "beam-foil"

7
method, which is proving prolific in yielding f-values

for many transitions in spectra of medium and very higl

stages of ionization (see Bashkin 1968)

.

Only during the last twenty years has much progress been made towards the experimental determination

and theoretical calculation of photoionization cross sections (Marr 19 67; Samson 1966) . These are importanl

in many fields of astrophysics, including stellar

atmospheres, interstellar material, and the field cov- ered by Menzel and his collaborators in their magnificent compilation "Physical Processes in Gaseous

Nebulae". The unhappy position of the astronomer for

many years in this respect is illustrated by the photoionization cross section of Ca I: early quantal calculations yielded a cross section at threshold that

proved fifty times too high when the first experimental

determination was reported by Ditchburn and Hudson

(1960) . The error lay in the dramatic effects of the

autoionization of doubly-excited states on photoionization continua. Though this process was first recognized by Shenstone (1931) and Majorana (1931) and was extensively illustrated by the work of Beutler in the

1930*s (see Boyce 1941), the recognition of its astrophysical relevance came rather later; see, for instance

Goldberg (1966) . Laboratory work of the last ten years

has shown that double-electron and/or inner-shell excitation in all of the alkaline-earth and alkali first

spectra produce drastic effects on the shapes of the

corresponding ionization continua somewhere in the

ultraviolet. Thus the Schumann region and shortwavelength part of the quartz-ultraviolet contain impo2

tant extensions of the spectra Ca I, Sr I and Ba I (Garton and Codling 1965, 1968; Garton and Tomkins

1969) . These spectra arise by transitions of the type

ms 2

h (m-1) dnp and nf

and yield a confused series of autoionization resonances, which converge on the metastable 2 D levels of

the corresponding ions. In addition to the work of

Ditchburn and Hudson (1960) on Ca I, measurements of

the strongly fluctuating photoionization continua of

Sr I and Ba I have been reported by Hudson et al. (19 6. 1970) .The universal importance of the autoionization

process on all but H-like atomic spectra is nicely

illustrated by the fine work of Madden, Codling, and

Ederer who, using the NBS 180 MeV electron-synchrotron

8
as a background light source for absorption spectroscopy, have reported on new absorption spectra of all

the inert gases in the short-wavelength part of the vacuum ultraviolet. For example, in He I, in the

region around 200 K, several Rydberg series of double2lectron transitions were found superposed upon the

ohotoionization continua shortwards of the first limit

! at 504 A (Madden and Codling 1965; Madden 1966). The

peculiar line-profiles often exhibited by a transition

(Involving an autoionizing upper state were first seen

by Beutler (1935) and shortly afterwards explained by

? ano. Much later, Fano (1961) developed this theoretical approach into a quantitative parameterization,

vhich has subsequently been further developed (Fano and

hooper 1965; Comes and Salzer 1966; Shore 196 7) and has

, proved of great use to the experimenter faced with

interpreting atomic and molecular absorption spectra.

?he type of line profile concerned is shown in Figure 3 ffhich represents photometric measurements of an absorption line of Tl I (6s 2 6p 2 Pj/2 - 6s6p 2 2 P 3/2 ); the line

Ls very reasonably characterized by the Fano parameters

p (the resonance half-width) and q (the "line-profile

Index") . The example of Figure 3 concerns an isolated

. Autoionization resonance. A few years ago at Harvard,

la more ambitious attempt was made (Garton et al. 1968)

,

Jkhich involved the unfolding of a whole group of overlapping and mutually interfering autoionization resonances; the results are displayed in Figure 4, where

:he full line represents the theoretical unfolding of

phe course of the photoionization cross section, and

the plotted points are observational. A similar analysis for the Ca I structures has been performed by

lewsom and Shore (196 8)

.

In addition to the likely relevance of autoionizapion processes in several astrophysical situations

[Goldberg 1966) and related problems concerning the

.nverse process of "dielectronic recombination" (A.

iiurgess 196 6) , there exists the interesting, though

.ittle explored, possibility of "forced autoionization"

Evidence was given by Garton et al. (19 6 2) , that a loubly-excited atomic energy level, which normally lies

»elow the first ionization potential, can be stimulated

.nto autoionization through the effects of microfields

>f charged particles present in a plasma. The evidence

^:ame from a comparison of the absorption spectra of

la I obtained respectively with a furnace and a shock

:ube. The interpretation provided in that paper is not

intirely certain although the occurrence of the forced

LUtoionization process has been established without

loubt by beautiful experiments of Feldman and Novick

9
m

o

©

CM

( 2 ujd 8| 0I)X NOI103S-SSOUD N0l±dU0S9V 0IW01V

10
m

CDUccow

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-P ow 

fd w 0 o

-p a o ^

CU P. >

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11
(1967), in which beams of doubly-excited alkali atoms,

metastable towards both radiation and autoionization

processes, were observed to autoionize in the presence

of a small electric field. This problem of forced

autoionization is closely connected with the still

thorny problems of the microfield depression of ionization potentials and the termination of the partition

function of a hot gas, both of great significance to

the astronomer.

Although the Schumann and near ultraviolet spectra

of the alkaline earths exhibit moderately complicated

effects of configuration mixing between the doublyexcited series lines themselves and with the underlying

continua, the spectra of these elements and those of

the alkalis show much greater complexity at even

shorter wavelengths, due to excitation of the first

underlying p-shells. Connerade ( 1970a, b) and Mansfield

(see Garton et al. 1969, Connerade et al. 1971) have

studied the absorption spectra of elements Na through

Cs in the range 200-900 A. Pioneer experiments by

Beutler in the 1930 's indicated some structures in Rb

and Cs due to excitation of the 4p e and 5p 6 subshells

respectively, but work at tfie Imperial College in the

last few years has proved that these studies certainly

needed revision. The complicated nature of the absorption spectra of this group of elements is illustrated

in Figure 5. The prime reason for the complexity in

the spectra of K I , Rb I and Cs I is the severe configuration mixing now known to occur amongst the low

levels of the corresponding ions; thus, in Rb II the

levels of 4p 5 5s and 4p 5 4d have overlapping structures.

Consequently, whereas Beutler imagined, reasonably

enough, that the spectra were arising from transitions

of the type

(m-1) p

6 ms 2 S >-(m-l) p

5 ms ns , nd

and thus would be expected to converge on the four

limits of (m-1) p

5 ms , the configuration mixing

increases to twelve the number of available limits on which the Rydberg absorption series of the neutral atom

converge

The p-shell absorption spectra of the alkaline

earths , Mg I through Ba I , have been photographed by

Newsom in the range 100-700 A and exhibit features of

increasing complexity with rising Z. Two of the spectra (Mg I and Ba I) are reproduced in Figure 6. The

only completed analysis to date refers to Mg (Newsom

12
(So) 7s p] K

(5.) bd

Wns[l] Va ,Vx

(^.)7s[l] K

(7.) 10* [I] (u ( )5d

(7t )Hs[i]v

^

(7.)'n*[l]

C506s [a] v

||||ii lu(i||| (7.) bs [\]^

Oo,)G*tO H

17,) 4i

(S0 7s[3] H

ft*) 8s [a]*

(6o)7s [o>z

13

19 71) which, though showing the simplest structure of

this group of spectra, also contains some surprising

features; for instance, the strongest transition of the

Mg I spectrum of Figure 6a occurs to the short-wavelength side of both the 2p 5 3s 2 limits and is tentatively classified, on energetic grounds, as arising

from a three-electron transition to the upper state

2p 5 3p 2 3d.

Much interpretive work remains to be done on all

these inner-shell spectra of the alkalis and alkaline

earths. It will be obvious from some of the spectra

shown in the plates accompanying this article that the

"raw data" expected of the experimenter must now include photometric records of the violently fluctuating ionization continua; information restricted to

| photographic records and analyses of transitions and

j Rydberg series becomes increasingly inadequate for pur-

' poses of theoretical interpretation. The absorption

spectrum of Be I, which has been photographed and

analyzed by Mehlman-Balloffet and Esteva (19 69) , is

particularly interesting, and the need for photometric

|! data is emphasized, because, rather unusually, theoret-

: ical calculation of autoionization resonances and half-

;

! widths has been made ahead of the experiment by Altick

(1968) . The Be I absorption spectrum produces a particular experimental challenge on account of the

l! extreme chemical reactivity of the metal and vapor, and

j it may be expected that a technique originated by

Nelson and Kuebler (1962) and previously mentioned by

Garton (19 66) under the name "flash pyrolysis" may be

| useful. This experimental technique has recently been

used with great success at Argonne and Harvard by

Tondello (19 71) in obtaining the absorption spectrum of

SI; the spectrum observed contains long absorption

| series in the range 900-1300 K, including important

j autoionization structures. This new spectrum of S I is

of obvious astrophysical importance, and, as in the

j case of Be I , the experiment has the added attraction

; that possibilities of comparison with theoretical predictions (Conneely et al. 1970) already exist.

Another area of experiment for which the "flash

pyrolysis" technique appears promising is in the observation of the absorption spectra of ions. To date, to

the author's knowledge, the only observation of

an extensive absorption spectrum of this sort is that

of La II. This was obtained a few years ago at Harvard,

by use of improved shock-tube techniques (Parkinson,

Reeves and Grasdalen, unpublished) . By careful manipulation of the shock conditions, a spectrum was obtained

almost entirely of La II, with La I present only very
weakly. Unfortunately the region between 900 and

1200 A, in which strong autoionization structure is

anticipated, was only poorly obtained because of the use of lithium fluoride optics. The case of La II has

a particular interest because the La+ and La++ ions

have very different electronic structures from the isoelectronic species Ba and Ba+ respectively.

Through cooperative work between Argonne, Harvard,

and Imperial College (unpublished) , some striking new

spectra have also been obtained on the absorption spectra of the Illb elements, Sc and Y. Not surprisingly,

the spectra of these elements, which immediately follow

the alkaline earths in the periodic table, show greatly

increased complexity, as a result of the addition of a d electron in each case. Some features of the new

spectra, each of which contains many hundreds of new

lines and several hundred identifiable new levels, some falling in a number of series, are shown in Figure 7.

The identification of series in these spectra for the

first time has enabled reliable values of ionization

potentials to be obtained; thus, in Y I the previously

listed value of the first ionization potential (Moore

1952) proved to be 2500 cm" 1 in error. In addition to

the need for photometric work on these spectra, analysis of the multitude of lines longward of the first

limit requires examination of Zeeman effects. These

two spectra are so crowded towards their first ionization potentials that progress was only possible through

the use of the fine National Bureau of Standards IOmeter vacuum spectrograph, made available to the

Argonne, Harvard and Imperial College workers for a week early in 1970.

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Anketell, J. and Pery-Thorne, A. 1967, Proc. Roy. Soc,

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Baranger, M. and Mozer, B. 1961, Phys. Rev., 123 , 25.

Bashkin, S. 1968, Beam Foil Spectroscopy , 1, 3 (London:

Gordon & Breach)

Beutler, H. 1935, Z. f. Physik, 93, 111.

Boyce, J.C. 1941, Rev. Mod. Phys. , 13_, 1.

Burgess, A. 1966 in Autoionization , ed. A. Temkin

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16

Burgess, D.D. and Grindley, J.E. 1970, Ap . J., 160 , 343.

Burgess, D.D. 1970, J. Phys. B, 3, L67, L70.

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1971, Ap. J. , 165, 203.

Cooper, J. 1969, Lectures in Theoretical Physios XI-C

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J. Q.S.R. T. , 7, 639.

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Ap. J. , 140, 1269.

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Physios, Vol. 2_ (New York: Academic Press), p. 121.

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(Baltimore: Mono Book Corp.), p. 1.

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Ap. J. , 156_, 1153.

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Conference on Optical and Atomic Line Shape,

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,

p. 331.

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Rev. , 180_, 77.

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Rev. , A2, 643.

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18
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(Baltimore: Mono Book Corp.), p. 129.

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.

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.

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.

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,

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.

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.

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19
TOWARDS AN ELEMENTARY THEORY OF THE

PERIODIC TABLE

David Layzer

Harvard College Observatory

The motivation of my talk has been well expressed,

in another context, by Wigner and Seitz (19 55)

If one had a great calculating machine, one might apply it to the problem of solving the

Schroedinger equation for each metal and

obtain thereby the interesting physical quantities, such as the cohesive energy, the lattice constant, and similar parameters. It is

not clear, however, that a great deal would

be gained by this. Presumably the results

would agree with the experimentally determined quantities and nothing vastly new would

be learned from the calculation. It would be

preferable instead to have a vivid picture of

the behavior of the wavefunctions , a simple

description of the essence of the factors

which determine cohesion and an understanding

of the origins of variation in properties

from metal to metal.

The purpose of this talk is to outline an explanation

of the kind favored by Wigner and Seitz for the wellknown regularities that characterize the periodic table

of chemical elements.

These are illustrated in Figure 1, which shows twoi

idealized versions of the periodic table. In each fig- ure a box represents a subshell consisting of orbitals

with given values of n and I. For highly ionized atoms

the order in which successive subshells are added is

that shown on the right. Each shell, labeled by a fixed value of n, is completed before a shell with the

next higher value of n is begun, and subshells, characterized by fixed values of n and I, are added in order

20
21
of increasing ft. In short , the order of adding subshells is (n, ft) -lexicographic.

For neutral atoms, on the other hand, a different

rule applies. As was first pointed out by Bohr, the

order in which subshells are added is determined first

by the value of n + £ and then by the value of ft; that

is, it is (n+ft , ft) -lexicographic. Thi«s rule is illustrated in the diagram on the left in Figure 1". Subshells are added along the diagonals in the diagram,

from upper right to lower left.

Both diagrams are, of course, idealizations. Espc

cially among the heavier elements, the building-up pro- cess does not take place in such a regular fashion.

Most of the departures from the simple order shown in

Figure 1 reflect the dependence of energy levels on quantum numbers other than those characterizing the sul

shells. For example, it may be energetically favorable

to add an orbital out of the order indicated in the

appropriate diagram if the resulting spectroscopic tern

has high multiplicity (a high value of S) . Such

effects are reasonably well understood, at the qualitative level, and I shall not discuss them further in

this talk.

What is the theoretical basis for the regularitie*

illustrated in Figure 1? I remember asking Donald

Menzel this question during my first meeting with him.

I knew nothing of atomic physics at the time - I had

not even heard of the Bohr atom. But instead of sending me off to read a book, Donald sat down with me and

covered the whole subject, from Bohr's theory of the

hydrogen atom to intermediate coupling in complex atom

in a single afternoon. One of the questions I remembe

asking concerned the regularities illustrated in Figur

1. Donald's reply, that no adequate answer had yet

been given, convinced me that atomic physics was still

a live subject, in which more remained to be done than

routine calculations.

Let me begin with the regularities that pertain t< the sequence of highly ionized atoms (Z>>N) , because

these are the easier to explain. The energy levels E

of an isolated atom can be expressed as functions of

nuclear charge Z in the form

• • ' Vi c - _'

i i E = E Q Z

2 + E 2 Z + E

2 + Erel + CKZ" 1

) . (lj

In practice the term 0(Z -1

) is usually negligibly smal

when the degree of ionization (Z-N) exceeds 3 or 4.

The remaining terms in this formula can all be calcu22
lated. Let me remind you briefly of the nature of

these calculations.

(1) E 0

. The coefficient of Z

2 is given, in atomic

units, by the hydrogenic formula

^2n2

the summation extending over all occupied orbitals.

(2) Ej. This coefficient can be evaluated with

"arbitrary precision by elementary calculations involving only hydrogenic wavefunctions . It was first calculated for atoms in the first row of the periodic table

jby Layzer (19 59) , and these calculations were later

^extended to more complex atoms by Godfredsen (1963,

3 1966). The coefficient has the following structure:

5 ; where a = nZ , 3 = n'£', and the summation extends over

all N(N-l)/2 pairs of electrons. The quantity [a, 3] is

a two-electron interaction energy. the notation indicates, it depends only on the two orbitals in question

.and not on the electron configuration or spectroscopic

jterm. The quantity AE 1 is responsible for the firstorder splitting of a configuration into spectroscopic

/terms. Its value for a particular spectroscopic term

depends in general not only on the interaction of electrons within a given configuration but also on interactions connecting different configurations characterized

jby the same set of principal quantum numbers (and the

f same parity) . [The interconf igurational contribution

to AE 2 is responsible for the well-known systematic

; deviations between predictions based upon the centralfield approximation and experiment (Layzer 1959) ]

.

(3) E

2

. The evaluation of this coefficient presents a substantially more difficult mathematical problem than the preceding one, but in principle E 2 can

also be evaluated with arbitrary accuracy. The basic

theoretical considerations are set forth by Layzer,

Horak, Lewis, and Thompson (1964), where it is shown

that E 2 can be split up into two terms,

E

2 = E 2 + E (4)

23
The one-electron part E 2

1 can be evaluated by means of | a finite calculation - most conveniently, using double | perturbation theory (Dalgarno and Stewart 1958; Layzer

et al. 1964) . The evaluation of the two-electron part

E 2

" can be reduced to a series of two-electron problems

from the solutions of which the value of E 9 " for any Nelectron atom can be evaluated in a systematic way.

(4) •^rel* This term represents the relativistic

contribution to the energy of a many-electron atom.

Dirac's relativistic theory of the hydrogen atom and

Breit's relativistic theory of two-electron atoms form

the theoretical basis for evaluating this term. The Z- dependent many-electron theory was given by Layzer and i Bachall (1962) and applied by them to configurations

consisting of s electrons. Holly Doyle (1968, 1969)

carried out complete calculations of Ere ^ for atoms in

the first row of the periodic table. Though extremely

intricate, these calculations are exact, and they are based entirely on Dirac one-electron wavefunctions

Snyder (1969, 1970, 19 71) has developed a simple but

surprisingly accurate approximation method for extending these results to heavier atoms.

From this summary it is clear that all regularities pertaining to highly ionized atoms are quantita- \ tively predictable through calculations using hydrogenic wavefunctions . In particular, the rule illustrated by the right-hand diagram in Figure 1 reflects

the properties of the coefficients E Q and E . The

ordering of subshells within a shell according to

increasing values of I follows from the explicit calculations of E 2 referred to above. By appealing to formula (3) , which shows how E 2 is built up from two-electron interactions, one can push the explanation back a step. The average value of E J for a given configuration is determined mainly by the sum of two-electron

contributions [a, $] and depends very little on the term

AE 2 . Thus one can base an explanation of the regularity on the properties of standard interaction integrals

involving hydrogenic wavefunctions

Turning now to the neutral atoms, we must consider

the term 0(Z _1

) = E

1 . If this term were negligible forj

neutral atoms, as it is for highly ionized atoms, the

periodic table would have the same structure in the two' cases. (This statement is based on calculations of E 1 and estimates of E 2 derived from experimental data on term energies in isoelectronic sequences.) Thus the

behavior of E

1 is instrumental in causing the transition from (n, I) -lexicographic ordering Z>>N to (n+£,£) -| lexicographic ordering as Z — N.

For a given value of N and sufficiently high val24
Iss of Z , the term E' has a convergent expansion in

owers of Z

1

, the leading term in the expansion being

roportional to Z" 1

. By subtracting the theoretically

nown quadratic and linear terms in Z from experimentlly determined term energies in an isoelectronic

jquence, we can examine the behavior of E' for Z - N.

'or this purpose we can neglect the relativistic conhibution Ere ^.) One finds that in general it is not

Issible to represent E' accurately in the vicinity of

j= N by the two leading terms in its Taylor expansion.

4e data suggest, in fact, that the series expansion

reaks down at a value of Z somewhat greater than N in

|

; neral. That is, E' is not in general analytic in the

j-ighborhood of Z = N. Thus the simple Z -expansion

eory does not afford an adequate theoretical basis

ur discussing the transition between the two idealized

rms of the periodic table.

Nevertheless, we can gain considerable insight

to this problem by very simple theoretical means. I ve mentioned that E 1 and Ere ^ can be evaluated by callations that involve only hydrogenic wavefunctions

.

j principle one can also evaluate E 2 directly from

cond-order perturbation theory, using hydrogenic

I sis functions, though in practice other methods are ually preferable (see Layzer et al. 1964) . To evalte E

1 we go one step further and introduce screened

drogenic wavefunctions P n £ (Z-s n £ ,r) , where the

reening parameter s n^ is a function of Z . We regard

e screening parameters as variational parameters, to

I determined in the usual way from the variation prinkple. The resulting theory is purely algebraic. It

also physically transparent, in the sense that the

jthematical results can be readily translated into

ysical language.

Before discussing some of the results of variaonal screening calculations, I must call your attengon to one technical point. Screened hydrogenic wavenctions belonging to the same value of Z but differrt values of n are not orthogonal unless they are also

laracterized by the same screening parameter. It is

Iks circumstance that has discouraged people from

raising calculations for complex atoms on such wavefuncons , since the standard formulae for matrix elements

! nnecting many-electron states depend on the assump-

!| on that radial wavefunctions belonging to the same

lue of I but different values of n are mutually

rthogonal. If one does not make this assumption, the

: rmulae become exceedingly complicated. We can, hower, use nonorthogonal radial functions in the stanird formulae and treat the effects of nonorthogonality

25
as corrections. Fortunately, these corrections often

turn out to be small. Moreover, it is not prohibitively difficult to estimate them in a first approxima

tion (see below) . A discussion of their physical significance is given by Layzer (1959)

Neglecting the effects of nonorthogonality , one obtains the following formula for the energy levels in

terms of the screening parameters

Here m denotes a configuration and the sum over hi runs over all configurations belonging to a given complex ( set of configurations characterized by a given set of

principal quantum numbers and a given parity) ; qa denotes the number of electrons occupying orbitals of

the type a in the configuration m. The screening para

eter s a depends on the configuration m as well as on

the type of orbital. Finally, the screening parameter

that figure in this formula are solutions of the varia

tional problem.

Formula (5) is identical, except for the sum over

m, with Moseley's well-known semi-empirical formula fc

X-ray term energies. (The sum over configurations in

complex is a necessary feature of the formula. It

ensures that the linear term, as well as the quadratic

term, in the Z-expansion of E is given correctly.)

Each electron contributes "hydrogenically" to the tenr

energy according to its screened nuclear charge. Now,

we know, from much more refined calculations that the

electric field seen by an electron in a complex atom

differs substantially from a screened Coulomb field,

and that accurate variational wavefunctions - for exan

pie, Hartree-Fock wavefunctions - depart markedly fron

the hydrogenic form. One might therefore expect formu

la (5) to provide a rather crude approximation to

observed term energies in many-electron atoms.

Some representative comparisons between theory ar experiments are shown in Figures 2 to 5. Figure 2 shows, in addition, the effects of the correction for

nonorthogonality of the radial wavefunctions for a cas where this correction is exceptionally large.

One sees from these comparisons (in which the

known quadratic and linear contributions to the energy

have been subtracted) that most of the discrepancy

between the observed and calculated energies comes frc

2 (5

26
-0.32

-0.31 -0.30

-0.29

-0.28

•0.27 0.26

0.25

0.24

•0.23 0.22

-A

LITHIUM SEQUENCE r r 7 2 . , p E-E n

Z -E .

Z

S AE

2 2 u l Is"

1 2s S

o a

a a a o a a a

• EXPERIMENTAL AE

D THEORETICAL AE ^ORTHOGONAL theor AE A A A

-i l i 9 10 11 12 13 14 15

Figure 2. Illustrating the effects of nonorthogonality

P on variational screening calculations of the energy,

n These effects have been included in the calculations

indicated by triangles and omitted in those indicated

i by squares. (From David Layzer, 1967, International

Journal of Quantum Chemistry , Symposium No. 1, p. 45.)

the constant: term E 2 and, at large values of Z, from

the relativistic contribution. The nonanalytic variation of E

1 for Z - N, which is our main concern in the

present discussion, is predicted with surprising accuracy by the variational screening theory - even in an atom as heavy as titanium.

It appears, therefore, that the nonanalytic behavior of E

1 results in large measure from the one-electron contribution to E

1 , and indeed from the part of

that contribution associated with the screening of the

nuclear Coulomb field.

To illustrate the connection between nonanalyticity and screening, consider the well-known phenomenon

illustrated by the variational screening calculations

shown in Figure 6. Plotted are the variational screening parameters and S4 S in the configurations -3p 5 3d

and -3p 5 4s, respectively, as functions of Z along the

argon isoelectronic sequence. For values of Z < 20.4,

the 3d electron is screened almost completely by the

other electrons (the variational calculations can be

27
1 .05

1 .00

0.95

1 .20

1.15

1.10

1 .05

1 .00

1 .40

1 .35

1 .30

1 .25

1 .20

1.15

1.10

BORON SEQUENCE

E- E nZ

2 -E, Z=AE

U 1

Is

2 2s2 2p2 p° 0 THEORETICAL

• w LArLKlntli 1 ML •

- D • m ° 8 s • •0

1 ! 1 1 i 1

•

1 s • •

o a n

i i i i i

_

1 S 2 2s 2p2 4

p #

• •

• " t3 Q

I I I—I I I 1

1

D ° J—1 I I

Is

2 2s 2p

2 2 D

a ° a D

i

i

i

i i

l

5 6 7 8 9 10 1 1 12 13 1 4 1 5 16

Z Figure 5. Predicted and observed ionization energies

in the boron isoelectronic sequence. The predicted

energies are given by the variational screening approximation with no allowance for the effects of nonorthogonality between radial wave functions belonging to the same value of I . Energy contributions proportional to

2

2 and Z have been subtracted from both theoretical and

experimental energies. The increasing differences

between the experimental and theoretical points at

large values of Z reflect relativistic contributions to

the energy.

(Figures 3, 4, and 5 are from David Layzer, 1967,

International Journal of Quantum Chemistry , Symposium

No. 1, p. 45.)
5.35

5 . 30 5.25 5.20

5.15 5.10

5.05

5.00 4.95 4.90

4.85

4.80

MAGNESIUM SEQUENCE

Is

2 2s

2 2p

6 3s 3d E-E„Z -E, Z=AE

•

a THEORETICAL

• EXPERIMENTAL

i I I 1 L 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Z Figure 4.

-0.22

-0.21 -0.20 -0.19

-0.18

-0.17 -0.16 -0.15 -0.14

-0.13

-0.12

TITANIUM SEQUENCE

4 3 4 3 3d

J H-3d J

D

-0.08 - -0.07 -0.06 -

-0.05 - -0.04

J I I I

3d 4 3 G-3d 4 3

H

J L 22 23 24 25 26 27 28

Z Figure 5.
Figure 6. Screening parameters: argon isoelectronic

sequence (N = 18)

carried out for arbitrary nonintegral values of Z) . Around Z = 20.4, s-^ changes abruptly, increasing by

about 33% in an interval AZ * 0.2. Thereafter S33

remains practically constant. Figure 7 shows how the

contribution to S33 from various subshells varies with

Z along the isoelectronic sequence, and Figure 8 illustrates the variation with Z of mean nuclear distance of

the 3d and 4s electrons. In the configuration -3p 5 4s, on the other hand, the screening parameter for the 4s

electron varies smoothly over the entire range of Z; see Figure 6. From formula (5) we see at once that for

values of Z < 20.4, a 4s electron is more tightly bound

than a 3d electron, while for Z > 21 the 3d electron is

the more tightly bound.

Similar results for the calcium isoelectronic

sequence are shown in Figures 9 and 10

The nonanalytic character of the variational 3d

screening parameter results from the form of the variational equations for the s a

:

3 a = VV' X

8 = ^ ' (6) a

30
FROM 3p ELECTRONS

FROM 3s ELECTRONS

FROM 2p ELECTRONS

FROM 2s ELECTRONS

FROM Is ELECTRONS

1 8 20 22 TOTAL NUCLEAR CHARGE Z Figure 7. Composition of 3d screening parameters.

where s a is a .homogeneous rational function of all the

xg. Thus it is clear that the expansion of s a in

powers of Z" 1 has a finite radius of convergence. The

quasi-discontinuous variation of the 3d screening parameter reflects the quasi-discontinuous character of

screening itself: near Z = 20.4, a small change in the

radial distance of the peak of the 3d wavefunction can

31
Figure 5. Expectation value of r /3d

Argon 3p 5 /

Ms

32
20

1918

S 17

16

S 15

1413

12

1110

3d(4s3d)

4s(4s3d)

4s(4s c

)

20 22 24 26 28 30 NUCLEAR CHARGE Z

Figure 9, Screening parameters:

Calcium sequence -3p 6 ^— 4s3d

^4s 2

cause a large change in the screening of the 3d electron. This situation is illustrated in Figure 11, a simplified schematic plot of and F^d [see formula

(6)] as functions of (Z - S33) for various values of Z. Note the abrupt change in F3^ between its two asymptotic values, corresponding to the passage of the 3d

electron through the 3p subshell, and the corresponding

abrupt change in the variational value of S3 d , determined by the intersection of the curves F3^ and S33.

These considerations suggest that very simply theoretical methods may suffice to explain the regularities

illustrated in Figure 1.

33
< r>

22 24 26 28 30 NUCLEAR CHARGE Z

Figure 10. Expectation value of r. Calcium sequences -3p 6 3d 2

, -3p 6 3d4s, -3p 6 4s 2

34
Figure 11. Illustrating the nonanalytic character of

s 3d' determined as the intersection of s-^ and F'33 as functions of Z - S33.

ACKNOWLEDGMENT

The calculations on which Figures 6 through 10 are based were carried out by Mrs. Judith Drake and Dr.

Margaret Lewis to whom I am indebted for permission to

quote the results in advance of publication. Most of

the work reported here has been supported by grants

from the National Science Foundation.

35
REFERENCES

Dalgarno, A. and Stewart, A. 1958, Proc. Roy. Soc.

(London) Ser. A, 247 , 245.

Doyle, H.T. 196 8, Thesis, Harvard University, (unpublished) . Doyle, H.T. 1969, Advances in Atomic and Molecular Phys

ics, 5, 337-413.

Godfredsen, E. 1963, Thesis, Harvard University (unpublished) . Godfredsen, E. 1966 , Ap . J. , 14_5, 308.

Layzer, D. 1959 , Ann. Phys., S_, 271.

Layzer, D. and Bachall, J. 1962, Ann. Phys., Y7_, 177.

Layzer, D. , Horak, Z., Lewis, M. and Thompson, D. 1964,

Ann. Phys . , 29 , 101.

Snyder, R. 1969, TEesis , Harvard University (unpublished) . Snyder, R. 1970, J. Phys. Soc. London B (2) 3, 177.

Snyder, R. 1971, Highlights of Astronomy (ed. de Jager)

(Dordrecht-Holland: Reidel Publishing Corp.), 338.

Wigner, E. and Seitz, F. 1955, Advances in Solid State

Physics ,

36
MANY-BODY CALCULATIONS OF ENERGIES AND

TRANSITION PROBABILITIES

Hugh P. Kelly

University of Virginia

I. INTRODUCTION AND REVIEW

This paper is concerned with the applications of

he many-body perturbation theory of Brueckner-'- and

oldstone^ to problems in atomic structure. Our

ethods for applying many-body perturbation theory to

corns have been discussed elsewhere^ t 4 r 5 # In the applications to an N-electron system we

tart with the simplified problem

ere

id

H o 0

o = E

Q $

0

, (1)

N

H = T H . , (2)

o . L , 01 i=l

v.

2

ie effective single-particle potential to be used is

rbitrary and could, for example, be chosen as the

irtree-Fock potential V_._ . The unperturbed solution

rlr is a determinant or linear combination of determiants of single particle states 0n which satisfy

H . 0 (r.) = e 0 (r.) . (4) oi *n ~i n'n ~i

37
Our exact non-relativistic wave function satisfies

= , (5

where

H = H

q+ H" , (6

with

N

• = I r-1 -

I V(r

i<i=l 13 i=l 1±

) . (7

J

Atomic units are used throughout this paper unless

specified otherwise. According to the theory of

Brueckner and Goldstone (BG)

,

L \ o o /

where £ indicates that only "linked terms" are to be

included.

Also,

E = E + <<f> I H ' I y> (9

o o

1 1 We note from Equation (8) that ¥ is not normalized to

unity, but rather <$ |¥>=1.

In order to carry out the perturbation calculations of Equations (8) and (9) , we use the complete se of single particle states 0 from Equation (4) . We

include only a limited number of orbital angular momer

turn states (usually &<4) . We explicitly calculate bou

states up to n=10 to 15 and then sum over perturbation

contributions from higher n values by the n~

3 rule 4 . We obtain perturbation contributions from continuum

states by numerical integration.

We have used these methods to calculate correlation energies for the ground state multiplets of

beryllium^ ,

r carbon^ , oxygen7 , and iron8. For Be, C

and 0, the correlation energies are in excellent agree

ment with experiment. As yet, there are no experimen-i

tal results for Fe. These methods may also be used tc calculate energies of excited states, although very

little work has as yet been done on them.

38
These methods have also been used to calculate

plarizabilities , shielding factors, and hyperfine contants^ , i n these cases we must add an additional term

fff (r.) to Equation (7). The dipole polarizability

,

ex ~ 1

br example, is proportional to the sum of all energy

isrms that are second order in IV and contain any num

ex

of interactions with the correlation term (ZrT^-ZV)

liese methods have also been used for electron-atom

ratteringlO , 11.

In this paper our major emphasis is on the calculation of transition probabilities and, in particular,

a transitions from bound to continuum states. Much of

jne important initial work in this area was carried out

U Professors Menzel and Pekerisl^. The importance of

lotoionization (bound-free transitions) in astrophyszs has also been stressed by Professor Menzel in his

pok Stellar Interiors^ . In Section II we present

ome oscillator strengths for bound-bound transitions

i Be including correlations. We also present prelimaary results for an oscillator strength in Fe . In

action III we present results for the photoionization

ross section of Fe in the ground state.

II. OSCILLATOR STRENGTHS

, Oscillator strengths for the transitions

2s) 2 1 S 2s np *P have been calculated 4 with electron

orrelations in the ground state included by use of

quation (8) . Our excited np states were calculated in

he presence of a "frozen core" (Is) 2 (2s) with the Is

nd 2s being Hartree-Fock orbitals for the ground state

esults are given in Table 1 and are discussed in more

retail in reference 4. Results for f n^ are expected to

e close to Hartree-Fock results. The large reduction

n the oscillator strength for n=2 is due to strong

onfiguration mixing in the ground state between the

-2s) 2 : S and (2p) 2 *S configurations.

We have very recently begun to calculate the

scillator strength for the Fel spectral line 3719.9 &

rising from the transition (3d) 6 4s (a 6 D) 4p ( z

5 F°

)

|3d) e (4s) 2 (a 5 D lf ) . The experimental value-14 for this

jscillator strength is 0.0421. Our calculations used

me single-particle states for Fe calculated preiouslyl5. The 4s and 3d orbitals are Hartree-Fock

olutions for the (3d) 6 (4s) 2 5 D ground state. The

xcited np states (n>4) were calculated with a "frozen

ore" (3d) 6 (4s). Our result without correlations is

39
TABLE I OSCILLATOR STRENGTHS FOR TRANSITIONS

(2s) 2 J S * 2snp 'P in Be

n f

.*

ni f . (corr) ni '

23

45

6

7

8

CO

2.0293

0.00541

0.00530

0.00318

0.00194

0.00125

0.00084

1.2540

0.01676

0.01013

0.00549

0,00321

0.00202

0.00135

z 0.00295 0.00467

n=9

Correlations not included. Excited np states calculated in field of frozen core (Is) 2 (2s).

f Correlations in the ground state included.

0.3962, which is almost a factor of ten from the exper

imental value. Including the lowest-order correlation

corrections among 4s and 3d electrons, we obtain 0.171

We estimated the normalization corrections^ as causing

a further reduction to 0.085. We are at present calcu

lating the normalization corrections explicitly and

investigating higher-order terms in the perturbation

expansion. The very great effects of correlations on

this oscillator strength are striking. In the ground

state, the mixing of (4s) 2 with (4p) 2 causes a signifi

cant reduction. However, there is also considerable

mixing of 4s3d with 4pkf . In the excited state there

is also configuration mixing, for example, of 3d4p wit:

4skf and of 4s4p with 4skp. It is clear that consider'

able additional calculations are required and that our present results are very preliminary.

III. PHOTOIONIZATION CROSS SECTION FOR Fe

This calculation was stimulated by its relevance

for astrophysics 1 ^ and by the fact that there does not seem to be any measurement of a(u)) for Fe 17 . In these

calculations we use the relation^

4 IT a(oo) = — a) Ima(aj) , (10

40
re is the frequency-dependent polarizaIn calculating the perturbation theory diagrams^O

a(o)), we treat energy denominators according to the

al prescription P-ifr6 , where P represents a princivalue integration. Then Im a (00) consists of all

grams in which we have an odd number of contribuns from — ±tt6 . The lowest order diagram contributing

a (co) is shown in Figure 1(a). The horizontal line

resents use of -ifrS. This notation has also been

d by Wendin who has discussed calculation of resoces in a (00) by many-body theory 2 !. In Figure 1,

heavy dot represents matrix elements of z. (In

culating a (00) we take the perturbing electric field

the z direction and average over MT

. ) Dashed lines

h no dot represent Coulomb correlations. In the

t order of perturbation theory, there are diagrams

shown in Figure 1(b) and 1(c). These diagrams also

ur inverted and there are corresponding exchange

grams. When there is no horizontal line, denominas are treated by principal value integration.

(a)

(d)

dre 1. Diagrams contributing to the photoionization

ss section or Im a(w) . The horizontal line indies that the denominator should be treated according

J~iir<$. The large solid dot indicates a matrix ele-

|p of z. The dashed line without the large dot repress a Coulomb interaction.

41
In calculating a (go) for the (3d) 6 (4s) 2 5 D groun<;

state of Fe, we have used our complete set of single

particle states from our calculation 15 of the hyperf

contact interaction in Fe. We carried out the calcu jj tions with M

g = +2 and averaged over ML

. Our cross section of course is independent of M

g

. There are higher-order diagrams 20 which shift the single-parti«l

energies e(n) to give correct ionization energies . e'(n). We calculated the shifted energies of e(4s")

| and e(4s~) agreed well with the experimental ionizat i energy22 . We used spectroscopic data 22 +to determine

J e(3d"), and we obtained an average e(3d ) by calcula | ing the difference from e(3d~). Our shifted energie I for e(4s") and e(4s+ ) are -.2903 a.u. and -.3104 a.u J respectively. For e(3d ) and e(3d+

) we obtained

-0.3965 a.u. and -0.5811 a.u. respectively. The dif I ference between e(4s~) and e(4s ) is due to the fact!

that (for Ms = +2) the 4s+ electron has exchange int||

actions with the five 3d+ electrons whereas the 4s"

electron has an exchange interaction with the single}

3d" electron.

Results for a (to) are shown in Figure 2. The

dashed line represents the Hartree-Fock result obtai

i

i i i i

i i i

i

i i i

i

i

i i

i

i i i

i

i i i—i—i—i—i—r| 20-

15-

eo

00O 10-

b

PHOTON ENERGY (eV) Figure 2. Total photoionization cross section of Fe

lowest order results.

including correlations for contributions fror

(4s) 2 and (3d) 6 subshells.

42
rom the diagram of Figure 1(a) . The solid line is the

esult including correlations. We included diagrams

} ike Figure 1(b) and 1(c), their inverses, and also the

; orresponding exchange diagrams. We also included some

jigher-order diagrams like Figure 1(b) and 1(c) in

ihich the part of the diagram above the horizontal line

is identical to that below. Diagrams like Figure 1(d)

lere approximately included. Diagrams like Figure 1(e)

[ere also included. The maximum contribution from

ligure 1(e) came near threshold and reduced a(o)) by

approximately eight percent. Our results in Figure 2 lave only included correlations among 4s and 3d elecF'rons and correlations of 3d electrons with 3p electrons. The 3d-3p correlations were found to be small,

tnd it was estimated that the omitted correlations

Jffect a (a)) very little.

The large increase over the Hartree-Fock result is

lue mostly to the diagram of Figure 1(b) when the bottom matrix element is <4p|z|4s>. This matrix element

Is so much larger than <kp|z|4s> that it more than

Compensates for the reduction due to the Coulomb matrix

jlement. This diagram corresponds to configuration

fixing in the many-particle final state between 4s kp

] nd 4p 4s. We expect that this effect will be found in

11 atoms with an outer (ns) 2 subshell with n>2. In

fipch atoms, Hartree-Fock results may be expected to

iffer significantly from experiment. In diagrams like

igure 1(d), when all but the top excited states are

\tp- and the hole lines are 4s ±

, we may sum the diagrams

ijfeometrically^

.

In Figure 2 we note the strong resonance at

-2.13 eV and lesser resonances from 14.26 eV to 15.81

V. The resonance at 12.13 eV is due to 3d+ * 4p+ jxcitations which are degenerate in energy with

IB* * kp± and 3d" -> kf~, kp" excitations. These resoances occur in diagrams like Figure 2 (b) in which the

^ottom excitation is 3d+ + np . It is to be emphasized

Hhat we have not made an accurate determination of the

i jeight and shape of the resonances, which would involve

i including many higher-order diagrams. There are also

arrow resonances (not shown in Figure 2) from

d

+ > nf+ excitations and from 4s + + np+ for high n. Many other resonances also occur in higher-order diagrams. We expect that the most important of these

nvolve (4s) 2 mpns or (4s) 2 * mpnd excitations. We

lan to investigate these effects in future work. The

present calculations merely indicate the presence of esonances

.

At higher energies than shown in Figure 2 , there

Ire contributions to a(oo) from the inner subshells, and

43
100 r 1

1 l |

i i i i

|

PHOTON ENERGY (eV)

Figure 3. Total photoionization cross section of Fe t|

10 keV.

lowest order result.

including correlations in contributions from

(4s) 2 and (3d) 6 subshells.

these are shown in Figure 3. Only the 3d * 4p resonance is shown in Figure 3. Correlations were not

included in the contributions from the (3p) 6 subshell

and inner subshells. A more complete account of this

work will be published elsewhere^3.

At present we are calculating contributions 0(b))

in which two or more electrons are ejected and also

processes in which one electron is ejected and the ato

is left in an excited state. The lowest order diagram

44
I (c) (d)

guve 4. Lowest order diagrams contributing to double

lOtoionization when both k and k

1 are continuum states,

.en either k or k

1 is a bound excited state and the

.her is a continuum state, these are the lowest order

agrams contributing to photoionization accompanied by

citation to a bound state. The cross section is pro-

•rtional to the square of the sum of diagrams (a) to (d).

ntributing to such processes are shown in Figure 4.

|r example, in the diagram of Figure 4(a) a and 3 uld be the 4s + and 4s~ states, k could be either a ntinuum £=0 or 1-2 state, and k'=4p. In this process

je photoabsorption has resulted in a 4s + electron

jing ejected and there is also a 4s"" * 4p excitation,

so, k

1 could represent the continuum state and k the

state. Contributions to the same excitations also

cur in the diagrams of Figures 4(b) , (c) , and (d)

.

I EL processes such as these should be included in the

Ijtal photoabsorption cross section.

ACKNOWLEDGMENT

This research has been supported by the Aerospace

search. Laboratories, Office of Aerospace Research,

CI ited States Air Force, Contract No. F33615-69-C-1048

.

45
REFERENCES

1. K.A. Brueckner, ?bs. -"s-;. , 97_, 1353 (1955); The

Many-Body Problem (Wiley, New York, 1959).

2. J. Golds tone, Pro 3. Roy. Soo. (London) , A239 , 267

(1957)

3. K.P. Kelly, ?>vs. i?sy w 131 , 684 (1963).

4. H.P. Kelly, ?hs. 136_, B896 (1964).

5. H.P. Kelly, Advances in Chemical Physics, Vol XIV

(Interscience Publishers, New York, 1969), p. 12

6. J.H. Miller and H.P. Kelly, ?bs. fleu., A3 , 578 , (1971)

7. H.P. Kelly, ?bs. J?g-;. , 144 , 39 ( 1966).

8. H. Kelly and A. Ron, Phys. Rev. to be published.

9. H.P. Kelly, Int. J. of Quant. Chem. HIS , 349

(1970)

10. R.T. Pu and E.S. Chang, Phys. Rev., 151 , 31 (1966

11. H.P. Kelly, Phys. Rev., 160_, 44 (1967); 166., 1 (1968) ; 171, 54 (1968)

12. D.H. Menzel and C.L. Pekeris, .V . Is . R . A . S . , 96_, 77

(1935)

13. D.H. Menzel, P.L. Bhatnager, and H.K. Sen, Stella

Interiors (Chapman and Hall, London, 1963).

14. R. Wagner and E.W. Otten, Z. Physik, 220 , 349

(1969) . 15. H. Kelly and A. Ron, ?bs. Rev., A2, 1261 (1970)

16. 0. Gingerich, private communication.

17. G.V. Marr, Photoionization Processes in Gases

(Academic Press, Inc., New York, 1967).

18. U. Fano and J.W. Cooper, Revs. Mod. Phys. , 40_, 44

(1968) . 19. A. Dalgarno, in Perturbation Theory and Its

Applications in Quantum Mechanics , ed. C.H. Wile

(J. Wiley & Sons, Inc., New York, 1966), p. 145

20. H.P. Kelly, Phys. Rev., 18_2 , 84 ( 1969).

21. G. Wendin, J. Phys., B3_, 455 (1970); 3 , 466 (197C

22. C.E. Moore, Atomic Energy Levels, National Bureai

of Standards Circular No. 46 7 (U.S. Government

Printing Office, Washington, D.C., 1949).

23. H. Kelly and A. Ron, Phys. Rev. to be published.

,6
RADIOACTIVE TRANSITIONS IN THE HELIUM

ISOELECTRONIC SEQUENCE

Alexander Dalgarno

Harvard College Observatory

1. INTRODUCTION

In collaboration with Bruce Shore, Donald Menzel

wrote a basic text, The Principles of Atomic Spectra

(Shore and Menzel 196 8) . In this paper I describe the

application of those principles to the quantitative

study of radiative transitions in two-electron heliumlike atomic systems.

2. QUANTUM THEORY OF RADIATION

The absorption and emission of a single photon in

tyl a radiative transition between two stationary states of

an atomic system described respectively by wave

functions ^ and tyf can be obtained from the matrix

i element < i^i | H | ipf > of the interaction H between the

radiation field and the atom. The interaction H can be

expressed in terms of the vector potential A of the

radiation field, which can be expanded as a sum over multipoles °f magnetic and electric type. The

multipole fields have well-defined parities (-i)

L+X+ ^ where X = 0 designates a magnetic and X = 1 an electric multipole. The transition matrix element vanishes

unless the parity selection rule is satisfied. If tt^ is the parity of the initial atomic state and tt^ the

parity of the final atomic state, the parity requirement is

TT i = TT f (-1)

L+1+X

. (I!

47
The allowed values of the photon angular momentum

L are further restricted by the angular momentum

selection rules

J

±

- J

f

| < L < J

± + J

f

(2)

but

J = 0 -A J. = 0

where J. and are the total angular momenta, spin and

orbital1

, of respectively the initial and final

states.

Apart from vector spherical harmonics, con- tains the spherical Bessel function gL

(na)r/c) where frw is the photon energy and r is the distance of the electron from the atomic nucleus. For small values of the

argument, gL can be expanded as the power series

rr r~\ 4tt (ix)

L

j n x

2

) gL

(x) = (2L+1) »! ) 1 " 2(2L+ 3) + ' ' ' } ' (3)

If the wavelength of the photon is large compared to

the dimensions of the atom, the major contribution to

the transition matrix element comes from the region

where wr/c << 1, and in most cases only the first term

of (3) need be retained. The assumption that the wavelength is large compared to the atomic dimensions

implies that the electron velocities are small compared

to the velocity of light so that the Dirac wave functions i|k and ip f can be replaced by non-relativistic

Pauli wave functions. The probability of a spontaneous

transition can then be related to the electric and

magnetic multipoles

* LM = e ^2L+r; r. Ym (r./r.)

(4)

48
S-here I. = r . x p . is the orbital angular momentum of the

i th electron of the N-electron atom and yj_ is the spin

ngular momentum eg. /2m. The explicit formulae are

, (1) „ 20±i) U

2L+1 |< f , Q

( 1) fi >| LM L(2L+1) [2L-1) !!] 2 LM (6)

(0) = 2011) 2L+ l| <f| (O),^!^ ^ (?)

L(2L+1) [(2L-1) ! I]

2

3. RADIATIVE DECAY OF HELIUM

The energy level diagram for the low-lying states

f helium is reproduced in Figure 1. For ions heavier

han C V, the ordering changes and the 2

3 P levels lie

elow the 2

2 S level.

Consider first the decay of the 2

1 P 1 level. It

as Jj_ = 1 and is of odd parity. Below it there lie

/?o states of even parity with = 0 . The selection

ales are satisfied by an electric dipole El transition

nd the 2

I P 1 - 1

1 S 0 and 2

1 P 1 - 21 S Q are typical examples

f strong allowed transitions. Reliable values are

Badily obtained from accurate variational ly determined

wo-electron non-relativistic wave functions and

able 1 contains a list of transition probabilities for

arious nuclear charges Z. The 2

1 P 1 - 11 S 0 transition probability increases

3 Z

k for large Z but because the 22 Pi and 2

1 S 0 states

:e asymptotically degenerate, the 2

1 P 1 - 2

1 S 0 non-

^lativistic probability increases only as Z. The 2

3 P levels are more interesting. They have

otal angular momentum J-j_ = 2,1 and 0 and are of odd

parity. They can all decay by an electric dipole El

-ansition to the 2

3 S 2 state. No change of multiplic-

:y is involved and the decay occurs through a typical

;Llowed transition. The corresponding transition

;obabilities are included in Table 1. As for the

49

I;
Figure 1. Energy level diagram for neutral helium sho

ing the ordering of the levels.

2

J P X - 2

1 S

0 transitions, the probabilities increase as

Z for large Z.*

The 2

3 P Q level can decay by no other single photo

mechanism because = 0 > Jf = 0 transitions are strictly forbidden. The selection rules allow the 2

3 P

level to decay by an electric dipole El transition to

the ground 1

1 S

? level. A change of spin multiplicity

is required which is effected theoretically by the

mixing of 1 P 1 and 3 P X states through the Breit interaction VB

. Thus the triplet wave function can be

written to first order in VB as

|23 Pl> = | 2

3 P 1>0

^^'PjVBln^iX^Ptl 1

n E - E(2 3 P X

) n

1

*The limiting Z dependence is modified by relativistic

effects on the transition frequencies.

50
TABLE 1 RADIATIVE TRANSITION PROBABILITIES A FOR THE

2

1 P

1 STATES OF THE HELIUM SEQUENCE IN SEC -1

System - 1

2 S

0 *

2

1 P

1 - 2

1 S

Q 2

3

4

56

7

89

LOLI

L2

1718

He I Li II

Be III

B IV

C V

N VI

O VII

F VIII

Ne IX

Na X

Mg XI

Al XII

Si XIII

P XIV

S XV

CI XVI

Ar XVII

80

56

22

72

8.87

1. 81

31

58

8. 87

1.34

1.96

2.76

78

07

66

59

09

(9) T (10)

(11)

(11)

(11)

(12)

(12)

(12)

(12)

(13)

(13)

(13)

(13)

(13)

(13)

(13)

(14)

1.97 (6)

5.14 (6)

8.73 (6)

1.25 (7)

1.65 (7)

05 (7)

46 (7)

87 (7)

29 (7)

70 (7)

4.12 (7)

4.54 (7)

96 (7)

38 (7)

80 (7)

22 (7)

64 (7)

From G.W.F. Drake

1.80 (9) = 1.80 x (unpublished)

10 9

^here

ind

Jhq

- E(2 3 P 1 )J

a Pj> |2 a F x . = 0

{

H

o

" E

n}l nlp

i>o = 0 '

(9)

(10)

being the non-relativistic electrostatic two-elecron Hamiltonian. The transition matrix element

educes to

^^iHi^ = S <

23 Mv

B

i"

ip

1 )<n

' p 1 i° 1

( :)

i iis

o>

E - E(2 3 P n n 1 (ID

51
The singlet-triplet mixing increases rapidly with

increasing Z, and the 2

3 P 1 - 1

1 S

Q transition prcbabili

increases initially as Z 10 (though ultimately as Z

h

) and the spin-forbidden 2

3 P 1 - 1*S El decay mode must

eventually dominate the allowed 2

3 P X - 2

3 S 0 El decay

mode.

The infinite summation (11) , which includes an integration over the continuum, can be evaluated to

arbitrary precision by a variational approximation to

the two-electron Greens function; the results (Drake

and Dalgarno 1969) are given in Table 2. For ions

heavier than C V, the forbidden transition is more

probable than the allowed.

Values for N VI and 0 VII have been measured by

beam foil techniques. The measured probabilities of

(l.TiO.SJxio^ec- 1 for N VI (Sellin, Donnelly, and Fan

1968) and (5 . 8±0 . 5) xio 8 sec" 1 for 0 VII (Sellin, Brown,1 Smith, and Donnelly 19 70) are in harmony with the thee

retical predictions.

TABLE 2 RADIATIVE DECAY TRANSITION PROBABILITIES OF THE

2

3 P STATES OF THE HELIUM ISOELECTRONIC SEQUENCE

IN SEC" 1

Z System 2

3 P -2 3 S

*

2

3 P

2 - 2

3 P

2 - lls

o 2 He I 1.02 (7) 1.80 (2) 3.27 (-1)

3 Li II 2.28 (7) 1.81 (4) 3.50 (1)

4 Be III 3.44 (7) 4.01 (5) 6.17 (2)

5 B IV 4.57 (7) 4.23 (6) 5.01 (3)

6 C V 5.72 (7) 2.84 (7) 2.62 (4)

7 N VI 6.89 (7) 1.40 (8) 1.03 (5)

8 0 VII 8.13 (7) 5.53 (8) 3.34 (5)

9 F VIII 9.44 (7) 1.85 (9) 9.23 (5) ! 10 Ne IX 1.09 (8) 5.43 (9) 2.27 (6)

11 Na X 1.24 (8) 5.10 (6)

12 Mg XI 1.41 (8) 1.06 (7)

13 Al XII 1.60 (8) 2.09 (7)

14 Si XIII 1.81 (8) 3.88 (7)

15 P XIV 2.06 (8) 6.91 (7)

16 S XV 2.34 (8) 1.18 (8)

17 CI XVI 2.67 (8) 1.96 (8)

18 A XVII 3.05 (8) 3.14 (8)

*These are weighted means of the individual 2

3 PJ

-2 3 S

J transitions

52
The 2

3 P

2 level cannot reach, the 1

1 S

Q level by an

51 transition but the selection rules are satisfied by

i magnetic quadrupole M2 transition. The calculation

)f the magnetic quadrupole transition probabilities is

traightforward. The values in Table 2 are taken from

he work of Drake (1969 , 1971). Because of the oj 2l+1

factor in (15) , the M2 probabilities increase rapidly

ts Z

8 along the isoelectronic sequence, and the magnetic

{uadrupole 2*P - l-'S decay is more probable than the

2 for ions more massive than 3 ilectric dipole 2 P S

£ :i XIV.

The M2 decay mode may have been detected experilentally. Marrus and Schmieder (19 70a) , using the

Berkeley heavy-ion linear accelerator, have measured a .ifetime of (1.7±0.3) nanosec for the 2

3 P 0 level of

i'r XVII. The predicted 2

3 P 2 - 2

3 S

1 |. 55x10 8 sec

_1 and the predicted 2

3 P

jltbility is 3 . 14x10 8 sec1 El probability is

1

A S 0 M2 probP giving a 2 2 lifetime of 1.5

lanosec. Without the M2 decay mode, the lifetime would

e 2.8 nanosec.

The 2

1 S 0 and 23 S 2 states of helium are metastable,

md there is no accessible state to which either can

lecay by an electric dipole transition. Because 0^0

Ls strictly forbidden, the 2

1 S

Q state cannot decay to

|:he 1

1 S 0 state by any single photon process, and Breit

Imd Teller (19 40) long ago pointed out that it would

lecay by a two-photon (El) 2 process

2

1 S

Q - 1

1 S 0 hv 1 + hv

giving rise to a continuum emission. The process

)ccurs through a second order interaction with the

radiation field and its quantitative description

.nvolves the evaluation of infinite summations of the

:ind

M S

<2^S 0 |Q 1

( J) |n 1 P 1)<n 1 P 1 |Q[jMl 1 S

0 >

(i)

E(2 1 S

j) ) E + V n

[these can be evaluated variationally (Victor and

jpalgarno 1967; Drake, Victor and Dalgarno 19 69)

.

The spectrum is symmetric about the central frequency where it reaches its maximum probability. The

53
TABLE 3 RADIATIVE TRANSITION PROBABILITIES A FOR THE

2

2 S

0 AND 2

3 S

: STATES OF THE HELIUM SEQUENCE

IN SEC - i

2

2 S

0 " 1

2 S

0 2 *S

(El)

1

L S

Ml

2

34

5

6

78

9 10

11

12

13

14

15

16

17

18

(1)

(3)

5.13

1.95

1.81 (4)

9.26 (4)

3.31 (5)

9.43 (5)

2.31 (6)

5.05 (6)

1.00 (7)

1.85 (7)

3.22 (7)

5.34 (7)

8.47 (7)

31 (8)

96 (8)

83 (8)

04 (8)

(-9)

(-6)

(-5)

(-3)

(-3)

(-2)

(-1)

9.73 (-1)

3.20

4.02

1.50

6.36

1.01

8.93

5.44

2,54

1.27

2.04

5.62 <- 6.70

4.86 (1

2.53 (2

1.04 (3

3.61 (3

1.09 (4

2.94 (4

7.24 (4

1.66 (5

3.56 (5

7.25 (5

1.41 (6

2.62 (6

4.71 (6

two-photon decay rates are given in Table 3. They

increase as Z

6 and the radiative two-photon emission I

the main decay mode for the 2

1 S states of the heavi I: o \m ions in the solar corona. However, the two-photon

processes do not contribute significantly to the sof

x-ray spectrum of the solar corona (Dalgarno and Dra

1969) .The two-photon emission spectrum of Ne IX has H

probably been observed in a high temperature laboratm

plasma (Elton, Palumbo, and Griem 196 8) , and two

measurements of the lifetime of the 2

1 S 0 state of neV

tral helium have been reported. Pearl (19 70) has me

W

ured a lifetime of (38 ± 8) millisec; and Van Dyck,

Johnson and Shugart (1970) a lifetime of (20 ± 2) mi 1 sec. The theoretical lifetime from two-photon decay!

19.5 millisec (Drake, Victor and Dalgarno 1969).

The selection rules also allow the decay of the I 2 S

? state to the 2

3 S 2 state by a single-photon mag-| 8 netic dipole Ml transition. This magnetic dipole dew

54
pde is more important in connection with the 2

3 S 1 pate which can decay to the 1

1 S 0 state with the emisLon of a magnetic dipole photon. 3ecause of the

lange in spin multiplicity and because the initial and

Lnal state parities are even, the single-photon tranition probability is very small. An estimate of the

inglet-triplet mixing induced by the Breit interaction

d to negligible probabilities (Breit and Teller

40), and it was generally believed that the 2

3 S 1 ate decayed by the two-photon (El) 2 process.

Two developments altered this view. It had been

apposed that apart from the singlet- triplet P state

fixing that was required for the 2

3 S X (El) 2 decay, the

3 S

1 decay process was similar to the 2

1 S

Q decay, and

e expected transition probability for the 2

3 S X - 1X S

0 1)

2 decay mode was of the order of 10~ 5 sec" 1

. Howver the fact that the triplet state has angular momentum of unity causes the transition probability to

anish at the central frequency (Drake and Dalgarno

968, Bely 1968) where the 2

1 S

Q probability is greatest.

;he predicted transition probabilities (Drake, Victor

f jnd Dalgarno 1969 , Bely and Faucher 1969) are listed in

able 3. The neutral helium value is 4><10"~ 9 sec" 1. The second development was the identification by

: abriel and Jordan (1969) of lines in the spectrum of

-he solar corona as 2

3 S 1 - 11 S 0 transitions of the

elium-like ions C V to Si XIII. Confirmation that the

I'Sj states decay by line emission was provided by beam

oil measurements on Si XIII, S XV and Ar XVII (Marrus

rl nd Schmieder 1970b) . The identifications by Gabriel

nd Jordan and the measurements of Marrus and Schmieder

rovided observational support for the revised twohoton decay rates and they also established that the

j.ain decay mode is the emission of a single magnetic

ipole photon; the selection rules permit no other posibility. The correct interpretation was soon put forward by Griem (1969, 19 70) who pointed out that a elativistic mechanism discussed by Breit and Teller

1940) for the metastable 2

2 S^ state of hydrogen, but

jhown by them to be negligible compared to the twophoton (El) 2 decay, also operated in the case of the

3 Sj state of helium. Using a hydrogenic model, Griem

howed that this relativistic magnetic dipole mechanism

m more efficient than the two-photon emission in

•ausing the decay of the 2

3 S

1 levels.

The original development by Breit and Teller

1940) used Dirac wave functions. In order to proceed

i.o more reliable quantitative predictions for twolectron systems, it seems necessary to express the

matrix element in terms of Pauli wave functions. The

55
contribution from the leading term in the fine. structure constant a vanishes and higher order terms must b

retained in the theory. The generalization has been

carried out by Drake (1971) and by Feinberg and Suchen

(1971) , who showed that it is also necessary to keep

the second term of (3) , a point made previously for th

2

2 S^ - l2 Si^ transition of atomic hydrogen by

Zhukovskii, Kolesnikova, Sokolov and Kherrman (1970).

Table 3 gives the transition probabilities calculated by Drake (1971). They increase with Z as Z 10

. His value of 1 . 27x10"" ^sec" 1 for neutral helium is in

harmony with, but more precise than, that of Feinberg

and Sucher (19 71) . It modifies in an important way th

theory of helium line emission in planetary nebulae.

Drake's values for heavier ions are consistent with th

interpretation of solar coronal observations (Gabriel

and Jordan 1970; Freeman, Gabriel, Jones and Jordan I 1971)

Schmieder and Marrus (19 70) have recently

succeeded in measuring the lifetime of the 2

3 S 1 state

of the Ar XVII. They obtain a value of (172 ± 30)

nanosec compared to the predicted value of 212 nanosec

It seems clear that Schmieder and Marrus have observed

the operation of the Breit-Teller relativistic mechanism. Whether or not the quantitative discrepancy

between theory and experiment is significant is unclee

It is interesting to note the rapidity with which

the astrophysical observation of line emissions led tc fundamental theoretical and experimental studies of th

interaction of matter and radiation.

ACKNOWLEDGMENT

This work has been supported partly by the

National Aeronautics and Space Administration and

partly by the National Science Foundation.

56
REFERENCES

ly, O. 1968, J. Phys. B. (Atom. Mot. Phys.), 1, 718.

fely, 0. and Faucher, P. 1969, Astron. Astrophys., 1,

37.

jreit, G. and Teller, E. 1940 , Astrophys. J., 91, 215.

algarno, A. and Drake, G.W.F. 1969, Men. Roy. Soo.

Liege , 17 , 69

.

rake, G.W.F. 1969, Astrophys. J., 158 , 1199.

rake, G.W.F. 1971, Astrophys. J., 163, 439.

rake, G.W.F. 1971, Phys. Rev.

rake, G.W.F. and Dalgarno, A. 1968, Astrophys . J. Letters , 152 , 121.

rake, G.W.F. and Dalgarno, A. 1969, Astrophys. J.,

157 , 459.

rake, G.W.F., Victor, G.A., and Dalgarno, A. 1969,

Phys. Rev. , 180 , 25.

lton, R.C., Palumbo, L.J., and Griem, H.R. 1968, Phys.

Rev. Letters, _20 , 783.

sinberg, G. and Sucher , J. 1971, Phys. Rev. Letters,

26_, 681.

reeman, F.F., Gabriel, A.H., Jones, B.B., and Jordan,

C. 1971, Proo. Roy. Soc. A. abriel, A.H. and Jordan, C. 1969, Mon. Not. Roy.

Astron. Soo., 145 , 241; Nature , 221 , 947.

abriel, A.H. and Jordan, C. 1970, Phys. Letters, 3 2A , 166.

riem, H.R. 1969 , Astrophys. J. Letters, 156 , 103.

riem, H.R. 1970 , Astrophys. J. Letters, 16

1

, 155.

arms , R. and Schmieder, R.W. 1970a, Phys. Rev.

Letters, 25_, 1689. arrus , R. and Schmieder, R.W. 1970b, Phys. Letters,

32A , 431.

earl, A.S. 1970, Phys. Rev. Letters, 2_4 , 703.

ellin, I. A., Brown, M. Smith, W.W. , and Donnally, B.

1970, Phys. Rev., A2, 1189.

sllin, I. A., Donnally, B., and Fan, C.Y. 1968, Phys.

Rev. Letters, 21, 717.

chmieder, R.W. and Marrus , R. 1970, Phys. Rev.

Letters, 25, 1245.

Qore, B,W. and Menzel, D.H. 1968, Principles of Atomic

Spectra (Wiley: New York)

.

an Dyck, R.S., Johnson, C.E., and Shugart, H.A. 1970,

Phys. Rev. Letters, 25, 1403.

ictor, G.A. and Dalgarno, A. 1967, Phys. Rev. Letters,

18, 1105.

;hukovskii, V.Ch., Kolesnikova, M.M. , Sokolov, A. A.

,

and Kherrman, L. 1970 , Opt. Spectrosc, 28_, 337 .

57

II SOLAR ASTRONOMY

Chairman: Donald H. Menzel

Harvard College Observatory

Once you've seen one of Menzel'

s

invisible prominences, you've seen

them all.

Harlow Shapley
I
SOLAR INSTRUMENTATION

(PART I)

John W. Evans

Sacramento T?eak Observatory

Solar astronomy, like other areas of experimental

:>r observational physical science, is increasingly

lependent on refined optical, mechanical, electronic,

md software equipment. All of it is expensive, a fact

fhich, unfortunately, narrows the range of experiment

fith new devices, which might or might not work. The

optical, radio, and space observations of the Sun are

ihree distinct technologies, each of which provides

essential information obtainable in no other way. A

neaningful discussion of all of them is beyond the

:apacity of this short survey. I shall, therefore,

:ake relief from necessity and consider only the field

ri.th which I have some acquaintance, the instruments

:or old-fashioned optical observations of the Sun.

Our optical solar studies naturally depend exclusively on the information brought to us by sunlight.

The best we can hope to do is to obtain a complete quan-

:itative description of this light, on the basis of

^hich we try to deduce some of the physical characteristics of the Sun. I have entertained myself while

enduring committee meetings and the like by reflecting

on what constitutes a complete description. It does

lot seem to be too complicated in principle. If we can

determine the four Stokes parameters, or their equivalent, as functions of wavelength, time, and position on

:he Sun in each AX At Ax Ay resolution element of the

smallest size compatible with the photon flux received,

:hen I think we know nearly all there is to know about

:he light delivered by a given aperture. This is the

lltimate observational goal. It is a pretty big order,

md there is little danger of our filling it very soon.

?he current efforts to improve our observations can be

iescribed, rather academically, as steps to reduce the

magnitude of the resolution element and expand the

observable intervals of X, t, x, and y for one or more

of the Stokes parameters.

61
Dr. Dunn, who follows me here, will talk about tY explicit down-to-earth problems he has encountered in

the wringing out of a rather complex system of a modei

telescope and its attendant accessories, problems he

brought on himself by designing the system originally.

The modern urge is to observe the smallest possible details of the solar atmosphere; that urge is

justified empirically by the fact that every advance j angular resolving power has led to important new

research results. This is a recognition that the inhc

mogeneities of the photosphere, chromosphere, and

corona are much more than small perturbations on a mea background. It is evident that many of the significar

physical processes of the Sun are small scale phenomer

Some of them must surely be too small ever to be

observed directly from one astronomical unit, but we

can hope to include the most important features if we

can study surface elements with characteristic dimensions approximately equal to the density scale height.

This means something like 150km, or 0.2 arc seconds fc features in the photosphere. It is reassuring to note

that at higher levels of the solar atmosphere, where

scale heights are larger, the smallest observed features also tend to be larger.

At any rate, my point is that much of the effort

in the development of solar optical instruments is

aimed at improved angular resolution in direct photographs, magnetograms , and high dispersion spectrograms

The primary instrument is, of course, the telescope,

and I think it is important to recognize its limitations. We are accustomed to rough and ready estimates

of resolving power in terms of the smallest distinguishable objects in a photograph or spatially resolve

spectrogram. This is certainly a useful estimate for

distinguishing between good and bad performance, whicl:

is usually limited by seeing rather than the telescope

But if we want to be able to take advantage of nearly

perfect seeing when it comes, we do have to be sure tl: telescope can do the job. Here something more than t! size of the smallest observable features is needed as measure of performance.

One very useful figure of merit is the two-dimensional modulation transfer function. Giovanelli (Atti

del Convegno Suite Maechie Solaris Rome Observatory,

196 4) has calculated this function for the mythical pe feet telescope undisturbed by atmospheric seeing

effects. His results are a little dismaying to those

of us accustomed to thinking in terms of a resolution

limit without thought for contamination of a resolved

element by light diffracted from the surrounding area.

62
he ultimate resolution where the image contrast of

'.nusoidal elements first vanishes is for elements seprated by angle 6=0.61A/A, the familiar Rayleigh limit,

mumbral filaments separated by 1.16, for instance,

buld be just barely separated by a slight intensity

.p. This is useful resolution for seeing the configujition of solar features, but the problem of restoring

iieir true photometric character in the presence of

jievitable observational noise is at best very diffiilt, and probably impossible. The smallest surface

.ements that are even moderately clean, with no more

Ian 20% contamination from the surrounding field, have

diameter of about 66. In terms of practical hardware,

1 5-inch telescope has a resolving power of 1 arc secid, but to do meaningful photometry on elements of

is size we need a diffraction limited system with an

<erture of about 30 inches, and seeing to match. (The

semblance to the aperture of the Sacramento Peak

;wer telescope is not entirely accidental.) The point

want to make here is that photometrically useful resotion and the kind of resolution we usually talk about

ffer by a factor of 5 or 6 . This factor is probably

t too far off whether the limit is set by diffraction

the telescope or by reasonably good seeing. The

sired photometric resolution dictates a minimum telejope size, and it is pretty big.

I do not intend to discuss the several forms a 'lar telescope can take. I think it has been demonrated that if the optical quality is really good, and

e seeing is good, the particular optical configuraijon is not crucially important. It is important, hower, to avoid air convection inside the telescope and

^om nearby external structures like domes near the

jtical paths. Several recent examples of solar tele-

: opes show careful attention to such details, with

;acuated optical systems and open air mounts equipped

ji th surface cooling devices and hot air scavengers. I

|| sure these measures pay.

There is no need for me to emphasize the fundamen1 importance of spectrographs, or to discuss the varus forms they may take. The performance of any we 11-

nstructed spectrograph of conventional type can be

uated with the performance of its grating. Very fine

ings have been happening in the improvement of gratis during the past few years. Dr. George Harrison at

JT began about 20 years ago to see what could be done

j the control of a ruling engine with interferometers

. place of the classical screw. I have watched as a

list interested spectator as he patiently overcame one

1 stacle after another. He realized at the outset that
there were many problems beyond that of simply moving

the grating blank on its ways a predetermined distance

for each stroke of the diamond. Compared with the acc racy of spacing required, the flexures of the machine

are enormous, and must be corrected somehow. He summa rized the difficulties back around 19 50 with the remar that the problems of ruling a good grating are analogous to those in the painting of a miniature portrait

with a floor mop on the end of a six-foot rubber hand]

Dr. Harrison has succeeded brilliantly in adapting twc

commercially available instrument-making machines to

interferometer control, and using them to rule gratinc

up to 16 inches wide. They very nearly achieve their

theoretical resolution, with ghosts of less than 10~ h at blaze angles of 63°, and blaze efficiency of more

than 50%. He told me the other day that his next

effort will be the ultimate grating he has been workir

toward -- a 16 by 24-inch ruling.

Parallel with Harrison's ruling development, sev- eral commercial firms have worked out methods for

making replicas of the original rulings. Over the pas

years, the best of the replicas have fully reproduced

the high qualities of the master rulings, except for

the blaze efficiency, which is invariably better in a first generation replica than in the master. The qua

ity of replicas has, however, been spotty. The most

usual fault has been a slight deviation from flatness

which results in serious astigmatism at large angles

diffraction, although the spectroscopic resolution at

the proper focus seems to be little affected. Our

experience at Sac Peak with large replicas has been

very satisfactory. If one insists on rigid specifica

tions for a replica it is now possible to secure one that is in no way inferior to an original ruling, is

appreciably more efficient, and, of course, much less

expensive. I am assured that we solar astronomers ar fussier about our gratings than anyone else, mainly

because of our requirement for spatial resolution alo

the slit as well as high spectroscopic resolution. H ever, the insistence on stigmatic replicas for astron

omy seems to have had a good effect, and the quality

replication has improved notably over the last couple

of years.

If we want the very best grating performance,

whether from an original ruling or a replica, we are going to have to get used to working with echelles.

These are coarse gratings working at high angles of d fraction in high orders, and they call for carefully

designed devices for isolating the relatively short

free spectral range. Dr. Harrison tells me that the

64
ptimum grating constant is about 79 grooves /ram when he

as to balance the problems of thick aluminum coats,

iamond loading, and diamond wear. He can blaze this

uling at 63° with extraordinary efficiency. At 5000 &

ne is working in about the 45th order with a free specral range of 110 A.

Right now ruled gratings are the practically availble dispersing elements for the classical style of

pectrograph. However, promising experiments are under

ay to produce gratings by a photographic etching proess. I do not know very much about this. The lines

riginate in interference fringes between two plane

;avefronts, and the grating constant is controlled by

arying the angle between these wavefronts. The

ringes are photographed and processed to produce a ash-off relief of successive ridges. When the surface

s aluminized we have a grating. I believe there are everal difficult problems of flatness and blazing that

ave not yet been completely solved, particularly for

arge grating spaces of more than a micron or so. Howyer , this process looks promising and may eventually

"sad to less expensive gratings.

Gratings are the basic elements in classical types

;f spectrographs -- nice direct devices that do the job

'sry well in ways that are easy to understand. Now we

ire hearing about other instruments for observing and

sasuring spectra, and among them may be some that

..Diar astronomers should investigate. The Fourier spectrograph is certainly the most interesting at present,

ince it has been spectacularly successful in defining

le infrared spectrum beyond the sensitivity range of

lotography and photomultipliers . I have had no experimental experience with a Fourier spectrograph, so my

emarks here are only those of an interested spectator.

Ithough there are possible alternatives, the practical

purier spectrograph is built around a Michelson intersrometer in which the path difference in the two arms

raries, either at a steady rate or in steps. When

I Lght in a defined spectral band (anything from a few

mgstroms to some thousands of angstroms wide) is fed

h, the resulting curve of transmitted intensity as a Miction of path difference is the Fourier transform of

le spectrum of the incident light. The Fourier specrograph has advantages over its classical analog, the

lotoelectric scanning spectrometer. First, the prod2t of angular area of the source and area of aperture

an be very much larger than for a normal spectrometer,

-fid the throughput is correspondingly greater. Second,

be whole spectrum is measured simultaneously. If

Btector noise is independent of light intensity, the

65
whole measurement can be performed in the same observing time as that required for one spectral resolution

element in a spectrometer of the same throughput. Thus

the speed of the system is greater than that of an equivalent spectrometer by a factor equal to the number

of resolution elements in the spectrum, which can be

enormous. This is known as the multiplex advantage.

Third, in any practical setup the significant signal

frequencies that define the spectrum are much higher

than those frequencies introduced by scintillation or scattered light. Hence these effects, which can be

very troublesome in a spectrometer, are easily and elegantly eliminated from the Fourier spectrogram.

With this rosy picture before us, one may wonder

why we are still fussing around with gratings. The

multiplex advantage of the Fourier spectrograph is

fully realized when the ratio of detector to photon

noise is large, since a spectrometer must average the

detector noise out for each spectral element separately

This is the situation for infrared detectors, which is

the reason for the vastly superior infrared performance

of the Fourier spectrograph. The picture is not so clear in the visible spectrum, however, where we have a)

relatively small ratio of detector to photon noise. Asj

the ratio approaches zero, the speed of the spectrometer approaches that of the Fourier spectrograph.

With the detectors presently available for the visible

spectrum, it turns out that the Fourier spectrograph

has little advantage in measuring a short section of

the spectrum from a 1 arc second area, but if the

range exceeds 10 angstroms or so, it begins to realize ]? a fraction of the multiplex advantage, which increases

steadily with the wavelength range. Hence for making a spectrum atlas, the Fourier spectrograph has a large

speed advantage

The throughput advantage of the Fourier spectro- » graph is somewhat diluted by the solar astronomer's

penchant for studying very small elements of the solar I surface. He can make this up completely, however, with

a multiple channel system that observes many small elements of area simultaneously, provided he can deal with

the overwhelming data rate entailed. Since the same £ option is available with the spectrometer, and with the same data rate, there is no real throughput advantage

in the Fourier spectrograph unless one is content with

the average spectrum for a large area of the solar disJ

Finally, I suspect that the Fourier spectrograph's

insensitivity to relatively low frequency fluctuations

in light intensity and scattered light is quite a genu-! j ine advantage. This alone is a strong reason for con-*'

66
idering the Fourier spectrograph for measuring the

jisible solar spectrum. The technical difficulties in

Achieving the resolving power and accuracy of a modern

jcanning spectrometer are enormous, however. The problems are not too different from those of ruling a gratpg each time one observes the spectrum. In spite of

he fearsome difficulties, Brault at Kitt Peak is under

aking the first attempt at a high resolution visible

ight Fourier spectrograph, while the cheering section

f less courageous souls looks on with interest.

A more recent addition to the solar astronomer's

ool kit is the magnetograph. Everyone agrees that

olar magnetic fields are fundamentally important, and

number of our theoretical friends express some impatience with the not too smart observers who cannot proide charts of the magnetic vectors at all levels in

tie solar atmosphere with 10-second time resolution,

ne Zeeman effect is right there, isn't it? Why don't

ou get busy and measure it? Well, there are problems,

ome of them very fundamental such as the finite flux

Uc photons

.

No one doubts the importance of determining the

agnetic vector, but I think it should be realized that

ye cannot measure it. What we can measure is the proile of the Stokes parameters across a Zeeman sensitive

ine. The magnetic vector must be deduced from the

esulting data, a process beset with some real uncerainties at present. So as far as instruments go, we

eed a Stokes polarigraph capable of defining the para2ters at enough points in the line profile to define

me Stokes profiles with sufficient accuracy for the

purpose . Furthermore, a quick calculation shows that

(tie limited photon flux from the solar surface will not

llow us the luxury of point by point measurement, if

a require a two-dimensional array of, say, 10 ^ magnetI'fe vectors in squares of one arc second and a useful

ime resolution. We are going to have to measure many

uch surface elements simultaneously. One can easily

nough dream up a digital video scheme with rapidly

) unable filters that would do the job. Components with

Ipsired qualities presently exist. I am afraid the

julfillment of this dream is still years away because

.he quantitative requirements are considerably beyond

he present capabilities, particularly in video systems

Ult I predict that these requirements will ultimately

3p met, and it will at least be possible to construct

[he dream Stokes polarigraph that simultaneously meaures the Stokes profiles of a line in 10 one arc

jecond squares with a time resolution of less than 10

leconds. By then, we may not want to because someone

67
has thought of an easier way.

Meanwhile, let's face the immediate prospects of

what we can do right now. The interpretation of the

circular polarization in the wings of Zeeman sensitive

lines in terms of the sightline field component is

fairly straightforward. Most investigators at present

are directing their efforts in this direction with variants of the Babcock magnetograph or the Leighton spectrohe liomagnetograph

There are several recent developments of interest.

Two of them are efforts to perform the image subtraction required by the Leighton spectroheliomagnetograph

method by means of video camera tubes. Leighton himself has assembled an analog system, and Janssens at

Aerospace Corporation Observatory has made a digital

system. Both have been in preliminary operation with

encouraging results, but I believe it is fair to say

that the pictures of the magnetic field obtained are not yet as good as those made by photographic subtraction.

I think the most promising advance is due to

Livingston at Kitt Peak. He has made a multiple chan- :. nel magnetograph of the Babcock type, which simultaneously measures the sightline components of the field

and mass velocity at 40 points along the slit of the

spectrograph. The beautiful pictures of the field he

has shown us have spatial resolution comparable with

that of the photographic spectroheliomagnetograms , and

the accuracy of the photoelectric method. This strong

arm approach has been so successful in Livingston's

hands that we are building a similar instrument in

which the channels can be distributed in a variety of

ways between many points along the slit in different

spectral lines or at several wavelengths in a single

line profile.

Perhaps the best prospect for determining Stokes | profiles from which to calculate the full magnetic vec-i

tors over an extended field is Alan Title's "spectra- 3 spectroheliograph" . This is a stepping spectroheliograph with an exit slit wide enough to transmit a band

sufficiently wide to include a whole line profile,

which is recorded on a stepping film. This is, of

course, an extension of Delandras 1 Spectro Enregistreur

for determining velocity distributions. I believe that

Title has used it so far to study the distribution of . sightline magnetic components and velocities with very 1 fine spatial resolution better than one arc second.

This instrument could clearly be adapted to the measure

ment of all the Stokes parameters to photographic

accuracy, which is certainly sufficient to give a rea68
lonable signal to noise ratio in the strong fields of

jctive centers.

The last instrumental item I will mention is the

|arrow band filter. For years the birefringent filters

ave been unchallenged here, but new types are making

heir appearance now. These are all variations of the

jabry Perot interferometer and have fairly stringent

ngular field limitations. Title has shown that the

liltering action of a single Fabry Perot filter is not

aite as good as that of a birefringent filter of the

ame bandwidth, but two Fabry Perot filters in series

jjre better. Practical experiments by Harry Ramsey and

itle with two types of solid Fabry Perot filters with

lass bands of 1 A or less give beautiful pictures of Ha

retail. There are still some deficiencies in uniforjity over the field, but I think these will be elimiated. These filters are now commercially available on notably shorter time scale than the birefringent filers, which should be an attraction. Unfortunately,

jiey are still quite expensive.

John Ramsay of CSIRO in Sydney has produced a

Esautiful filter consisting of three conventional Fabry

2rot interferometers in series. Each interferometer

\k held in adjustment and tuned by an ingenious servo

/stem, which is capable of modulating the wavelength

IE the transmission band over a long spectral range,

ly passband from 0.01 A up is possible, but the free

oectral range of the filter is only about 100 times

le bandwidth. Blocking the unwanted transmission

mds becomes a serious problem for passbands less than

L 1 A wide

.

I think the only new development in birefringent

Liters is the production of achromatic A/2 and A/4

Lates by Zeiss. This removes the only obstacle to

ill tunability over a very wide spectral range. Zeiss

; presently making a filter for Sac Peak that will be

mable over the range from about 4200 to 7000 A. o The

indwidth is roughly proportional to A

2

, and is hA at

it. Telescopes, spectrographs, magnetographs , and nar- w band filters, with some of their derivatives like

^ectroheliographs , are the primary optical tools of

olar astronomy. We have seen important improvements

i all of them over the past 10 or 15 years that have

^suited in an enormous improvement in solar observallonal data. I see no reason to expect the developmts of these tools to stop now. But I think we have

great need for a new detector that will have the high

lantum efficiency and signal to noise ratio of the

ist photoelectric surfaces, and record simultaneously

69
the intensity distribution over an extended field. We

could reduce the effects of poor seeing very appreciably with a detector 20 or 30 times as sensitive as a photographic plate. If one is willing to ignore the

inconvenience of conducting a campaign comparable to

preparation for an eclipse expedition for a set of sev eral photographs, the electronographic camera of the

type developed by Lallemand probably comes closest to

meeting the need. Other image tubes of various types,

and signal generating video tubes find occasional use,

but all of them are deficient in photometric accuracy.

At present we lack the detector we need, and I hope

this will be one of the major developments of the next

ten years.

70
SOLAR INSTRUMENTATION

(PART II)

Richard B. Dunn

Sacramento Peak Observatory

I. INTRODUCTION

Jack Evans has discussed the broad aspects of the

tate of the art of solar instrumentation in the first

art of this joint presentation. In the following I fish to emphasize a few of the facets of the Solar

acuum Telescope, in particular: (1) the thermal distortion of the window and mirrors; (2) the slit- jaw

iewing system on the spectrograph, which represents a ypical observing aid presently required by solar

stronomers; and (3) recent photographs of the spicules

t the limb and on the disk.

II. THERMAL DISTORTIONS

The Vacuum Solar Telescope described by Dunn

1964, 1969) eliminates the turbulence caused by the

un's heat on the optical path of the telescope by

vacuating the telescope. The conventional dome is

eplaced by a "turret" that withstands the elements and

s sealed by a vacuum window to form a boundary between

he telescope and the atmosphere. In spite of these

fforts the image is not perfect due to distortion of

he glass vacuum window, which is 34 inches in diameter

nd 4 inches thick, and to thermal bending of the

4-inch diameter, 8-inch-thick flats made from fused

uartz situated in the turret. These and other effects

ave been described elsewhere (Dunn 1971)

.

The vacuum window is studied by using the telecope to collimate laser light onto the window. This

ight is reflected from the two surfaces of the window

[lack into the telescope, which focuses an image of the

laser source. A small lens at this focus forms an

i! 71
image of the window and combines the two reflected

beams, one from the outside surface of the window and

the other from the inside, to form an interferogram

that shows the optical path difference within the win

dow. The window has a slight wedge that causes 76

fringes in the interferograms . These fringes would b

straight and evenly spaced if the window were perfect

Shortly after sunlight strikes the window, or if the

ambient temperature rises, the fringes show a turned-uj

edge. By afternoon the edge has distorted by a dozen

or so fringes. If a circle could be drawn through one

of the central fringes one would have a spherical wave

front, and only the focus would be changed with no los

in image quality. However, Figure 1 (left) shows that

this is impossible, and so we have spherical aberrati

and consequently a "soft" image after several hours

exposure to sunlight.

We tried several methods of eliminating the heat

ing of the edge, including shading the cell, insulatin

the turret, spacing the window away from the metal ce by an epoxy-glass spacer, and insulating the edge of

the window. None of these schemes effected any improv

ment. However, circulating a cooled water-glycol

mixture around the edge of the window and cell does

appear to solve the problem. Figure 1 (right) shows

the state of the fringes after the window was exposed

all day to sunlight. The chiller was simply turned on for 5 minutes every 30 minutes, and the liquid was cir

culated continuously. Ideally the liquid solution

should be kept at the temperature of the center of the

window. The tolerance on the straightness of the

fringes is 1 fringe. This represents a path differenc

of 1/6 wave when the window is used in transmission.

We plan to add a control system, and perhaps this

problem will be solved.

The two turret mirrors have been studied by obse

ing the change in focus of the telescope, which is

14.5 cm after several hours exposure to sunlight. Ca

culation shows that the mirrors are deformed about 3 waves convex. This would only change the focus of th

telescope and not spoil the image if the angle of

incidence of the light on the mirrors were 0°. Unfor

nately, our mirrors are mounted at 45° and the tolerance for flatness to prevent astigmatism is 1/4 wave. We must improve the coefficient of expansion by a fac

tor of approximately 10. The present mirrors are fus

quartz so the obvious solution is to change to one of

the new low expansion materials like "Cer-Vit" . With

our operating temperature range (-10° to +30 °C) , the

published curves of coefficient of expansion of Cer-V
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compared with fused quartz indicate that we would gain

the factor of ten required. More recent measurements

by Jacobs (19 70a) , on our new Cer-Vit blanks (see

Figure 2) , show the published curve is very optimistic

and that in fact the entire expansion curve is shifted

downwards and to the hot end. This is in agreement

with Bradford's (19 69) and Jacobs' et al. (19 70b)

measurements on another sample of Cer-Vit. The slope

of the curve is approximately six times greater than

advertised, and in the opposite direction. It is

actually equal to fused quartz at -10°C! The coefficient of expansion of the new Cer-Vit mirrors will be

enormously improved over fused quartz only near 14 °C.

These are two examples of thermal problems in

solar telescopes. We expect to obtain greatly improved

pictures when we are able to show that the telescope is

o

X

T n 1 1 1 1 1 r r 1 1 1 r

FUSED QUARTZ

CER-VIT

C-IOIx /

/o Do-'0

"

I I I 160 H40 H20 -100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 °C

Figure 2. Coefficient of expansion of Cer-Vit and

fused quartz. Operating temperature range of the tele,

scope is -10 to +30°C. Dashes and circles: Advertised

curve for Cer-Vit C-101. Squares: Jacob's measurement

on Cer-Vit. Crosses and dots: Jacob's measurements on the center and edge of the Sac Peak Cer-Vit.

74
jeally diffraction limited after the sunlight has shone

pi it and through it for many hours.

III. A SLIT-JAW VIEWING SYSTEM

Solar astronomers are often unsatisfied with simly the spectra of an event. We find that they want to

ee the relationship of their spectra to pictures taken

n white light, Ha, or the K line. We have evolved a nique slit-jaw viewing system that allows simultaneous

hotographs and viewing of all these wavelengths. In

ddition it allows the observer to view the white-light

Tiage on a TV monitor. The image on the TV is good

aough to show the granulation and sunspot details,

hus seeing quality and guiding inaccuracies are learly visible. The TV image has become indispensable

or those observers who want to follow a particular

2tail or who want to take their pictures only at

nstants of the very best seeing.

A diagram of the system is shown in Figure 3.

ight comes up from the telescope and is reflected by

ne polished slit jaws down to lens LI. This lens must

2 large enough to accommodate the field and the expanion of the field at the distance of the lens from the

lit jaw. In our case the field is 7.5 cm and the beam

xpands at f/72. A 10 cm diameter lens with a focal

ength of 87 cm is adequate. This same lens forms an

Tiage of the telescope objective in the vicinity of the

edge beamsplitter at W . The beamsplitter Wj consists

it an uncoated glass wedge whose front surface reflects

I of the light to L2 and thence to a white-light

amera. Its rear surface reflects 4% of the light to

3 and thence on to a Vidicon TV camera. The remainder

f the light is transmitted and strikes the wedge beamplitter W 2

. Its first surface is coated to reflect

7% of the K light to L4 and to a Halle K-line bireringent filter. The same coating transmits 9 5% of the

h light to L5 and to a Halle Ha birefringent filter.

s ie lens system L6 is flexible and can accommodate

agnif ications of 1:1 to 1:\ and also various polarzing optics. L2, L3 and L4 have the same focal length

3 LI.

The system and its relationship to the spectrograph are shown in Figure 4.

Figure 5 is a picture through the slit-jaw system

|i a prominence and the chromosphere taken by William

agner. The slit opening shows as a horizontal gap.

yo vertical hairs locate the picture along the slit.

75
*f- TO K FILTER

FLOOR LEVEL Figure 3. Diagram of the optical system of the slit

viewing system.

76
\gure 4. The Slit Viewing System. The TV camera

ows on the top left. Directly below it is the Ha cama. To the right is the white light camera. (Sacranto Peak Observatory, Air Force Cambridge Research

•boratory)

Jiguve 6. Photograph of television monitor showing

granulation and sunspot. (Sacramento Peak Observatory,

Sir Force Cambridge Research Laboratory)

fcratches on the slit surface are clearly visible to

'the left of the hairs and show that the surface of the

eflecting slit jaw could be greatly improved. Granu-

.ation is clearly visible in the picture of the TV

lonitor in Figure 6.

IV. RECENT PHOTOGRAPHS WITH THE VACUUM TELESCOPE

In spite of the thermal problems described in

jiiection II, we have managed to obtain some fine pictures of the solar granulation and chromosphere in Ha,

especially with the aperture of the telescope reduced

:rom 30 inches to 20 inches to lessen the effects of

:he solar heating on the window. So far we have not

ised the new Cer-Vit flats or the window cooling system.

The first scene, Figure 1 ^ is a montage of the

chromosphere taken through a ^A-bandwidth Zeiss filter

It different wavelengths near Ha. Comparison of the

'plus lk with the minus 1& scene shows that spicules are

noving rapidly along the line of sight. Since 1A near

79
-I

I

Figure 7. The Ha chromosphere at the solar limb take

with a 1/4 A bandwidth Zeiss filter tuned through the

Ha line, Oct. 14, 1970. (Sacramento Peak Observatory

Aiir Force Cambridge Research Laboratory)

80
ifewge 5. The Ha chromosphere on the disk with the

( 4 A bandwidth Zeiss filter tuned +7/8 A off the cenr of the Ha line, Feb. 13, 1971. (Sacramento Peak

servatory, Air Force Cambridge Research Laboratory)

81
Ha corresponds to a radial velocity of 45 km per

second, and the measured velocity of spicules in the

plane of the sky is about 40 km per second (Lippencott

1957) , spicules must be highly inclined. Note the lac}

of correspondence between the spicules in the plus and

minus lk scenes, which indicates the line profiles are not widened, but are really narrow and displaced by

radial velocity. Also note the lack of spicules in th<! OA picture. The o "gap" near the photosphere is clearly

visible in the 1A pictures. Spicules are seen almost

detached in the l^A pictures. The "double limb" in th

OA scene is due to continuum light leaking through the

filter. This line of demarcation disappears when a 1&

interference filter is placed in front of the Zeiss.

This montage is a great improvement over the pictures

in my thesis (Dunn 1960) . Part of this improvement is

due to the better telescope resolution, but most is du

to the ^A-bandwidth Zeiss filter as compared to the

3 . 4A-bandwidth filter used in the earlier study.

Clearly a 3. 4A fi Iter melds all the pictures in the

montage together.

Figure 8, taken with the %A-bandwidth Zeiss filte

7/8 & off the center of Ha, shows spicules on the dis

They are seen to form "picket fences" at the edges of

supergranule cells. At the base of the spicules one often sees a gap in the spicule and then, in the

photosphere, a bright dot very similar to an "Ellermai

Bomb" or "moustache" as seen on spectra. Perhaps thi

picture links Leighton's (1964) picture of the random

walk of magnetic fields away from active regions and

the motion of Sheeley's magnetic knots (1969) with th

Ha chromosphere structure and detail. We are anxious

trying to obtain movies at various wavelengths of the

bright network below the spicules.

These two scenes are typical of many photographs

accumulating with this tower telescope.

82
REFERENCES

radford, James N. 1969, Ultraprecise Measurement of

ij Thermal Expansion Coefficient , Technical Report

ij 48, Optical Sciences Center, U. of Arizona.

junn, R.B. 1960, Thesis, Photometry of the Solar

! Chromosphere , Harvard University.

,unn, R.B. 1964, Applied Optics, 2_, 1353.

!unn, R.B. 1969 , Sky and Tel., 3S_, 368.

;unn, R.B. 1971, Optical Performance of the Vacuum

I Solar Telescope , presented at the AAS meeting in

^ Huntsville, Alabama, in press.

.acobs, S.F. 19 70a, private communication.

acobs, S.F., Bradford, J.N. , and Berthold III, J.W.

j 1970b, Applied Optics, 9_, 2477.

ieighton, R.B. 1964, Astrophys. J., 140 , 1547.

:ippencott, S.L. 1957, Smithsonian Contr. Astrophvs.,

2, 15.

fheeley, N.R. 1969, Solar Phys., 9, 347.

83
THE SOLAR CHROMOSPHERE AND THE GENERAL STRUCTURE

OF A STELLAR ATMOSPHERE

Richard N. Thomas

and

Katharine B. Gebbie

Joint Institute for Laboratory As trophy sic s*

I. INTRODUCTION

The aim of this symposium is to say thanks to Don

Menzel for the ideas and people he has launched on the

astronomical world. Useful ideas evolve in a successively more realistic sequence. Productive people

ensure such evolution. Whether the resulting picture

supports or refutes the original ideas is less important than the generation of such a sequence. Evolving

ideas and productive people characterize the Menzel

school.

As an example, we outline the evolution of the

interpretation of the "solar chromosphere anomaly".

This interpretation, which began as a purely solar one now has broad implications as a key to the general

structure of a stellar atmosphere. By "solar chromosphere anomaly" , we mean certain observed features

,

first identified in eclipse spectra, that cannot be

reconciled with the classical model of the solar atmosphere, We begin by classifying the essential feature

of these anomalies and then show how Menzel 's interpre

tation in terms of a collision-free atmospheric appendage has evolved into a more general one in terms of a arbitrary atmosphere diagnosed by what we call the "ne

spectroscopy" . By linking the diagnostic methods of

the new spectroscopy to some of Menzel* s suggestions o the interpretation of symbiotic spectra, we extend the

evolution to a general stellar model. By invoking the

concept of transfer and population effects, we distin-

*of the National Bureau of Standards and the University of Colorado.

84
guish those aspects of the solar chromosphere anomaly

that are peculiar to the chromosphere as a distinct

region from those that are common to the atmosphere as

a whole.

The evolution of the interpretation of the solar

chromosphere anomaly reflects a more general evolution

| in the whole approach to stellar atmospheres. It began

with the classical approach, and has, for some of us,

culminated in an interpretation of the atmosphere as a (transition region between the interior of the star and

the interstellar medium. Classically, the atmosphere

,was viewed simply as the surface of the stellar interior and was assumed to be described by the same state

parameters as were used to construct the interior model

pressure, density, and temperature. The single aim of

the associated diagnostics was to determine the boundary values of these parameters. Model atmospheres were

by assumption, constructed in terms of these parameters

and the relations between them that were used for the

interior model. Viewed, however, as a transition

|region extending from the deepest observable layers to some point at which the star ceases to be the dominant influence on the medium, the atmosphere includes

chromospheres, coronas, shells, nebulae, circumstellar

dust, and any other phenomena controlled primarily by

the star. Here tlie state parameters and the relations

jbetween them must be determined, and a diagnostic procedure developed to obtain the distribution of these

parameters from all the available observations. Similarly, tfie construction of models must be attempted

without any a priori assumptions either on the state

parameters or the relations between them. In practice,

because of our lack of experience with such transition

regions, the empirical analysis of observations must go

hand in hand with the theoretical construction of

•node Is.

Initially the classical atmosphere was thought of

|^as a thin homogeneous surface layer throughout which

tithe interior state parameters were constant at their

poundary values. The debate over whether such a model

Iwas consistent with the observations first arose over

ithe implications of the existence of a line spectrum.

JHould a line be produced by scattering in an isothermal

atmosphere (Schuster-Schwarzchild) or did its presence

require a temperature gradient in the observed layers

-(Milne-Eddington) ? The view prevailed that it did

require a temperature gradient, and diagnostic methods

oased on a non-homogeneous model, but one locally in

thermodynamic equilibrium, were introduced to interpret

the observations.

II

85
The essential characteristic of the classical

approach was the use of conventional thermodynamic equi

librium parameters to describe the observable atmosphere. The approach was defined by the five assumptions: local thermodynamic equilibrium for the microscopic distribution functions of matter (LTE-R) , hydrostatic equilibrium (HE) , radiative or quasi-static con- vective transport of energy (RE or CE) , a spherically

symmetric atmosphere (SS) , and the absence of macroscopic electric and magnetic fields. The essential

physics of this approach is developed in Unsold' s book,

Physics of Stellar Atmospheres , which, properly supplemented by subsequent developments in atomic physics and

computing techniques, remains the classic reference in

the field today. The approach has been used to investi

gate the variation, as a function of Te ff, g, and abundances, in the boundary values over the HerzsprungRussell plane. If the physical basis of the approach

were sound, these analyses would provide the essential

link between the observations and their interpretation

in terms of atmospheric structure and evolution. If,

however, the classical assumptions are not valid, the

results of these diagnostics provide only a preliminary

survey, the meaning of which remains to be assessed.

Not only may the derived values of the parameters be

unreliable but in particular their physical significance may also be in question. Such ad hoc parameters

as turbulence, excitation and ionization temperatures,

and mixing lengths have been introduced to reconcile

the observations with the classical model, but the self

consistency and influence of these parameters on the

state of the gas has not been satisfactorily explored.

If , on the other hand , the atmosphere is regarded

as the transition region between the stellar interior

and the rest of the Universe, all those phenomena asso ciated in any way with, the domain of influence of the

star must be taken into account. The innovation of

Menzel and his early collaborators was that in ana- lyzing stellar spectra and constructing stellar models

they implicitly attached as much weight to the chromospheric anomaly, symbiotic spectra, circumstellar

shells, and nebulae as to the Fraunhofer spectrum of

the star itself. Their early results gave insight int

the kind of microscopic interactions that are importanl

in gaseous matter under atmospheric conditions.

At this point, we should perhaps ask whether we

are discussing two different but equally valid

approaches to a stellar atmosphere, each of which fulfills the purpose for which it was designed. Can the

solar atmosphere, for example, be divided into two ind

86
pendent regions? The lower region would then produce

the observed disk spectrum; its structure would be

obtained, and its spectrum analyzed, by the classical

approach. The upper region, including all the other

phenomena in our more extended definition of an atmosphere, would require more general diagnostic methods

and data but would in no way affect either the lower

region or the disk spectrum. The significance of the

solar chromosphere anomaly lies in the answer it provides to this question.

Until recently, most people would have agreed that

such a division of the atmosphere was indeed possible.

About a decade ago, however, the results of a longrange program of observation and analysis proved to the

contrary, showing conclusively that the chromosphere

does seriously affect the disk spectrum (Thomas and

Athay 1961) . The observational approach was a refinement of that pioneered by Menzel (19 31) and developed

I by his students (Evans, Roberts, and Thomas 1950-51).

The diagnostic approach evolved from a viewpoint intro-

\ duced by Menzel and his associates (Menzel 1931; Cillie

j and Menzel 19 35; Goldberg and Menzel 19 48) , as extended

and refined by his students (Thomas 1948 et seq.; 1950

et seq.). The results of this program showed that (1) as a part of the atmosphere that affects the disk spectrum, we must include a definite region called the

I "chromosphere", the structure of which is fixed by con- ditions that violate a number of the assumptions defining the classical model, and (2) there are also parts

of the disk spectrum formed in regions below the chromosphere to which the classical diagnostic methods are

1 not applicable.

It is being gradually accepted that neither of

these two conclusions is peculiarly solar, but rather

c that the solar chromosphere anomaly is of great significance for our general picture of a stellar atmosphere.

Although the original solar investigations focused on

the first conclusion, it is the second that has been

more widely accepted in the stellar context. In

j essence, the second conclusion implies that the assumption of LTE-R should be dropped. It is now becoming

fashionable to build models of a classical atmosphere

3 without this assumption; that is, the "New Classical

Atmosphere" (Mihalas 19 70) . That the assumption of

LTE-R is untenable was demonstrated by some of us from

the Menzel school who, using the solar disk spectrum,

showed that LTE-R precluded a self-consistent interpretation first of the chromospheric lines, then of all

lines for which the optical thickness at the line center exceeded about one, and then of the chromospheric

87
continuum. By establishing the theoretical basis for

the empirical conclusions, we showed the results to

apply to stars as well as to the Sun. We suspect that

this conclusion has now become popular mainly because

models can in some cases be computed as accurately with

out LTE-R as with it. The problem remains, however,

that again some of us from the Menzel school have shown

that the assumptions of hydrostatic equilibrium, radiative (or convective) equilibrium, and spherical symmetry are also invalid in parts of the solar chromosphere

and a great variety of observational work on solar magnetic fields indicates that the remaining assumption of

the classical model is also doubtful. Furthermore, we

now realize that the whole rocket UV, the far-infrared,

and the radio spectrum of the Sun all originate in the

chromosphere and corona. Thus "chromospheric effects"

on the "normal disk spectrum" can be ignored only if

the "normal spectrum" is limited to the visible continuum and weak lines. We doubt that even the strongest

proponent of the classical atmosphere would maintain

such a position.

We conclude then that in any model of the solar

atmosphere, some of the classical assumptions must be

dropped in almost all of the atmosphere, and all of the

classical assumptions must be dropped in some of the

atmosphere. We suggest this may also be true for most

stellar atmospheres. Is it perhaps significant that

model builders are now apparently willing to construct

wholly theoretical model atmospheres for any star

except the Sun?

In Section II we review the observations and ideas

that have led to the rejection of each of the classical

assumptions in the solar chromosphere and discuss our replacements for them. In Section III, we suggest how

this overall picture of the chromosphere clarifies our general picture of a stellar atmosphere.

II. THE SOLAR CHROMOSPHERE ANOMALY

There are two ways to try to resolve the chromospheric anomaly. The first way is to examine individually the validity of each classical assumption, theoretically and empirically. Unfortunately, we don't

know enough about the character of transition regions

in astronomical environments to treat the theoretical

problem in full generality; and since the assumptions

are coupled in their observational consequences, a

88
wholly empirical approach is ambiguous. A second way

to try to resolve the anomaly is to abstract the essential features of all the observed anomalies into a few

coherent groups. It is this approach that in practice

has proven the more productive. Indeed, the evolution

of Menzel's original ideas into our present picture

reflects the evolution of the categories into which the

anomalies have been grouped and of our understanding of

; the implications of these categories.

A. The Observed Anomalies

1, Emission Height Gradients, Anomalously low

emission height gradients as observed at eclipse in

both lines and continua, and the variation in these gra

dients with excitation and strength of lines, and among

the various lines and continua.

Menzel was the first to obtain extensive eclipse

data of sufficient precision to allow a quantitative

determination of these well-known qualitative effects.

Subsequent HAO-Sac Peak eclipse expeditions increased

the accuracy and height resolution to the point where

differential values of emission height gradients could

be investigated as functions of excitation and line

strength. At atmospheric densities predicted by the

classical model, these observed emission gradients

should not be affected by self -absorption and could

therefore be identified with the gradients of the occu- pation numbers. If these gradients were in turn identi

fied with the total density gradient, it would be lower

1 by factors of up to ten than that predicted by a purely

thermal classical model; the same density gradient

interpreted on the basis of a "turbulence" arbitrarily

introduced into the classical model implies supersonic

velocities for the turbulent elements. If, on the

other hand, the gradient of the occupation numbers is

not identified with the density gradient, the implication is that the excitation and ionization increase for

some lines and decrease for others in the same atmospheric region.

2. Excitation State. Anomalous relation between

emission in lines and continua of the same ion as observed at eclipse, and anomalous intensities and

structures of the cores of strong lines as observed on

the disk and at the limb.

Eclipse observations in the H~, Balmer , and

Paschen continua, interpreted simultaneously, give temperatures and densities inconsistent with the classical

model. Nor do combined observations of the Balmer

lines and continuum give occupation numbers for the

89
energy states of hydrogen that are consistent with the

classical model. Recent observations of the Lyman con- tinuum lead to the same conclusions.

Interpreted on the basis of an unblanketed classical model, disk observations of certain lines (Na I and

the hydrogen Balmer lines) imply temperatures of up to

about 1300 °K below those predicted, while others (Ca II)

require that the temperature first decrease, then

increase, and then decrease again. The appearance of

emission lines on the disk, such as those observed in

the rocket UV, has no interpretation on the basis of a classical model.

3. Ionization State, The observation of ions

that should not exist.

The earliest example, often emphasized by Menzel,

is the presence of He I and He II lines. Identification of the coronal lines by Edlen intensified the prob

lem, and more recently many more such ions have been

identified from the rocket UV spectrum in both the

corona and chromosphere.

4. Inhomogeneities . The presence of inhomogeneities in at least the upper chromosphere.

Menzel' s early picture of the upper chromosphere

was that of a "burning prairie" . Later studies at HAO

and Sac Peak defined this phenomenon more specifically

in terms of the properties of the spicules. Additional

evidence is obtained from the anomalous emission in dif

ferent lines and continua as observed at the solar limb

during eclipse.

B. The Implications

This grouping of the observed anomalies suggests

the following implications for the structure of the

atmosphere and our interpretation of it. (1) Those

parts of the atmosphere that contribute to the observed

spectrum, including the disk spectrum, extend to

greater heights than would be predicted from the solar

gravity and effective temperature on the basis of the

classical model, which thus represents at most some lower part of the atmosphere. (2) Either the distribution of excitation is quasi-random or this effect is an artifact produced by faulty diagnostics. (3) The

energy available for ionization is greater than the

classical limit set by the effective temperature. (4)

The outer atmosphere is unstable against the production

of inhomogeneities. Whether the instability arises in

radiative processes or in a differential input of non- j radiative energy or momentum or possibly in other

sources, remains to be established.

I
Thus to resolve the chromosphere anomaly, we must

identify, describe the operation of, and assess the

relative importance of those effects that can cause a real or apparent distribution of absorbing and emitting

atoms to differ from that predicted by the classical

model. Because the distribution of excited atoms

reflects the distribution of both density and excitation, we must specify the factors that fix the density

(input of kinetic energy and momentum, and the stability of a homogeneous structure against their differential input) and those that fix the excitation (input of

internal energy and its partition) . The classical

assumptions impose a particular set of relations that

j fix these distributions in a way that requires no knowl1 edge of the details of the microscopic processes; but

j in doing so, these assumptions are all coupled in their

' effect on any empirical test of their validity.

I Because equipartition is assumed for the kinetic and

i internal energies, and it is assumed there are no microscopic, non-quasistatic velocity fields, the density

j and excitation distributions are completely coupled and

measured by the distribution of the single parameter,

T

e

. Thus we seek a more general approach in which

there is neither coupling between nor restrictions on the distributions of density and excitation. To

j approach the problem in full ' generality is impractical.

We do, however, have the observational guide that the

l| anomaly increases outward in the atmosphere, whereas

the applicability of the classical model improves with

increasing depth. Furthermore, there is nothing in the

structure of the classical assumptions that incorporates an effect of the boundary. Since the chromosphere,

as part of the transition region, appears to have many

of the physical properties associated with a true nonI adiabatic boundary, a first logical step toward underI standing its structure would be to include boundary

I] effects in such a way that the structure produces the

chromospheric anomalies at large heights and approaches

the classical model at great depths. We now examine

the character of a chromosphere viewed as such a trans iI j tion region.

C. The Chromosphere as a Transition Region

The presence of a non-adiabatic boundary may

affect a system in two ways. First, the exchange of

energy at the boundary will, in general, result in an energy flux that causes a gradient in the state parameters. Second, the microscopic rate processes that

determine the density and excitation distribution func91
tions will become inhomogeneous and so depart from

detailed balance.

We consider first the effect of an energy flux.

In an adiabatically bounded system, there is no energy

flux; the particle concentrations and the distribution

of internal energy levels may vary with position, but

the temperature and excitation are uniform, fixed

wholly b^ the total energy of the system. In a stellar

atmosphere, however, which is characterized by a non- adiabatic boundary and an energy flux, the excitation

at each point depends upon: (1) the amount of energy

available to be absorbed, (2) the amount of energy actu

ally absorbed, and (3) the process by which the

absorbed energy is apportioned over the various energy

states. The amount of available energy is fixed by the

transport processes, and the amount of energy absorbed

is fixed by the density and relative populations of the

energy levels, which also describe bow the energy is

apportioned. Transport and population processes are,

in general, coupled. The classical approach restricts

the kind of coupling: LTE-R describes the absorption

and partitioning of the available energy; radiative

equilibrium, hydrostatic equilibrium, and spherical sym

metry specify the available energy by eliminating all

but radiative transport processes. A more general

approach, from which these assumptions are removed,

must make possible the calculation of (1) to (3) in

terms of the total energy flux and certain other proper

ties of the star that remain to be determined. According to the classical approach, ^e ff and g suffice.

We consider next how the presence of the boundary

introduces inhomogeneities into microscopic processes

causing departures from detailed balance. There are four such effects: (1) Radiative processes reflect the

boundary-induced asymmetry in the radiation field and

the effects of the resulting discrepancy between color

and density of radiation often referred to as dilution

effects. (2) Collision rates will decrease with

decreasing density; hence there will be an increase in

the relative importance of radiation rates. (3) Aerodynamic motions will amplify with decreasing density,

ultimately providing a non-radiative energy source with

a potential for excitation that is not necessarily

related to that of the radiation. (4) These aerodynamic motions, together with any material instabilities

associated with radiative effects, may induce geometric

inhomogeneities, hence additional boundaries.

To include these boundary effects, we must, in

practice, combine two approaches: (1) a synthetic

approach, in which theoretical models incorporate these

92
fects, and (2) an analytical approach, in which a agnostics is developed to infer empirically the relave importance of the effects. In the latter approach

major problem has been to avoid imposing diagnostic

thods that, while more general than those of the clas

cal model, still pre-condition the derived results.

. the following sections, we consider Menzel's origi1 suggestions and then show how they have evolved

.to our current approach.

The original Menzel approach

At the time the Menzel school began to worry about

mclassical effects, astronomers implicitly assumed

tat collisions maintained LTE-R in a stellar atrao-

)here. Any departure from LTE-R would then be

rpected to occur in low-density regions, where, it was

.so assumed, the optical depth in all but the Lyman

mtinuum and lines was sufficiently small that the con

.nuum radiation field could be described as the prodit of a dilution factor and a Planck function charac-

;ristic of the central star. In their initial investi

Ltions , therefore, Menzel and his early collaborators

>nsidered only the first and second effects of the

>undary on the microscopic processes in a pure hydrosn atmosphere (Menzel 1937 et seq. ; Cillie and Menzel

35) . This limitation appeared to be justified by

•servation: the excited energy levels in planetary

ibulae and in the solar chromosphere appeared to be

iderpopulated relative to the local value of Te

, in

:cordance with the theory of recombination in a dilute

tdiation field.

The electron temperature, Te , in planetary nebulae

.s determined by the balance between "dilute" photoion

:ations in the Lyman continuum - a non-LTE process -

id free-free radiative transitions - an LTE process -

i radiative equilibrium. Thus the computed value of

i lay below the radiation (or "color") temperature of

p central star, its value in a collision-free region,

tt well above its LTE value as determined by the

iergy density of the radiation field. Embarrassingly

lough, this approach was not applied to non-nebular

-mospheric regions until 196 3 when it was reintroduced

I Cayrel who applied it to the H~ free-bound continuum

:

l the solar chromosphere. It is interesting for the

'olution of the classical model that if the collision-

*ee solution were valid down to Te- 1, and if there

;re no LTE processes, the model would closely resemble

tat of the Schuster-Schwarzchild isothermal atmosphere

93
Such an atmosphere would include everything we have

defined as the transition region, including the solar

chromosphere and planetary nebulae. The presence of

lines would not affect this picture as long as they

were formed by pure scattering. Thus we see that devi

tions from such an isothermal atmosphere arise from cc lisions, from non-scattering processes in line formation, and from deviations from radiative equilibrium.

In both the prediction and interpretation of the

Balmer and Paschen spectra, the error of the Menzel

approach lay in assuming the solar atmosphere to be

optically thin in the Balmer lines. An empirical ana]

ysis (Thomas 19 50) allowing for a non-zero opacity in i these lines showed the energy levels n > 3 to be over rather than underpopulated. A theoretical analysis

(Thomas 19 49) showed that the partition of energy amoi

the internal degrees of freedom was controlled by the

radiation field in the Balmer lines. Thus the stage

was set for the modern non-LTE approach in which the

populations of the energy levels and the transfer of

radiation are inescapably coupled. Because this

approach in terms of a collision-free region with a dilute radiation field suffices for the Balmer, Pasch<

and higher spectra, it gives information on the parti

tion of energy over the discrete energy levels, but n

over the energy levels of the electron continuum. Th" it is relatively insensitive to T

e

.

2. Subsequent evolution

The most significant empirical extension of

Menzel 's work was that of the HAO-Sac Peak eclipse ex ditions of 1952 and 1962. The aim of these expeditic was first to repeat Menzel 's 1932 observations with

greater accuracy and height resolution and second to

extend his analysis along the directions just summarized. The primary idea was to adopt the above

approach to an empirical analysis of the Balmer and

Paschen continua and lines, but to treat the Lyman

region theoretically (Pottasch and Thomas 1959) in m

order to obtain the ionization equilibrium for hydrocn.

Combined with an analysis of the H" continuum, this

approach gave an accurate interpretation of the enero

in the continua, i.e. of T . At this point, one had for hydrogen an empirica.

measure of the partial distribution of an unspecifie(

total amount of energy. By not forcing the value of

j

this total energy to be that of the radiation field, ! but rather by comparing the empirical Te with values

94
mited by radiative equilibrium, one obtained an empiral measure of the validity of radiative equilibrium,

is interesting that this empirical analysis, incori gating for the first time a correct treatment of cou-

! ad line and continuum effects, produced a Te

(h) disibution toward which the various subsequent models

.em to be converging (Utrecht Reference Photosphere

54; Bilderberg Continuum Atmosphere 1968; Revised

lderberg Continuum Atmosphere 1969; Harvardithsonian Reference Atmosphere 1971). In Figure 1,

reproduce this model (Thomas and Athay 1961)

I gether with other representative models. The out-

[ anding success of this model was that its wholly theoI tical prediction of the Lyman continuum of hydrogen

[Tie within a factor of two of the observed value. The

|

. bsequent models, all of which include some part of the

I assical assumptions, still failed by several orders

i magnitude to predict the Lyman continuum. The curi nt models based explicitly on the Lyman continuum

oyes and Kalkoven 1970) and one including the effect

spectral lines in the rocket UV (Avrett, Vernazza,

d Chipman 19 70) predict a T e

(h) distribution very

,ose to that of the 1961 model.

In extending the non-LTE approach to the Lyman

gion, one had to take into account the third effect

the boundary on the microscopic processes; namely, a ssible difference in energy between collisional and

diative processes. In doing so, one had extended the

nzel approach to include all such effects except a ometrical departure from spherical symmetry. And

en this effect could be studied from the eclipse obrvations by comparing the free-bound emissions in

drogen and He I (Athay and Menzel 19 56) , and the emison in neutral and ionized metals (House 1961). These

mparisons provided evidence for departures from spheral symmetry at heights of about 1500 km and possibly

[en as low as 750 - 1000 km.

To analyze Balmer and higher lines in the disk

ectra, we extended the Menzel approach to opaque but

ill collision-free atmospheric regions. The evoluonary step was the recognition that it was necessary

J solve equations of radiative transfer in order to

tain either the source function or the occupation numrs of the energy levels; that is, it was finally

cepted that radiative processes in the line dominated

; 1 other terms in the source function. In the trans-

; r equation for the radiation field in the line, the

- otoionization terms became recognized as source and

nk terms rather than as competitive processes in fixjig the numerical value of the source function at a

95
An

id

T 0 Q) U r

Q) & U £ CU CD h P W M-) 0 <U 0 0 r

J

1 O -H •H 0 G J WOO

>i G W s

Ck U -P - ; m g -l.

1 (D 05

i j U T$ - W -P u • (h £ fd o >

(D 5-1 • u fd ^ -P K

-

96
1

1

I

i

i

I

i %

Nj-1 ^

*is-P07

<D 0)

(T\ U

>—\ (D

I O

U

OQ) O N O

id to h

o

e -p 43 H W

-P 0 -H H

0) T5 N 0)

4-> 0+"w

U XI -H

= 5-10)

Q) (UK QJ

si <u •

<—I ^-i CD H <U £

P-i -

I W Q) 0 rH u -p o H •» (D dJ 0 CD U £ n u 53

a) a> m

D-t d) (D o m -p ft o o^ c

co ft (d

0) w u o H

>i C 01 U -P

0) ft H U

i a; ^

& i U HQ) w -p m

ft ^ fO -p u >

. n tu c

c\> -P EC D

i 3 <

^ft a

ft w

ttj D S

u • c

G rH

97
'7

16

f I

1

ZOO 400 600 800 /OOO /ZOO /400 /600 /ifkm)

Figure 3. PSC - "Physics of the Solar Chromosphere'

(Thomas and Athay 1961) ; URP - Utrecht Reference Pho

sphere; BCA - Bilderberg Continuum Atmosphere; HSRA

Harvard-Smithsonian Reference Atmosphere. Height ze is at T5QQQ =1. In placing the PSC model on the sa scale, we have shifted its height zero by 410 km.

given point. Because the source function is thus "c

trolled" by photoionization rather than by the local

value of Te , the population of the Balmer ground sta

increases and with it the importance of self-absorpt

effects. Thus both empirical analysis and theoretic

computation indicated an over rather than an underpc

lation of the energy levels, as had been implied in

earlier investigations. The change came, however, f|

98
irrying Menzel's original approach to its logical conjus ion.

In contrast to the above extension of Menzel's coljjsion-free approach, the interpretation of the disk

:ofiles of such lines as H and K of Ca+ and Mg+ 'efferies and Thomas 1959) extended the approach folNwed in the analysis of the Lyman eclipse data. This

ipresents an application of the third effect of the

, undary on the microscopic processes, greater energy

J collisional than in radiative excitation, which

fleets a coupling between departures from radiative

juilibrium and LTE-R. However, we found that, as with

ie photoionization effect for the Balmer lines, this

Hisional effect was manifested through the source

Id sink terms in the transfer equation for the line

|fd not, as in LTE-R, directly in the source function,

kis both collisionally controlled and collision-free

ieatments of the disk spectrum could be incorporated

.to the same general framework (Thomas 19 57; Jefferies

j.d Thomas 1959 et seq. ; Thomas 1965; Jefferies 1968).

| a rough sort of way, this uncouples the departures

ifom the various classical assumptions. The non-LTE

proach gives the general form of the source function

source function

radiation field

considered + source terms

1 + sink terms

i>gether with expressions for the source and sink terms

; functions of the state parameters. To determine the

irmitted range in values of these state parameters and

mce of the source and sink terms, we study departures

;om hydrostatic equilibrium, radiative equilibrium,

id spherical symmetry.

j Integration of theoretical investigations

Just as the various observational anomalies could

a grouped into four classes, so the different theoretiil investigations can be brought together into two catTories. Those in the first category, which has been

ailed the "new spectroscopy" (Thomas 196 5) , aim at

Lassifying the types of source and sink terms that

cist and identifying them with the kinds of profiles

Be lines and continua they produce in different atmobheres. As such, this approach is concerned with what

spears to be the unsystematic distribution of excitaion with height. The investigations in the second catbory aim at determining those factors that fix the val99
ues of the state parameters and hence at selecting

those components of the source and sink terms that con trol the source function in any given situation. This

approach is concerned with the absolute level of excit

tion and ionization, the density distribution, and pos

sibly the departure from spherical symmetry. The firs

approach has been developed to a considerable extent;

the second is in a less advanced stage.

(a) The new spectroscopy . This approach arose

from attempts to systematize the methods for predictir

the kind of profile expected of a given line or contir

uum in a given atmosphere. It consists of classifying

the various transitions, ions, and atmospheres according to the physical processes controlling the source

function. Such a classification is essential in idenl

fying those atmospheric parameters about which inform*

tion can be obtained from the analysis of a given spe<

tral line or continuum.

In LTE, the spectroscopic behavior of a small vo. ume element depends only on the local values of tempe:

ature, density, and chemical composition; except for

the effect of electron scattering, it does not depend

on the radiation field. The observed spectrum depend:

only on the distribution of temperature throughout th

atmosphere. Density and composition determine the atr spheric region, hence the range in T^ , that is observ

in the line or continuum of a given ion. Thus for a fixed chemical composition but an unspecified distrib

tion of temperature and density, the relation between

the location of a volume element and its spectroscopi

state is two dimensional. But if to the assumption o LTE, we add the other assumptions of the classical

model, we force both the temperature and density to

decrease monotonically outward. Then the relation

between the position of a volume element and its spec

troscopic state is one dimensional. In this case, a sequence of lines and continua arranged according to

their depth of formation would show a moriotonic chang

in excitation, and conversely.

Without the assumption of LTE, the spectroscopic

behavior of a small volume element depends not only c the local values of the temperature, density, and che

ical composition, but also on the radiation field. Tl

radiation field, in turn, depends on the physical pre

erties of the surrounding atmospheric regions, in par

ticular on the distribution of source and sink terms.

The kind of source and sink terms that control a giveu

line or continuum will depend on the properties of be

a

the ion and the atmosphere. Hence there is no longerla one-to-one correspondence between the excitation of a

100
jine and its depth of formation, nor do the usual cri te- la for excitation level necessarily apply. For examlie, absorption lines with emission cores (collision

'jominated) may arise in the same atmospheric regions as jbsorption lines without emission cores (of which some

jre photoionization dominated) . Thus the apparently

andom behavior of excitation with height - an important feature of the chromospheric anomaly - reflects

imply the dependence of the spectroscopic state of a plume element on its environment and on the ionic con- iguration of the gas. The aim of the new spectroscopy

% to develop systematic methods for introducing order

(here there appeared to be none. We study the apparent

ixcitation level as a function of position in an atmohere in which the distributions of T

e

, n

e

, and chemi1 composition are specified.

We first determine whether there are atmospheric

gions in which collisions dominate over radiative pro- sses in all transitions. If so, these regions are in

E-R. In most stars, any such regions occur only in

e deepest photospheric layers; for some stars, they

y occur throughout most of the photosphere; but they

ver occur in a chromosphere. In those atmospheric

Regions that are not collision dominated, there are,

len, transitions with source functions that depend on

One radiation field in the transition. Thus the distribution functions are coupled to the radiation field,

[Aid it is necessary to specify the details of this couling. These details will depend on whether the atmooheric region produces its own radiation field in the

[Liven transition, i.e. on whether its optical thickness

3 greater or less than about one in the transition,

f less than one, the source function is controlled by

le external radiation field, and we study the region

roducing this field: for example, in all but the Lyman

°2gion, the radiation field in a planetary nebula is

roduced by the central star. If, however, the optical

2pth in the transition is greater than one - as occurs

ften in th.e solar chromosphere and the cores of all

trong lines on the disk - the radiation field is determined by the distribution of source and sink terms.

Ipe aim then is to identify these terms and hence the

:ocesses, collisional or radiative, that fix them for

lae particular transition in a given atmosphere.

Since, in general, the ion must be treated as a lole, and since the source and sink terms for its var3us lines and continua may be coupled, it is often difficult to isolate individual processes. To use a line

fe a diagnostic tool for the atmosphere, we must obtain

Lther an algebraic expression for the source and sink

101
terms or a sufficient number of numerical solutions to

distinguish the significant processes in fixing these

terms. Many "devices" such as the equivalent two -level

atom (Thomas and Athay 1961) have been introduced to

facilitate the algebraic approach, but whichever

approach is used, the formulation in terms of source

and sink terms enables us to place collision-controlled

source functions, photoionization-controlled source

functions, and various mixtures of the two all in the same framework. In the solar atmosphere, the prototypes of these three kinds of source functions are,

respectively, the Ca II lines, the Balmer lines, and

the Lyman lines . In other atmospheres , the behavior

can be quite different. The prototypes have, however,

enabled us to check the general structure of the theor

and to verify, theoretically and empirically, the inf1? ence of the four boundary effects on the microscopic s processes

Thus the new spectroscopy tells us what governs

the partition of energy and hence the type of spectrum

for a given atmosphere. But to study the detailed varl*

ation in the behavior of the lines and continua across

the spectral sequence, we need to know the distributic;

of state parameters in each class of atmosphere. The

purpose of analyzing the observations is not to determine the partition of energy in a prescribed atmospheij,

but to determine the properties of the atmosphere simultaneously with the partition. The development of

methods, to do this without preconditioning the result j has followed two lines: one empirical, exemplified by j the analysis of solar eclipse data; the other theoretic

cal.

(b) An empirical approach to state parameters . This is an extension of Menzel's approach to a quantiijtive analysis of the solar chromosphere from eclipse j observations of the hydrogen lines and continua. The

j aim is to obtain an empirical distribution of electro:;

temperature, density (which is essentially the hydrogiji

concentration) , ionization, and excitation, and thus p infer the energy input, momentum input, and partition!

of energy. In order to do this, we require the distributions of Tg, n

H , ne , np

, and bj for all energy leve is j. Observations in two continua plus lines, a knowl-j

edge of the relative abundances of metals to hydrogen

and a theory for b 1 and b 2 of hydrogen make the probl

determinate. In constructing an applicable theory, i is essential that the expressions for b 1 and b 2 be inJs- pendent of any assumptions on the input of momentum | and energy and that they include all relevant radiatin ; fields, which in practice means the Lyman, Balmer, arj

10 2
^aschen continua and H . The chromosphere is transparent in the Balmer and Paschen continua, but the transfer problem in the Balmer lines and in the Lyman continuum must be included. This treatment showed for the

first time the effect of this coupled transfer solution

jpn b x and h 2r hence on the empirical determinations of

|Ee

. The model obtained from this analysis is included

In Figures 1, 2, and 3.

The conclusions of the 1961 analysis most relevant

to this paper are as follows: (1) Because the values

pf Te , b 1

, b 2

, and the Lyman continuum radiation are

jstrongly coupled, each depending on an analysis of the

atmosphere as a whole, the coupling in the tests for

radiative equilibrium and LTE-R stand out. Departures

from radiative equilibrium occur as low as 500 km

(below this height the temperature distribution is not

sufficiently reliable for us to draw definite conclusions) . Departures from LTE-R occur in all the

observed regions. (2) The physical reliability of the

results is confirmed by comparison with independent

lata. The intensity of the Lyman continuum predicted

from the empirical model is within a factor of two of

the observed value. He I and He II lines are observed

just where the model shows a steep rise in Te to some

value exceeding 10,000°K. (3) The analysis breaks down

at the start of this abrupt -rise in T

e

. Empirically,

Ijfthe combined He I and Balmer continua require a geometrically inhomogeneous structure in the region where

He I appears. Theoretically, the assumption of

detailed balance in the Lyman lines is questionable in

the same region. These conclusions on the Lyman continuum have been confirmed recently by Noyes and Kalkofen

M1970) who used data in the rocket UV. By treating the

Lyman lines and some lines of C II, Avrett, Vernazza,

iand Chipman (19 70) have re-examined and improved the

theory in the region of the steep rise in T^.

The Standard Reference Models included 'in Figures

1, 2, and 3 are an amusing contrast to our empirical

nodel. No account has been taken of eclipse data. The

assumption of hydrostatic equilibrium has been applied

>to what appears to be a freehand extrapolation of T e

(h)

in the region t

5 < 0.05. Non-LTE effects have been

either neglected entirely or included in a patchwork,

t non-consistent fashion. The original justification for

constructing such models was that a standard model

tfould provide a means whereby various theories of line

formation could be compared. However, it was perhaps

^inevitable that once published, these models were

accepted as valid representations of the Sun. The con- struction of numerically accurate but physically incon103
sistent models is in direct contrast to the approach of

the Menzel school. It is interesting that these refer- ence models appear to be approaching the 1961 model,

which, while it will certainly be modified in detail,

seems to be holding up quite well.

Co) A theoretical approach to state parameters

population and trans fer effects. The new spectroscopy

gives the spectroscopic state of a small element of gas

for a given distribution of state parameters. An empir

ical analysis, such as that described in the previous

section, suggests how we might obtain these distributions when we have the range of observations available

for the Sun. The question remains of how to obtain

them under less favorable conditions. With the exception of certain eclipsing systems, this must be done

theoretically.

The values of the state parameters are in general

fixed by a combination of transfer processes and local

interactions. A solution of the transfer problem

throughout the atmosphere provides a value for the

transfer quantity at a point, e.g. the energy in the

radiation or velocity field; the interaction with the

local population of energy levels gives a value for the

energy absorbed. Interactions among the energy levels

determine the final partition of this absorbed energy.

Although these steps are coupled, we can obtain a clearer physical picture by isolating the physical pro

cesses and quantities that determine the character of

each step. For example, for a grey atmosphere in LTEand radiative equilibrium, Jv is determined by the dis

tribution of Te. To a first approximation, Te is fixe

by the local value of the integrated Jv

. Thus Jv is

coupled to tne distribution of Te

, but neither Te nor

J v is coupled to the v-dependence of J.

We attempt to isolate the above steps by separating what we call population and transfer effects.

Thus far we have applied our formulation only to the

determination of Te

. In doing so, we have distinguished between changes in the local value of Te due t< changes in the energy supply, which we call transfer

effects, and changes in the value of Te due to changes

in the relative importance of the microscopic processe:

fixing the populations, which we call population

effects. For radiative equilibrium and a one-level

atom, we have expressed the kinetic energy of the phot'

recombining electrons, which depends on Te alone, as the product of two factors: (1) the rate at which

energy is supplied to the electron continuum per photo

ionized electron, and (2) the number of photoioniza- 1 tions per recombination. The first factor depends on

10 4
I the energy transferred and controls the transfer

jeffects; the second depends on the populations and conjtrols the population effects. It is the behavior of

Ithe population factor that determines the explicit

dependence of Te on the process determining the ionization equilibrium. For this reason we have called it

|the temperature control bracket. For a multilevel atom,

iwe take the weighted average of the photoionized and

photorecombined electrons in each continuum. The

weighting factor is the product of the temperature control bracket and the relative numbers of photorecombinajtions or ph_otoionizations in each continuum. Thus far,

| the applications of this approach have been only exploratory. We believe, however, that it will give the same

'physical insight into those factors that determine the

values of the state parameters as the new spectroscopy

jgave into identifying types of observed line profiles

with classes of source and sink terms.

The interpretation of the solar chromosphere anom-

'aly in terms of the physical processes associated with

m transition region suggests that the conclusions of

ijsection II on atmospheric structure and diagnostics are

not peculiarly solar but relate more generally to stellular atmospheres. These conclusions may be summarized

las follows, corresponding roughly to the classes of

.'observed chromospheric anomalies. (1) The observed

disk spectrum is formed in an atmospheric region that

extends to far greater heights than that predicted by

the classical model, which represents at most the deepest layers of the atmosphere. (2) The major contrast

between the spectrum predicted by our method and that

by the classical approach is that our method predicts a non-uniform variation of excitation with height in the

atmosphere. This corresponds on the one hand to a [diversity in the types of source functions, which is

associated with differing source and sink terms, and on

: the other hand to the diversity in non-radiative energy

TOupplies and departures from hydrostatic equilibrium

and spherical symmetry. (3) To understand the complete

Iptructure of this extended region, it is necessary to

'allow for departures from all the classical assumptions

successively with increasing height. The details can pe expressed in terms of population and transfer

C

' effects: the former is associated with departures from

ijLTE-R near the boundary, the latter with the production

III. A GENERAL STELLAR MODEL

105
of a chromosphere. (4) The initiation of any horizontal inhomogeneities by atmospheric instabilities introduces the possibility that any effect associated with aj

variation in height may also occur in the horizontal

direction.

We suggest that just as with the Sun, what appears

to be anomalous in stellar spectra is actually the key

to the structure of the atmosphere. "Peculiar" spectra are then seen to indicate not something out of the ordi

nary but simply accentuated features of atmospheric

structure common to all stars. The extreme peculiar

spectra, known as "symbiotic", represent an enhancemenl

of the same combination of high and low excitation

effects already encountered in the solar chromosphere.

This suggestion again reflects an early idea of

Menzel's, which has been overlooked in recent years.

The details of his idea differ from ours, but the basi<

physical point is the same.

A. Menzel on Symbiotic Stars

'lX |

* Symbiotic stars are those whose spectra include

both high and low excitation lines and continua. Many

years ago, a number of people, including Menzel, suggested that the obvious interpretation was in terms of

binary stars, one hot, one cool. Subsequently Menzel

modified this picture by suggesting that such stars

were not in fact binaries but single stars divided int

two regions: a central, hot nucleus surrounded by an extended, cool atmosphere supported by a combination c radiation pressure, turbulence, and stellar rotation.

If the atmosphere were optically thin, the photosphere

j

would be formed close to the hot nucleus, and we mighii

observe a Wolf-Rayet type spectrum. If, on the other

hand, the atmosphere were optically thick, the photosphere would be formed near the outer boundary, and t] continuum would mimic that of a red giant. He elaborated this model to suggest that a single rotating stt

could produce both a hot and a cool continuum. The

equatorial regions of the atmosphere, distended by rojition, would be optically thick, so the photosphere

would be formed in the outer, cooler regions, whereas I the polar regions would be optically thin, so one wou

see the hot continuum characteristic of the stellar

nucleus

We suggest that Menzel was correct in attributing

symbiotic spectra to a single star rather than a multjr

pie system. We would, however, alter the details of

his model and greatly extend the number of stars to

which it applies. Our picture is the following: All

106
stars are symbiotic, the differences being only a matter of degree, reflecting the relative importance of

the classical and non-classical regions of the atmosphere in producing the observed spectrum. The symbiotic properties arise in two ways. In stars without

^transfer effects, and therefore without chromospheres,

they originate in population effects. In this case,

the high and low excitation lines cannot be associated

with any distinct regions. In stars with transfer

effects, and thus with chromospheres, there will be a height asymmetry in ionization, which will, in fact, be

the reverse of that suggested by Menzel but in the

direction of that suggested by one of us for Wolf-Rayet

stars (Thomas 19 50) and by Mrs. Payne-Gaposchkin for

the Sun (1956 unpublished). You will recall her remark

that on the basis of rocket UV spectra alone, she would

classify the Sun as a WC6 star, a remark that suggested

a similarity in the origin of the two spectra. Thus

from disk observations, at least one star, the Sun,

appears to be a cool star as seen in the visual spectrum, which originates in the lower atmospheric regions,

and a hot star as seen in the UV, which originates in

'the upper regions. The principle is the same as Menzel' s: symbiosis reflecting the schizophrenia of a single star. The reversal of the hot and cold regions

,comes from experience with Menzel ' s favorite star, the

Sun, and follows the direction that he himself took in

exploring the He I and He II anomaly. He can hardly

object to this change in detail.

B. A General Stellar Atmosphere

In the deepest layers of the atmosphere, we have a region represented by the classical model. Here LTE-R

'.is established by the predominance of collisions over

every other kind of excitation process. The source

function is fixed by Te

, which is in turn fixed by

either radiative or quasi-static convective energy

transport. As we move higher in the atmosphere, colli-

,jSional processes decrease relative to radiative, and

I eventually we reach a point where radiative processes

dominate. Here we may still have LTE-R in limited spectral regions provided the important radiative processes

-maintain a homogeneous radiation field. Effectively

I this means that no radiation can be observed in these

"transitions, but other transitions, to which these are

coupled, can be observed. On this basis, we impose conditions on the maximum value of T e and the minimum value of density, hence of gravity and momentum supply,

107
for the existence of an observable LTE-R region (Gebbii

and Thomas 1971). It cannot be assumed a priori, however, that this region represented by the classical

model can in fact be observed.

Above the region represented by the classical

model, we must allow for departures from any or all th

classical assumptions. Whether departures from LTE-R

occur can be computed in terms of density and optical

depth, if we know the distribution of state parameters

Thus, as we have stressed, we must investigate both po

ulation and transfer effects, either empirically or theoretically or both. In one atmosphere, we may have

only population effects; that is, we may have departures from LTE while the other classical assumptions

remain valid. In another atmosphere, with transfer 1

effects , several of the assumptions may break down

simultaneous ly

If in the region above that described by the clas

sical model, there are only population effects, we ca]

it a non-classical photosphere. Here Te may rise to some maximum value limited by the value of Te ff. The

possible presence of several kinds of source and sink

terms may give rise to the apparent anomalies in excitjtion reflected in the disk spectra.

If, on the other hand, this region has both popu];-

tion and transfer effects, we call it a chromosphere.

(We do not distinguish between a chromosphere and core na.) Here Te will rise to a value limited only by the

input of non-radiative energy. Our understanding of

this process is not yet sufficient to predict this ma:imum value of Te in terms of the observed characteristics of a star. Thus the chromosphere is characteriz<|

by the presence of transfer effects, of dTe /dh > 0, ail. of T

e > Teff

We now consider how we might establish at least

the existence of a chromosphere from the observations

From the continuum formed in the deepest atmospheric

levels, we can try to fix the general excitation level

of the spectrum. This corresponds roughly to the effftive temperature of the classical model. We then try

to estimate the variation of excitation level with

height using as our criteria the diversity of the spe -. tra. If this excitation level exceeds that of the

limit set by population effects alone, we conclude thjt

transfer effects are contributing and that we have a \ stellar chromosphere.

For example, from the visual continuum of the Su,|#

we obtain an excitation level of about 5800 °K for the

regions represented by the classical model. Moving c It- ward through the regions in LTE-R, T e decreases to scjs10 8
ling less than 4700°K - current estimates favor a val3 of about 4300 °K. In the non-LTE regions, population

ffects could raise Te to 5300 - 5500°K in radiative

^uilibrium (Gebbie and Thomas 1970) . The observation

f He I in the disk spectrum by itself suggests an exciation level close to 10,000°K. The central emission

ores of Ca+ H and K tend to confirm that the excitaion level rises above the limit set by population

ffects alone. The rocket UV and radio spectra also

jpport this conclusion. Thus from disk spectra alone,

2 infer the presence of transfer effects and hence of

chromosphere. Until we obtain a satisfactory treatment of the aerodynamic problem, we must, of course,

j^termine the final model empirically.

Another example is the Wolf-Rayet stars. From the

Lsual continuum alone, we infer an excitation level of

bme 40,000°K, give or take 10,000°K. Yet from the

Lne spectrum in the visual region, we infer excitation

Snditions corresponding to some 200, 000 °K. Again we

lifer the presence of transfer effects and a chromo-

! ohere.

These examples can be extended to other stars as

»11 as various stages of novae and binary systems consisting of an extended supergiant and a small hot com-

' anion. We believe this provides a picture of how

snzel's original ideas on the solar chromosphere, flavored by suggestions on symbiotic spectra and passed

-irough the strainer of non-LTE diagnostics, have led

3 suggestions for a general model for a stellar atmoDhere.

ACKNOWLEDGMENT

We are indebted to J-C. Pecker for continuous

interchanges on the ideas in this paper and to Alice

svine for valuable advice on the expression of them

BIBLIOGRAPHY

If thay, R.G., Billings, D.E., Evans, J.W. and Roberts,

W.O. 1954, Ap. J. , 120_, 94.

thay, R.G. and Menzel, D.H. 1956, Ap . J., 123 , 285.

vrett, E.H., Vernazza, J. and Chipman , E. 1970, presented at the "Second Workshop on Orbiting Solar

109
Observatories" at Goddard Space Flight Center,

December 2-4, 19 70 as reported in Sky and Talescope, 4JL, 268, 1971.

Bilderberg Continuum Atmosphere, Gingerich, O. and

de Jager, C. 1968 , Solar Physics, 3_, 5.

Bilderberg Continuum Atmosphere, Revised, Gingerich 0.

1969, as reported at AAS Solar Physics Meeting,

Pasadena.

Cayrel, R. 1963, C. R. , 2jT7, 3309 . Cillie, G.G. and Menzel, D.H. 1935, Harvard Observatory

Circular No. 410.

Dunn, R.B. 19 60, Thesis, Harvard.

Edlen, B . 1942, Zs. f. Ap . , 22, 30.

Evans, J.W. , Roberts, W.O. and Thomas, R.N. 1950-51,

unpublished planning documents for HAO 19 52

eclipse expedition.

Gebbie, K.B. and Thomas, R.N. 1970, Ap . J., 161, 229.

Gebbie, K.B. and Thomas, R.N. 19 71, Ap . J. , m press.

Goldberg, L. and Menzel, D.H. 19 48, Harvard Observator

Monograph, No. 7.

Harvard Smithsonian Reference Photosphere, Gingerich,

O., Noyes, R.W., Kalkofen, W. and Cuny, Y. 1971,

Solar Physics, submitted.

Henze, W. 196 8, Thesis, University of Colorado.

House, L.L. 1961, Thesis, University of Colorado.

Jefferies, J.T. 1968 , Spectral Line Formation (Walthair

Massachusetts: Blaisdell Publishing Company).

Jefferies, J.T. and Thomas, R.N. 1959 et seq. , The

Source Function in a Bon-Equilibrium Atmosphere

(series) , Ap . J. , 129 , 401, et seq.

Linsky, J.L. and Avrett, E.H. 1970 , P.A.S.P., 82,, 169

Menzel, D.H. 1931, Pub. Lick Obs. , 11_, Part 1.

Menzel, D.H. 1937 et seq., Physical Processes in

Gaseous Nebulae (series) , Ap . J. , 8_5, et seq. , 3 Menzel, D.H. 1947, A. Cressy Morrison Prize I, New Yoi

Academy of Sciences.

Mihalas, D. 1970, Stellar Atmospheres (San Francisco:

VI. H. Freeman and Company) . Noyes, R.W. and Kalkofen, W. 1970, Solar Physics, 15 , 120.

Pottasch, S.R. and Thomas, R.N. 1959, Ap . J., 130, 94

Pottasch, S.R. and Thomas, R.N. 1960, Ap . J . , 122, 19

Roberts, W.O. 1945, Ap . J., 101, 136.

Thomas, R.N. 1948 et seq., Superthermic Phenomena in

Stellar Atmosphere (series), Ap . J., 108 , 130, e seq.

Thomas, R.N. 1949 , Ap . J., 109_, 480 . Thomas, R.N. 1951 et seq., Thermodynamic Structure of

the Outer Solar Atmosphere (series) , Ap . J. , 111

165, et seq.

110
Thomas, R.N. 1957, Ap . J., 125. , 260.

Thomas, R.N. and Athay, R.G. 1961, Physios of the

Chromosphere (New York: Interscience Publishers)

.

Thomas, R.N. 1965, Non-Equilibrium Thermodynamics in

the Presence of a Radiation Field (Boulder: University of Colorado Press)

.

Utrecht Reference Photosphere, Heintze, J.R.W., Hubenet,

H. and de Jager, C. 1964, B.A.N. , 17, 442.
THE CORONA

J. B. Zirker

Hawaii Institute of Geophysics

University of Hawaii

INTRODUCTION

This paper discusses some recent trends in the

study of the solar corona. Progress in this field has

been accelerating steadily during the past decade,

partly as a result of new observations (especially in

the EUV and XUV) and partly because of improved understanding of coronal atomic processes. Rather than try

to review the literature exhaustively, a task beyond

the scope of this short work, I have selected three

topics that illustrate current interests in the quiet

corona. They are: the relation of coronal forms to

the magnetic field, the physical state of the gas, and

the mass (and energy) balance.

These topics form a chain of successively higher

abstractions: it is natural to begin to study the

solar atmosphere by describing its structures and their

evolution; later one is concerned with a quantitative

interpretation of its radiation, and this leads to the

determination of gas density, temperature, and composition. Later still, we seek an understanding of the

phenomena in terms of basic transport processes. In a more rational world, the development of coronal physics

might have followed this simple linear progression. In

fact, each area of study (form, constitution, and process) is under active investigation today, and our knowledge of them will advance rapidly in the next few

years

FORM

Solar astronomers have suspected for many years

that coronal forms arise from the interaction of the

coronal magnetic field and the electrically conducting j gas. The idea occurred to the earliest eclipse

112
pservers who interpreted polar plumes as evidence of a ^neral dipole magnetic field. Trajectories of falling

Itrominence material (McMath, Menzel, Dunn, Roberts, and

Drral) suggested the influence of a guiding magnetic

lield over active regions. Arches and rays, visible in

he forbidden iron line A5303 in coronal enhancements,

suggested tubes of magnetic flux outlined by the gas

jLyot, Dunn, Dollfus) . The similarity between the

igration patterns through the sunspot cycle of largepale photospheric magnetic field regions (studied

rincipally by the Mt. Wilson group) , prominence fi laants , and coronal streamers, is indirect evidence for

he close association of forms and fields. The idea is

srtainly plausible and is widely accepted but has not,

ptil recently, been tested.

Unfortunately, direct measurements of coronal magjstic fields are few and rough: some of the best estimates come from radio observations of very low spatial

^solution (Newkirk 1967). It is important, therefore,

|D try to use photospheric magnetic field measurements

0 estimate at least the direction of coronal fields.

H. U. Schmidt (1964) devised a numerical technique

pplicable to this and other problems. He showed how

b calculate a potential field above a surface on which

be normal field component is known. Newkirk and

ltschuler have extended the Schmidt method to magnetic

ibservations covering the whole disk. They have comared (1970) white-light observations of large-scale

pronal structures with calculated magnetic field lines.

In general, the correspondence between field lines

id coronal forms is good. Helmet streamers appear

/er "magnetic arcades" that link bipolar magnetic

°2gions. Coronal condensations apparently coincide

jlth open-field configurations. Filaments separate

jleld regions of opposite polarity. Polar plumes, as fqpected, coincide with open-field lines. The potential field approximation is evidently sufficient to

utline the gross features of the corona, even though

t is based upon observations averaged over a month.

To my knowledge, no one has applied the potential

Leld method for a comparison with smaller features of

ie corona, such as the arches and rays visible in

Dronal enhancements. Dunn (1971), who has summarized

1 decade of coronal green line observations of enhancesnts, has drawn attention to the importance of the

potpoints of individual arches. Presumably, some fecial physical property distinguishes footpoints of

lluminated arches. An extension of Newkirk and

iltschuler' s work to these arches may help to isolate

fie footpoints in the chromosphere.

113
D. Rust (19 70) has carried out this kind of com- parison for a loop-prominence system. Individual loops can be identified with individual flux tubes. However,

it has not been explained why only certain tubes in the

field radiate strongly.

Applications of this method to coronal active

regions can lead to a useful unraveling of their interior structure, provided the potential field approximation is valid there. Figure 1 shows one of the remarkable X-ray photographs of the corona obtained by the

American Science and Engineering (ASE) group with a rocket-borne grating-incidence telescope. Active

regions seem to consist of a tight, sharply defined,

hot core and a cooler halo, as viewed in 10 A to 60 A.

Occasionally, arches that connect distant active

regions are visible in the X-ray photographs. Other Xray structures, so far not identified with chromospheric features, are also present in the quiet corona. Comparisons of these forms with the computed field

lines should help to elucidate both.

Up to the present time, observations of largescale structures in white light have been limited

mainly to occasional glimpses during solar eclipses,

with supplementary limb data of limited radial extent

coming from ground-based K-Coronameter observations.

As a result, we probably know more about the evolution

of these coronal structures on a time-scale comparable

with the solar cycle than over a period of a month.

Similarly, although active regions in the corona have

been followed by a succession of Orbiting Solar Observe

tory (OSO) experiments in the EUV and XUV, these observations have generally lacked the spatial resolution t< permit a detailed comparison with the magnetic field.

These limitations may soon be relieved by experiments

to be flown on OSO-H and the Apollo Telescope Mount

mission. The latter, in particular, includes an externally occulted coronagraph (the High Altitude

Observatory experiment) capable of following the evolu

tion of coronal streamers throughout a month or more;

the ASE group will fly a grazing incidence telescope,

which will record the structure and evolution of the

corona over the disk with 5 arc-second resolution. We

may expect fruitful comparisons of these new data with

further magnetic field calculations.

Hopefully, it will be possible in the near future

to measure, rather than calculate, coronal magnetic

fields. A Babcock type of magnetograph at the High

Altitude Observatory has detected circular polarizatio

in the coronal green line (Harvey 196 8) but with low

signal to noise ratio. More sensitive coronal polarin1

114
'Figure 1 . The corona on March 7 , 19 70 . The large

panel is a composite, showing the white-light corona at

jthe limb (photographed by the High Altitude Observatory

expedition) and the x-ray corona on the disk (photographed by the American Science and Engineering group)

.

115
eters are now under development at the High Altitude

Observatory and the University of Hawaii, and one is in use at the Pic Du Midi Observatory (Charvin 1970)

„

PHYSICAL CONSTITUTION

The determination of the physical state of the

coronal gas has been a long-standing objective of solar

astronomers. We wish to find the distribution of temperature, density, composition and, if possible,

velocity and magnetic field. To this end, observations

covering the entire electromagnetic spectrum have been

gathered and analyzed. Unfortunately, the corona is

optically thin throughout much of its spectrum (even in

the permitted lines) so that the distribution of physical parameters along a line of siaht is difficult to

find.

In the past, some investigators have met this difficulty by constructing non-geometric models to represent their observations. For example, we show in

Figure 2 the distribution of emission measure

[/n| dV] with coronal temperature in an active region,

as determined from XUV line spectra by Batstone et al.

(1970) . Their observations have low spatial resolution

a limitation that, coupled with the low intrinsic

opacity of the gas, permits them only to find the

amount of material at each of several discrete temperatures . This type of representation, originally applied by

Pottasch (1964) , has been extended by Athay (1966) and

Dupree and Goldberg (196 7) to observations of permitted

lines arising in the quiet corona within the temperature range 10 5 - 10 6o K.

If the corona is assumed to be spherically symmetric and isobaric, the emission measure versus tempeij

ature distribution can be interpreted as a height distribution of temperature (or density) . The resulting

temperature distribution is nearly discontinuous, suggesting the concept of an interface between the chromosphere and corona. Moreover, the inferred temperature

gradient is consistent with a constant downward flux of

heat, conducted from corona to the chromosphere. The

assumption of constant heat flux has been incorporated

in subsequent models of coronal active regions (Noyes

et al. 1970)

Alternatively, some assumption of geometrical

symmetry can be introduced to interpret observations 1 from an active region. Figure 3 shows the hemispheri116
ATe

47 -3 (units of 10 cm )

7

Te (units of 10 K)

7 igure 2. The distribution of emission measure as a function of temperature in a coronal active region

fBatstone et al. 1970).

2^.5-3 A source

$$$$$ 1-8 A source 8-20 A source

photosphere

3' 2' r

0' r

2' figure 3. Model for a coronal active region, based

pon XUV fluxes (Landini and Monsignori-Fossi 19 71)

117
cal model suggested by Landini and Monsignori-Fossi

(19 71) to represent their XUV fluxes. Note that high

temperature and high density are associated in this

model. Similar results have been found from EUV observations by Boardman and Billings (1969)

High resolution filtergrams in the visible or XUV

show, however, that the active corona, at any rate, is

asymmetrical and inhomogeneous : arches , loops , rays

,

and filamentary structure abound in enhancements. As

the spatial resolution of spectroscopic observation

improves, it will become feasible to isolate individual

fine structure against the sky or the disk, and to

apply more directly analyses like the previous ones. Recently, intensive efforts have been made to find

and apply diagnostic methods specifically designed to

determine the local value of electron density and temperature. These methods generally rely on line ratios

from a single ion or related ions. One method that

initially yielded useful results was devised by Gabriel

and Jordan (1969) . For ions in the helium iso-electronic sequence, they showed that the ratio of the forbidden ( 3 S -

1 S) to inter-combination ( 3 P -

1 S) line

intensities is sensitive to electron density. Table 1

shows the results found by Rugge and Walker (19 70) when

they applied the method of Gabriel and Jordan to their

XUV spectra of active regions. Very high densities are predicted by this method, the density increasing, more

over with the electron temperature of the region.

These preliminary results have been modified by a subsequent redetermination of the lifetime of the 3 S state

TABLE 1

LINE RATIOS AND PREDICTED DENSITIES

20 MARCH 1969

Ion

Approx. temp,

of line

formation 10 Go K

0604 UT

N

e (cm" 3

) 0 VII

Ne IX

Al XII

Si XIII

S XV

1.8

3.5

7.3

8.9

12.2

2 x 10 8 1.5 x 10 10 2 x 10 11 3.5 x 10 11

4 x 10 12

From H.R. Rugge and A. B.C. Walker, 1970, Astron. and

Ap, , 5, 4.

118
Dupree (1971) has developed a similar diagnostic

for electron density, using the lines from berylliumlike ions (CIII, OV) which appear in the spectrum of

the temperature transition region

10 5 < T < 2.5 x 10 5o K . The intensity ratio of the 3 P -

3 S line and the *P -

1 S line is moderately sensitive to electron density.

Typical electron densities inferred from 0S0 IV and 0S0

VI data are 10 10 cm" 3 for quiet regions, 10 11 cm

-

3

for

active regions, and 5 * lO^cm-3 in a flare.

The optical forbidden lines can also be analyzed

in this fashion. Figure 4 shows the variation of

selected line ratios with electron density (Zirker

1970) . Each pair of lines arises from transitions

within the ground configuration of a particular ion,

which is labeled on the curve. Each of the ions shown

is abundant over only a limited range of temperature.

Fe XI is present mainly between 1.2 and 1.7 x lo 6o K,

and Ni XV between 2.2 and 10 6o K. Thus it is possible

to determine from a line ratio the electron density of

material that lies within a narrow temperature range in

the line of sight. Fisher (1971) has applied this

technique to the study of a coronal enhancement

observed with the coronagraph in Hawaii. Figure 5 shows the derived density at two temperatures, as a function of position across the enhancement. Jefferies,

Orrall and Zirker (1971) have developed a general formulation of the method and applied it to eclipse observations of coronal enhancements.

In order to find suitable diagnostic methods,

reliable calculations for the excitation and ionization

equilibrium of a wide variety of coronal ions are required. These, in turn, rest ultimately on a knowledge of atomic transition rates and collision cross

sections. The latter, particularly, are still very

sparse. Considering the effort (and expense) invested

in obtaining adequate observations, especially from

satellites, it is unfortunate that so little effort is

expended in calculating atomic parameters.

A series of satellite experiments, to be flown in

the near future, should provide new and excellent spectroscopic data for the determination of coronal models.

Among these we might mention the Harvard and Naval

Research Laboratory instruments on board ATM and the

Goddard spectrometer on OSO-H. The interface with the

chromosphere will be studied by the High Altitude

Observatory and Paris experiments on OSO-I. Intens

119
Figure 4. Electron density variation of optical forbidden line ratios (Zirker 19 70)

120
12

10

ro'eo

00O

X

A

0>

- T = 2.3xl0 6o K

(NiXff)

2 -

T= I.8XI0 6 °K

(Fe XIE)

80° 83° 86° 89° 92° 95° 98°

RA.

02° I05 <

?igure 5, Electron density in a coronal enhancement

as determined from optical forbidden line ratios

[Fisher 1971)

.

if forts to observe coronal regions on the limb will

:ontinue at several ground-based observatories.

MASS AND ENERGY BALANCE

One of the ultimate objectives of coronal research

s to understand how the observable atmospheric phenomena arise from the transport of mass and energy. The

'asic ideas in the theory of the coronal energy balance

ave been recognized for over 30 years; however, the

etails have changed continuously. Heating is thought

o accompany the dissipation of some form of mechanical

ave energy that propagates out of the solar convective

one. Cooling occurs by the combined effects of radiaion, heat conduction and convection (i.e. in the solar

ind) .

121
-4-2

Log (R/R -1)

0+2

Figure 6. Height variation of different energy densities in a spherical, shock-heated corona (Kopp 1967)

One of the main uncertainties is the type of wave

motion responsible for the heating. Sound (or shock)

waves have been examined most thoroughly. Figure 6 shows some results drawn from R. Kopp's thesis (1967),

122
in which the equilibrium of a spherically-symmetric

corona, heated by shock waves, is considered. The fig- ure shows the height variation of the different types

of energy present. Kopp's models predict very reasonable values for the maximum coronal temperature and the

radial distribution of density, although only three

free parameters (shown at the top of the figure) determine a model.

•Pneuman and Kopp (19 70) have recently considered

the equilibrium of a helmet streamer, taking into

account the pressure due to its magnetic field. Few

observations are available to check the model, but it

predicts a reasonable density enhancement of the

streamer with respect to its surroundings.

Such models certainly reproduce the main characteristics of the observable corona. However, they

give a poor description of the phenomena at the temperature transition zone. Moreover, they ignore the

internal circulation of gas within the corona and con- sider only the net flow that escapes in the solar wind.

More complete models are needed, but can only be

attempted after a number of questions are settled obser

vationally

.

For example, Athay (19 71) has pointed out that the

"observed" downward heat flux from the corona is too

large to be dissipated by radiation in the chromosphere

even though the latter radiates at maximum efficiency.

Kuperus and Athay (196 7) have suggested that a fraction

of the corona heat flux is absorbed in the generation

of macroscopic gas motions within the temperature

interface. They ask whether chromospheric spicules are produced as a consequence of this coupling of the heat

flux and gas motion.

Kopp and Kuperus (196 8) have developed ideas along

the same lines. They also seek to balance the observed

radiative and heat flux terms in the interface. They

postulate a plausible two-dimensional distribution of

magnetic field, which, at chromospheric levels is con- centrated mainly on the borders of the supergranulation

cells, but at coronal heights is approximately uniform

and radial. Such a field would channel a sizeable

fraction of the downward heat flux into the borders,

where it presumably drives macroscopic motions and is

lost eventually in some (unexplained) radiative processes. Most of the observed radiation from the interface would arise from the regions overlying the interiors of the supergranulation cells, where the temperature gradient is less precipitous.

At the moment, then, the sinks of coronal energy

in the chromosphere have not been identified observa123
OUTER

CORONA

INNER

CORONA

CHROMOSPHERE

Figure 7. Elements in the mass balance of the corona

(schematic)

tionally, although reasonable possibilities have been

suggested. Moreover, a variety of wave motions (slow

mode, Alfven, fast mode, ion-cyclotron and gravity)

still remain as plausible means for transferring energy

upward. Critical observations could help to sort out

the possibilities.

The sources and sinks of coronal mass are also

uncertain. Figure 7 is a sketch illustrating our ignorance. The numbers attached to the different solar

features represent total mass fluxes (over the whole

Sun). For example, the upward motion of spicules (far

left) represents a mass flux of order 10 1 k g/sec.

Only 1% of this flux is required to balance the

eventual losses from the Sun in the solar wind

(10 12 g/sec). However, appreciable mass transfer may

also occur at the interface away from spicules; for

example, Howard (19 71) has detected coherent downward

motion in regions with dimensions of the order of a solar radius.

Mass flow within a helmet streamer prominence

(center of Figure 7) can only be estimated crudely from

solar wind observations near the Earth. Solar wind

models (such as that of Pneuman and Kopp 1970) indicate

that the net outward flux of mass might be very difficult to detect in the inner portions of the streamer:

hydrostatic equilibrium seems to prevail to a good

approximation, and only at several radii does the wind

velocity reach the sonic point. However, these calculations are based on a rather simple model for the way

in which the base of the streamer is heated and on the

124
^sumption that interstreamer magnetic fields exceed

le streamer field strength. Conceivably, the actual

aservational situation may be more favorable than imiied by these models.

Clearly, to make further headway with the study of

ike corona's mass and energy balance, better observa-

_ons are required. Velocity and density must be

apped in the coronal interface with a spatial resolu-

_on sufficient to resolve at least the supergranula-

_on boundaries and preferably individual spicules.

ie High Altitude Observatory and University of Paris

{periments planned for OSO-I are designed to attack

:-iis problem. The flux of heat conducted downward must

i mapped in two dimensions over the solar surface and

referably in height. This will require a determina-

_on of the vector gradient of temperature - no small

^servational problem. Possibly the Harvard experiment

Doard the ATM will supply some of this data. Tran-

.ents in velocity, density or temperature, if detect3le, could provide evidence on the types of waves that

arry mechanical energy into the corona. The equilibLum of the corona in open and closed magnetic field

?gions needs to be compared. Mass fluxes through quiscent prominences need to be better defined since they

ay constitute an important internal cycle of coronal

ass. In summary, we have seen that an important trend

a coronal research today is to combine diverse obserations from the entire electromagnetic spectrum in

:der to attack a few major questions. Within the near

ature, new coordinated observations can be made that

111 bear directly on the solution of these major

roblems

.

REFERENCES

11thay, R.G. 1966 , Ap . J., 14_5, 784.

5thay, R.G. 1971 in Physios of the Solar Corona, ed.

C. Macris (Dordrecht, Holland: Reidel Publishing

Co. ) . atstone, R.M. , Evans, K. , Parkinson, J.H. and Pounds,

K.A. 1970, Solar Physios, 13, 387.

oardman, W.J. and Billings, D. 1969, Ap. J., 15£, 731.

harvin, P. 1970, paper given at IAU Symposium 43 on Solar Magnetic Fields, Paris, France.

125
Dunn, R.B. 1971, in Physios of the Solar Corona, ed.

C. Maoris (Dordrecht, Holland: Reidel Publishing

Co.) . Dupree, A. 1971, paper given at AAS Meeting Nov. 17-19

19 71, Huntsville, Alabama.

Dupree, A. and Goldberg, L. 1967, Solar Physios, 1, 22

Fisher, R.R. 1971, Solar Physics, in press.

Gabriel, A. and Jordan, C. 1969, M.N.R.A.S., 145, 241.

Harvey, J. 1968, Astron. J. , 7_3, S 63.

Howard, R. 1971, Solar Physios, 16, 21.

Jefferies, J.T. , Orrall, F.Q., and Zirker, J.B. 1971,

paper submitted to Solar Physios.

Kopp, R. 1967, Doctoral dissertation, Harvard University.

Kopp, R. and Kuperus , M. 1968 , Solar Physios, _4, 212.

Kuperus , M. and Athay, R.G. 196*7, Solar Physics, 1, 36

Landini, M. and Monsignori-Fossi , B.C. 1971, Solar

Physics, in press.

Newkirk, G. 1967, Ann. Rev. Astro and Ay., _5, 213.

Newkirk, G. and Altschuler, M.D. 1970, Solar Physics,

13, 131.

Noyes, R. , Withroe, G.L. and Kirschner, R.P. 1970,

Solar Physics, ljL, 388.

Pneuman, G.R. and Kopp, R. 1970 , Solar Physics, 13_, 1' Pottasch, S. 1964, Space Science Reviews, 3_, 816.

Rugge, H.R. and Walker, A. B.C. 1970, Astro and Ap . , 5_ 4.

Rust, D. 19 70 , paper given at IAU Symposium 43 on Sole- Magnetic Fields, Paris, France.

Schmidt, H.U. 196 4, in "NASA Symposium on Physics of

Solar Flares," NASA Spec. Publ. No. 50, ed. W.

Hess

Zirker, J.B. 1970, Solar Physics, 11, 68.

J

126
THE CHEMICAL COMPOSITION

OF THE PHOTOSPHERE AND THE CORONA

George L. Withbroe

Harvard College Observatory

1. INTRODUCTION

The problem of determining the chemical composition of the solar atmosphere has attracted the attention of astronomers for over forty years. Knowledge of

the chemical abundances in the Sun and other astronomical objects, such as the Earth, moon, meteorites, stars

and planetary nebulae is important to several areas of

astronomy and astrophysics in the development of (1)

reliable models for the interiors and atmospheres of

the Sun and stars, (2) nucleogenesis theories, and (3)

theories describing the formation and subsequent evolution of the solar system, stars, and stellar systems.

Studies of the Sun are particularly useful because

the solar spectrum can be observed over a very broad

wavelength range with high spectral resolution. In

addition, due to the relative nearness of the Sun to

the Earth, we can attack the problem of the solar chemical composition with a greater variety of techniques

than is possible with other stars. Information on the

solar chemical abundances can be derived from observations of the photosphere, chromosphere, corona, solar

wind, and solar cosmic rays. This paper discusses the

chemical composition of the photosphere and corona. Quantitative analysis of the chemical composition

of the solar atmosphere was initiated by Henry Norris

Russell in 1929. He determined photospheric abundances

of 56 elements and 6 molecules from intensities listed

in the Rowland atlas and a simple photospheric model in

which it was assumed the absorption lines originate in

a reversing layer located above the photospheric layers

producing the continuum; and the reversing layer is

characterized by a uniform temperature and pressure.

Soon after Russell's pioneering work appeared in

print, Donald H. Menzel (1931) published his classic

study of the solar chromosphere. This massive work

127
discusses in detail the theory of line formation and

its application to the quantitative analysis of chromospheric flash spectra. Among the many valuable contributions contained in Menzel's paper is the first determination of the chemical composition of the chromosphere. Using a method of analysis similar to the one Russell applied to the photosphere, Menzel derived

chromospheric abundances for 20 elements.

In the years that followed, Menzel, his students,

and associates continued working on the problem of

solar abundances. Two of these students, Lawrence H.

Aller and Leo Goldberg, have been particularly influential and active in this field. In 19 43 they published

some of the results obtained by Menzel and his associates, and in 1960, along with Edith A. Muller, they

published what has become the standard reference work

on solar abundances (Goldberg, Muller, and Aller 1960)

,

hereafter referred to as the GMA abundances. This veryii

thorough analysis of 42 elements made use of new solar

observations, new f-values, a photospheric model based

on continuum limb-darkening observations, and a precise

theoretical treatment of the line formation for both

weak and moderate strength lines with different ioniza

tion and excitation potentials. Over the past 30

years, Menzel, Goldberg, and Aller have stimulated the

interest of numerous students and associates in the

solar-abundance problem.

Other important work of historical interest that

preceded the GMA analysis is that of Stromgren, Unsold,

and Claas. In 1940 Stromgren pioneered the modern

approach to abundance analysis by developing a photospheric model in which the temperature, gas pressure,

and electron pressure were given as a function of

optical depth. For the first time the abundance of

each element could be derived relative to hydrogen,

since the equivalent width of a line depends upon the

ratio of the line to the continuous-absorption coefficient, where the continuous absorption is produced by

negative hydrogen ions as discovered by Wildt in 1939.

Unsold in 19 48 and Claas in 1951 performed extensive abundance analyses based on curve-of-growth techniques. Unsold used a simplified solar model that

neglected the effects of temperature and pressure gradients on the formation of lines with different excita

tion and ionization potentials; Claas used a more

sophisticated model that included these effects.

In the decade since the publication of the GMA

analysis, numerous individuals, too many to mention by

name, have been active in photospheric abundance work.

The basic techniques have not changed much except for

128
le treatment of lines in crowded sections of the specrum. In the more sophisticated analyses, abundances

fe generally derived from such lines by computing

lort sections of the spectrum so as to take into

jcount the influence of lines neighboring on the pro-

.le of the line under investigation.

2. THE PHOTOSPHERIC IRON ABUNDANCE

ji The most important recent work on photospheric

mndances is the revision of the iron abundance. For

number of years one of the outstanding problems of

)lar physics was the order of magnitude discrepancy

ttween the photospheric and coronal abundances of

}on. However, starting in the mid 1960's, evidence

|;gan appearing which indicated that the photospheric

lundance was incorrect. The first evidence was prodded by the identification of the forbidden Fe II

.nes in the photospheric spectrum. The work of Swings

id his associates (Swings 1965, 1966; Grevesse and

tings 1969; Nussbaumer and Swings 1970) in this area

Is been particularly important. They found that in

rder to account for the presence of the [Fe II] lines,

photospheric iron abundance an order of magnitude

iirger than the value determined from the permitted

; I and Fe II lines was required.

Soon after the fFe II] results became available,

T idence for large systematic errors in the permitted

: I and Fe II oscillator strengths began appearing

jith the publication of new measurements by Huber and

)bey (1968), Grasdalen et al. (1969), Whaling et al.

.969), Garz and Kock (1969), Wolnik et al. (1970),

ischeck et al. (1970) , Bridges and Wiese (1970) , irtinez-Garcia et al. (1970) , Huber (1971) , Wolnik

I al. (1971) and others.

Of special significance were the results of the

.el group whose new laboratory oscillator strengths

pr the permitted Fe I and Fe II lines (Garz and Kock

169; Bascheck et al. 1970) and subsequent solar

|ialyses (Garz et al. 1969a, 1969b; Bascheck et al.

Ip70) resulted in a photospheric iron abundance in good

jreement with the photospheric value determined from

le [Fe II] lines and the coronal value.

Some of the reported photospheric iron abundances

:e listed in Table I.* The values are on a logarithmic

•:ale where the hydrogen abundance, log N„, is set

fables I-VI are on pages 136-144.

129
equal to 12.00. The most reliable values are in the

bottom third of the list beginning with the [Fe II]

results of Grevesse and Swings (1969) . The abundance

most consistent with recent revisions of the permitted

line oscillator strengths and recent abundance determinations from the permitted and forbidden lines of

both Fe I and Fe II is log N

p = 7.4 ± 0.3. The

assigned error limits take info consideration the sma." systematic differences between the recent oscillator

strength determinations and the uncertainties in the

photospheric models and line-damping constants. As ! will be shown later, a photospheric iron abundance of

log N = 7.4 is in fairly good agreement with the co: onal value.

3. PHOTOSPHERIC ABUNDANCES

Table II summarizes some recent results on the

chemical composition of the photosphere. The "adopte

photospheric abundances are values selected from a variety of references too numerous to cite. The

sources of the adopted values are given in column 7.

For comparison with the adopted values, the GMA value are given in column 3, and meteoritic values are give

in column 5. The meteoritic values are scaled such

that log N

g

. = 7.55. These abundances were determine

from a class" of carbonaceous chondrites that might be! representative of the primordial material out of whicj

the solar system was formed and hence might have a ex- position similar to that of the Sun. The difference;

between the photospheric and meteoritic abundances a:j given in column 6.

For the first 20 elements the agreement between

the solar and meteoritic values is very good, except

for lithium and chlorine. Lithium can be destroved If burning in the solar interior, which may explain why

the solar values are so low. For chlorine, both the],

solar and meteoritic values are uncertain. The sola;

value is based on only one line, while the meteoriti;

value is questionable because chlorine is a highly via

tile element.

For the elements with atomic numbers between 20]

and 40 the agreement between the adopted values and He; meteoritic abundances is better than the GMA results!

particularly for the iron group. There are still a e discrepancies, however, and in such cases these sole!

values may be questioned because of uncertainties ir

the oscillator strengths or because the element is j

130
represented by only a few lines, which might be blended,

jhe same statement holds for apparent discrepancies in

Elements with atomic numbers above 40. Note the significant increase in the number of elements whose solar

Ibundances have been determined since 1960.

Although there are a number of elements for which

;he relative solar and meteoritic abundances exceed 0.3

hex (0.3 dex = 10°

*

3

) , it is premature at this time to

jlonclude that the meteoritic and solar abundances are ither the same or different. For one reason or nother, solar abundances of most of the discrepant

lements may be in error. How reliable are these photospheric abundances?

I here are three basic sources of error: (1) inadequate

heory of line formation; (2) inadequate models for the

emperature and density structure of the photosphere;

.nd (3) inadequate atomic data, especially oscillator

trengths and, to a lesser extent, damping constants.

Almost all photospheric abundance determinations

.re based on the assumption of LTE; that is, it is

r ssumed that excitation and ionization of atoms in the

•hotosphere are governed by the Boltzmann and Saha

squations, respectively, with the excitation and ionzation temperatures at any point in the atmosphere

,»eing set equal to the local electron temperature.

Uiiller (1966) reviewed work on this subject and concluded that departures from LTE do not significantly

I if feet abundances determined from equivalent widths of

reak and moderate-strength lines. Some of the more

recent evidence for departures from LTE that have shown

Jfp in analyses of equivalent widths (cf . Jefferies

J.966 , Withbroe 1969a) can now be attributed to systematic errors in the oscillator strengths used in the

Analyses (cf. Huber and Tobey 196 8, Garz and Kock

Miiller has also discussed the influence of uncer- tainties in the assumed photospheric models and damping

constants and concluded that the uncertainties in these

parameters produced errors in the abundances no larger

<:han 0.3 dex.

With the exception of elements that are represented by only a few lines which may be blended, the principal source of "uncertainty in the photospheric abundances stems from doubts about the reliability of the

oscillator strengths. The most widely used oscillator

/strengths for abundance work are still those of Corliss

'and Bozmann (1962) , which unfortunately contain a num- ber of systematic errors (Warner and Cowley 1967; Zwann

1967; Huber and Tobey 1968; Wolnik et al. 1968, 1969,

1970, 1971; Grasdalen et al. 1969; Whaling et al. 1969;

969) .

131
Garz and Kock 1969; Bridges and Wiese 1970; MartinezGarcia et al. 19 70; Takens 19 70; Huber 1971; and

others) . Consequently any abundances based on the oric

inal Corliss and Bozmann oscillator strengths may be

in question. Several elements between atomic numbers

20 and 40 and most elements with atomic numbers greate

than 40 fall into this category. Corrections to the

Corliss and Bozmann oscillator strengths will be published in the near future by the National Bureau of

Standards. This should improve the situation.

5. CORONAL ABUNDANCES

Coronal abundances have been determined from two

types of data: forbidden-line observations made from

the ground and extreme ultraviolet (XUV) observations

made from above the Earth's atmosphere. We will con- sider the forbidden-line results first.

The emission lines in the visible spectrum of the

corona have been observed for over 100 years during

numerous solar eclipses, and during the past 30 years

on a more routine basis thanks to the development of

the coronagraph. The identification by Grotrain in

1939 and by Edlen in 19 42 of the coronal-emission lin

belonging to forbidden transitions of highly ionized

atoms provided astronomers with their first opportuni

to determine the chemical composition of the corona. Observations in which abundances are derived fro

coronal emission lines usually consist of equivalentwidth measurements where the intensity of the emissio

line is directly compared to the intensity of the con tinuum at the same wavelength. The intensity of the

line depends upon the chemical abundance of the eleme

producing the line, the fraction of atoms in the appr

priate stage of ionization, the line excitation

mechanism, and the density of the corona. The corona

density can be inferred from the intensity of the con tinuum, which is produced by scattering of photospher

radiation by coronal electrons. The ionization can b

determined from the relative intensities of lines pro

duced by different ions of the same element. Excitation is generally computed theoretically by assuming

equilibrium and taking into account the various processes that can populate and depopulate the relevant

atomic levels.

The pioneering work on the chemical composition I the corona was performed in 19 48 by Woolley and Allen;

who determined the coronal abundances of Ar , Ca, Fe

,

132
nd Ni . Their abundances, along with values from other

investigators, are given in Table III. With the excepion of Nikolskii's, all of the iron values are in good

greement. The adopted values for iron and the other

ilements are given in the last column. Before averjging, all of Nikolskii's values were systematically

jaised to agree better with the absolute scale defined

|y the other investigators. Pottasch (196 4b) has disjussed various sources of systematic errors in

orbidden-line analyses and concluded that the systemtic errors are on the order of 0.3 dex.

With the advent of rockets capable of carrying

instrumentation above the ultraviolet-absorbing layers

if the Earth's atmosphere, the XUV portion of the solar

pectrum became accessible to observation. The solar

UV spectrum contains the coronal resonance lines,

including lines of several elements whose line emissions have not been observed in the visible. The first

rIjUV solar spectrum was obtained in 19 46 by the U.S.

jjjaval Research Laboratory using an instrument launched

In a V-2 rocket. Since then numerous solar XUV experiments have been flown on suborbital and orbiting

ehicles

.

Ivanov-Kolodny and Nikolskii (1961, 196 2)

,

ottasch (1963a, 1964b, 1967) , Athay (1966) , and others

ave developed techniques for determining relative

ioronal abundances from XUV observations. The intensity of an XUV line depends upon the abundance of the

arent element, the fraction of atoms in the ionization

imitate producing the line, and the electron density in

hhe layer of the atmosphere where the line is produced,

yince atoms in a given state of ionization are abundant

jjver only a small range of temperatures, XUV lines will

he formed in the layer of the atmosphere where formation of the appropriate stage of ionization is most

"trongly favored. By comparing the relative intensifies of lines coming from different chemical elements

jut produced by ions formed in the same atmospheric

jayer, one can determine relative abundances.

To determine absolute abundances (abundances relative to hydrogen) from XUV data it is necessary to

determine the electron density in the atmospheric layer

"rhere the lines are formed. Two techniques have been

Tsed. One (Pottasch 1963a; Dupree and Goldberg 1967;

1 eimers 1970) is based on solar radio-brightness temeratures , which depend on the run of temperature and

'lensity in the solar atmosphere. The other (Withbroe

970 , 1971) utilizes measurements of the intensity of

i he coronal white-light continuum of K-corona caused by

" cattering of photospheric light by coronal electrons.

133
Table IV lists the relative coronal abundances

derived by different investigators. The abundances are given on a linear scale relative to the silicon abundance, which is set at 100. Generally there is agreement within a factor of 2 to 3 (0.3 to 0.5 dex) , the

major exception being iron where there is an order of

magnitude difference. The best determination of the

Si/Fe ratio is that of Jordan and Pottasch (196 8) who

obtained a value of unity, which is the value adopted

here. The data of Athay (1966) and Dupree and Goldberg

(1967) can be represented by a Si/Fe ratio of unity.

The "adopted" values are the relative abundances that

the author believes best represent the XUV results.

Table V places these abundances on a scale relative to hydrogen, based on data from several sources.

As indicated earlier it appears that the Fe/Si ratio : unity and, therefore, the most reasonable estimate for

the coronal silicon and iron abundance is 7.5 on the

normal logarithmic scale. The higher values found by

Pottasch (1963a, 1964b, 1967) and Withbroe (1970) are

less reliable than the other results. The absolute

scale for the adopted values is accurate to ±0.5 dex.

Table VI summarizes the coronal results of Table

III for forbidden lines and Tables IV and V for the XU

lines. There is a systematic difference in scale

between the two sets of abundances, with the forbidden

lines giving abundances about 0.3 dex higher on the

average. I arbitrarily split the difference to obtain

the adopted coronal values. For comparison the differ

ences between these abundances and the adopted photospheric and meteoritic values are also given. In

general, the agreement is good except for potassium ar cobalt. However, on the basis of the overall agreemer

between the coronal, photospheric , and meteoritic

values, I would like to suggest that at least for thes

elements a useful working hypothesis would be that the

values for these three sets of abundances are equal.

6 . SUMMARY

Tables II and VI contain the adopted chemical cod

positions of the photosphere and corona. From the di I- cussion of the results presented in these tables we

|| summarize the following major points:

1. As shown in Table II, we are gradually building

fairly complete picture of the composition of tl

solar photosphere for the first 92 elements.

134
2. The problem of the solar iron abundance appears

to have been largely resolved by recent work.

Further analysis will probably not change the

photospheric value adopted here by more than ±0.3

dex.

3. The photospheric and coronal abundances are equal

to within a factor of 2 (0.3 dex). Since the

systematic errors in the abundances are of this

magnitude, it seems reasonable to adopt the

hypothesis that the two sets of abundances are equal until there is better evidence to the contrary.

4. There are some large discrepancies between the

solar and meteoritic abundances for a number of

elements, but because of uncertainties in the

oscillator strengths, line identifications, or blending problems that may affect the discrepant

solar values, it is premature to conclude that

these two sets of abundances differ significantly.

5. There is still a need for better measurement of

oscillator strengths for a number of elements

whose abundances are based on measurements of

questionable reliability. This is probably the

outstanding problem remaining in solar abundance

studies

.

ACKNOWLEDGMENTS

I wish to thank Professor L. Goldberg and Dr. R. N.

Thomas for the invitation to participate in the Menzel

Symposium. I am indebted to Professor L. H. Aller and

Professor L. Goldberg who stimulated my interest in the

solar-abundance problem. This work was supported in

part by the National Aeronautics and Space Administration through contract NAS-5-9274 and grant NGL-22-007-

006 .

135
TABLE I SOME REPORTED PHOTOSPHERIC IRON ABUNDANCES

Ions Investigators Values*

Fe I Russell (1929) 7.70

Fe I Goldberg and Aller (19 43) 6.99

Fe I Unsold (1948) 7.72

Fe I Claas (1951) 7.62

Fe I Weidemann (19 55) 7.01

Fe I Goldberg et al. (1960) (GMA) 6.57

Fe I Leftus (1963) 6.76

Fe I Baschek et al. (1963) 6.18

Fe II Baschek et al. (1963) 6.78

Fe I Teplitskaya and Vorobeva (196 4) 6.78

Fe I Mtiller and Mutschlecner (1964) 6.70

Fe I Warner (196 4) 6.81

Fe I Goldberg et al. (1964) 6.54

Fe I Aller et al. (1964) 6.57

Fe II Aller et al. (1964) 6.59

[Fe II] Swings (1965) 7.80

[Fe II] Swings (1966) 7.40

Fe I Miiller (1967) 6.80

Fe I Withbroe (196 7) 6.85

Fe II Warner (1968) 6.51

Fe I Withbroe (1969a) 6.80

[Fe II] Withbroe (1969b) 7.63

Fe I Grevesse (1970) 6.61

Fe II Grevesse (1970) 6.72

[Fe II] Grevesse and Swings (1969) 7.50

Fe I Garz et al. (1969) 7.60

Fe I Rogerson (1969) 6.85

Fe II Baschek et al. (1970) 7.63

Fe I Cowley (19 70) 7.00

Fe I Takens (1970) 7.48

Fe I Ross (1970) 7.20

[Fe II] Nussbaumer and Swings (1970) 7.50

Fe I Richter and Wulff (1970) 7.55

[Fe I] Grevesse et al. (1971) 7.50

Fe I Martine z-Garcia and Whaling (1971) 7.45

*Log NA+12.0 where A is the abundance of the element

relative to hydrogen.

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TABLE III

CORONAL ABUNDANCES FROM FORBIDDEN LINE DATA

At. #

Element

Woo 1 ley

,

Allen

(1948)

Reported Values

Pottasch Nikolskii

(1964a) (1967) Other

Adopted

Values*

1 H 12.00 12.00 12.00 12.00 12 .00

16 S 7.10 7 . 10

18 Ar 5.00 7.10 6.30 7 . 00

19 K 5.90 c n ft 5.90

20 Ca 6.30 6. 80 6. 10 6.60

24 Cr 6.00 6.00

25 Mn 5.70 5.70

26 Fe 7.80 7.87 7.30 7.85f 7.85

27 Co 5.60 4.80 5.50

28 Ni 6.40 6.72 6.00 6.55

*In the case of Nikolskii

values before averaging.

tOther Fe values (the average is 7.85):

7.86 (Pottasch 1963)

7.70 (Jordan 1966b)

7.80 (Malville 1967)

8.00 (Dupree 1968)

(1967), 0.55 was added to the

8.00 (Shkolovskii 195Qa,b)

7.60 (Suzuki & Hirayama 196 4)

>7.00 (Jefferies & Orrall 1966)

7.90 (Eddy & Malville 1967)

TABLE IV

XUV CORONAL ABUNDANCES RELATIVE TO Si

Ele- Pottasch

At.# ment (1964b., 67)

Reported Values

Jordan, Dupree, Widing,

Pottasch Athay Goldberg Sandlir

(1968) (1966) (1967) (1968)

1 H 1000000

2 He 200000

6 C 1000 1900 1200

7 N 120 340

8 0 500 1300 2900

10 Ne 70 100 <500

11 Na 4 7.5

12 Mg 60 100 250

13 Al 4 6.3

14 Si 100 100 100 100 100

15 P 0.8 0.7

16 S 40 62

18 Ar

20 Ca 3 26 Fe 100 100 12 12 150

28 Ni 9 10* 20

Originally measured by Jordan (1966a)
TABLE V

ABSOLUTE XUV CORONAL ABUNDANCES*

Values Reported

XUV & XUV & K-Coronameter

Investigators Radio Data Data

tasch (1963,1964b,1967) log N si =8.0

ree, Goldberg (1967) log Nsi=7.5

pert (1967) log NFe=7.35

hbroe (1970) log N si =7.7

hbroe (19 71) log Nsi =7.5

|mers (1970) log Nsi=7.56

lue adopted: log N

g

^ = log N

Fe

= 7.5

TABLE IV

(continued)

Reported Values

Withbroe Reimers Withbroe Dupree Adopted

(1970) (1970) (1971) (1971) Values*

30000

50000

667

100 290

2000 1000

100

6.7

133 98

10

100 100

33

10

13

67

6.7

3200000

510000

1000 1200

430 280

1300 1700 1400

85 80 79 84

8 5.4 6 200 80 85 100

7 10 7 100 100 100 100

0 . 7 58 53

10

4

5 112 56 100

10
IIu

' <

c c

u *J 0 D

< 4

8-2 < u

tn CO r-N o H o

O C O ^ rH (H

CM (N (N LO h ^ ^

10 O CN O CN SP <N o o o o c o

X H CC H H ffi (N ^

H © © CN <-<©©© O

o o o o o ©

o o ©

I I © c c o o o

c Is in in in iTi r- © i—i m cn cc cn ©©©©©©©

© m ^ tfl m tfi in m if) m © m lt p*s in m

© c © h in «3- © © ©

©©©©©©©©©©©© ©

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1 ©

I ©

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0 Hi

I 4J 9 4 CJ»i<4<r| M CV-CC

<

f—i c > cc c i->{N(^«c, L.~^cc;r©«^, L~ycr^cc

r«, r- , CN CN CN CN CN CN

144
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148
Ill

GASEOUS NEBULAE

Chairman: James G. Baker

Harvard College Observatory

I've just discovered that astronomy

is a science that requires a little

less than no-place accuracy.

Leland Cunningham
i
OPTICAL LINE SPECTRUM

S. J. Czyzak

Perkins Observatory

The Ohio State and

Ohio Wesleyan Universities

and

T. K. Krueger

General Physios Laboratory

Wright-Patterson Air Force Base

I. INTRODUCTION

In his introduction to Selected Papers on Physical Processes in Ionized Plasmas (1962), Professor Donald H. Menzel points out that for the astronomer,

hydrogen is the most important element in the universe.

It constitutes 90% of all atoms. However, the 9% of

helium and the remaining 1% of the atoms also play an important role in unraveling the mysteries of the

universe. Thus, in the field of astrophysics, the

study of the elements and their spectra, i.e. line

intensities and continua, is fundamental to the understanding of the physical processes that take place in

stars, nebulae, and galaxies.

Professor Menzel considered this aspect of astrophysics sufficiently important that in 19 35 he and

C. L. Pekeris started a study of hydrogen. In 1937 he

initiated a thoroughgoing study of the various types of

physical processes occurring in highly ionized gases,

which included radiative and collisional interactions

of the various atoms. For the next decade, he and his

co-workers pursued this effort intensively. The

results of this first phase of the work are well known

through the series of publications entitled "Physical

Processes in Gaseous Nebulae"

.

The work at Harvard did more than improve and

extend the earlier investigations of Zanstra,

Ambarzumian, Plaskett, Carroll, and Menzel on hydrogen

and helium spectra, and those of Bowen, Condon, and

151
Pasternack on forbidden-line spectra. It inspired

investigations on forbidden-line strengths by Garstang

and Aller, Ufford and Van Vleck; on collision strengths

by Seaton and his collaborators; and on the physics of

gaseous nebulae by some of Menzel's original collaborators, e.g. Goldberg and Aller, and also by Osterbrock

and his associates, Seaton and his team, Peimbert, and

many others.

The continued effort of many scientists has

enabled us to explain today at least some of the physical processes in gaseous nebulae.

The incentive to seek accurate measurements of

spectral-line intensities was largely provided by the

precise predictions of Menzel's theoretical work. His

important contributions include: (1) absorption coefficients and hydrogen-line intensities (with Pekeris)

(2) the theory of recombination (with Baker) ; (3) forbidden line strengths (with Shortley, Aller, and Baker)

(4) the first quantum mechanical calculations of collision strengths (with Hebb) ; (5) the first quantitative

treatment of the Bowen fluorescent mechanism.

In spite of the tremendous effort by Professor

Menzel and other scientists, there is still no com- pletely adequate interpretation of optical line spectra

II. THE PROBLEM OF MEASURED INTENSITIES

As is well known, line intensities in gaseous

nebulae may be obtained by spectrophotographic and

spectrophotoelectric methods. Generally, both methods

are employed because each has certain advantages in

estimating various line intensities. In the spectrophotographic method one can use a slit spectrograph, a slitless spectrograph, or narrow band filters to

evaluate, respectively, the line intensities of the

nebula, the spectrum of the central star, and the radia

tion in specific regions. With these one can then make

appropriate comparisons, all of which are essential to

a satisfactory evaluation of the spectrum. Also, by

varying the exposure one can obtain graded intensities

and thus the opportunity of measuring not only strong

lines but also weak ones. The present photoelectric methods enable us to

obtain an "integrated" intensity for the various spectral lines from the entire nebula in both the blue and

visible regions. In particular, this method gives

excellent confirmation of the strong and medium intensity spectral lines. By a combination of photographic

152
Figure 1. Spectrograms of NGC 3587 taken at the

Perkins 72" telescope of The Ohio State and Ohio

Wesleyan Universities at the Lowell Observatory,

Flagstaff, Arizona. These spectrograms were taken by

G. Boeshaar, S. J. Czyzak and Kent Ford. Exposures

were 30 minutes and 145 minutes duration.

and photoelectric means, one can then obtain a more

detailed analysis of a particular spectrum, i.e. the

former can be used to obtain weak line intensities

through long exposures, and the latter can be used to

obtain strong and medium lines.

More recently the innovation of the image tube has

been helpful in spectral analysis. Here too, by using

a slit spectrograph and off-set guiding, one can obtain

spectrograms of high and low excitation regions separately. The great advantage with the image tube is the

relatively short exposure time necessary to obtain useful results. Figure 1 shows two spectrograms of

NGC 3587 for the region X4800 to X7500, at two different exposures, which were done with Dr. Kent Ford's

image tube at the 72-inch telescope at Flagstaff,

Arizona.

We use all these methods in order to gather the

153
data necessary to determine the spatial distribution of

ions and atoms. However, we still face certain difficulties in the measurement of our line intensities.

Generally, the measured intensities are good to ±10%

for the strong lines, ±20 - ±40% for the medium

intensity lines, and for the weak lines the uncertainty

may be as high as 100%.

Much of the problem in assessing the line intensities is due to irregularities within the nebula itself.

If the structure of the nebula is reasonably uniform,

so that the line intensities in particular regions or condensations can be measured, then it is quite

feasible to explain the general structure of a nebula,

for example, IC 418. If, on the other hand, the structure is irregular and local condensations are present

throughout, then one obtains more or less integrated

intensities rather than intensities representing specif

ic regions only. In these cases a satisfactory explanation of the structure is very unlikely. Two examples

of such a complex structure would be NGC 6543 and

NGC 1514.

Considerable improvement has been made over the

years in the techniques used for spectral investigation

of nebulae; however, we have not yet reached the stage

where we can make accurate detailed studies of the

regions in which the ions occur. This is not to imply

that there has not been any success in identifying

regions in which some of the ions are formed, but this

depends upon the degree of symmetry and size of the

nebula. For example, for stellar types it is not

feasible, and we have been able to obtain only integrated intensities for the spectral lines, i.e. the

regions of high and low excitation cannot be isolated

for spectral analysis. In summary, our present combination of techniques allows us to arrive at a reasonably good estimate of the ionization distribution and

structure for some of the nebulae.

III. THEORETICAL CONSIDERATIONS IN LINE

INTENSITY MEASUREMENTS

In gaseous nebulae, we are concerned with the following kinds of lines:

(1) permitted lines (electric dipole radiation)

that arise from photoionization and recombination;

(2) forbidden lines (magnetic dipole and electric

quadrupole radiation) which arise when electrons that

have been collisionally excited to metastable levels of

154
a configuration cascade to the lower levels of the s configuration

;

(3) fluorescent lines (Bowen 1934), which arise in

high excitation nebulae when 0

+2 ions absorb Hell

(Ly a) radiation and when N

+2 ions absorb one of the

fluorescent OIII lines.

Accurate intensity measurements are important for

all of these lines because we have an accurate theory

with which to interpret them, thanks to Menzel's

pioneer work, which has been amplified and extended in

recent years. One might truthfully say that the theory

is ahead of the observations in many instances; for

example, critical lines are often weak and difficult to

measure accurately.

A proper account of the above three mechanisms

would require more space than is available and has been

given in the literature by many writers. Therefore, we

shall confine our attention to one illustrative problem, the excitation of the forbidden lines of ionized

sulfur because they appear in many nebular filaments.

Now that reliable atomic parameters are available,

at least so we believe, the relevant forbidden lines

become correspondingly more useful for the diagnostics

of nebular plasmas, i.e. for deducing densities and

temperatures of the individual condensations or filaments in which these lines originate.

The basic equations of statistical equilibrium for

the five levels of [SII] may be written in the following manner:

00s

i *<

I

5 Nq +N V N q + 5" N A

e^mn e L n^mn

m=2=n m mn o

rH CO

r-» r<

D 3 5 7' 7 n { n y n e L m=n=l

q + y A } ^mn L mn m<n

with n = 2,3,4, & 5 where q = the rate of collisional excitation of upper

! mn

level n to lower level

m = 8.62 x 10 6 ft(m,n) *mn/kT

03 T m

175-

155
q = the rate of collisional de-excitation of

level n to level m = 8.62 x lo" 6

, a) T ±/z n

Q - the collision strength for electron impact

excitation to level n from level m. A = the total transition probability, which is mn

due to the sum of the magnetic dipole and electric

quadrupole contributions in the [SII] problem, that is,

A

(M) (J,J') +A (Q) (J,J') where

A

(M) (JfJ1) = 3.532^ 10* „

3 S

(M) (j.j.)

A

(Q) (J , J

. ) = 2^48_i_10l, 5 s

(Q) (J(JI)

where v is the frequency in wavenumbers.

The equations involving the q*s are based on the

following two assumptions: (1) electron velocities car be represented by a Maxwellian distribution, and (2)

the energy change is small over the range under consid

efation.

From the above expressions we see that it is

essential to have accurate S*s and fi's. Both quantities, except in the case of the magnetic dipole contribution for S, depend very strongly on the wave functions, and until relatively recently this was one of

the main "stumbling blocks" in obtaining accurate A's

and ft

1 s

Today, these wave functions are calculated by the

Hartree-Fock Self-Consistent Field Method developed by

Charlotte Froese-Fisher , Roothaan and his co-workers,

Mayers and Hirsch, and others. These highly sophisticated programs are the result of the expansion and

improvement of the early pioneer work of Hartree and

his students (Garstang, Douglas, Mayers and FroeseFisher) , and Fock.

Here also it is essential to mention Bates, Lowdi

Hylleraas, Dalgarno, Layzer, H. Kelly, and others in

connection with their fundamental work on atomic struc

ture. For it is the advancement and developments in

156
atomic structure that significantly contributed to I solution of the problems encountered in calculate

atomic parameters

.

The intensity ratio

I (A6716)

r

i I(X6730)

of [SII] is particularly useful for getting a good

estimate of the density Ne if 0.5 < r 1 < 1.15. This is

because the solutions of the equilibrium equations for

the five levels of the ground state configuration lead

to values of r 1 that, when plotted as a function of

log x (where x = 10" 2 Ne //T^) , give curves lying very

close together (Figure 2) and nearly vertical for

0.75 < t < 1.5 (where t = 10 _l+ Te ). Since this is the

approximate range of Te in planetary nebulae, the value

of x and hence Ne for an assumed Te should be fairly

good, especially since the line intensities, X6716 and

1X6730, are well measured. For example, consider

' NGC 7662 for which Weedman (1968) reports an r 1 = 0.62.

If one assumes Te = 10,000°, then Ne = 1.04 x lOVcm 3

.

I If, on the other hand, one assumes either Te = 7500°K

or T e = 15,000°K, the spread in Ne is 1.00 x 10 4 < Ne

< 1.00 x 10 h

. Consequently, it is seen that r 1 can

, be used to give Ne to within 5 to 10%, and this would

certainly be at least as reliable as the measurement of

f

r

2 and the atomic parameters used to predict it. Thus,

it certainly can be said that the use of r x gives reli-

; able results for Ne provided, of course, that the measured line intensities are reliable, as is the case for

the X6716, X6730 lines in [SII].

The ratio r 2 cannot, however, tell us much about

j the temperature, and for a good estimate of T e we must

therefore consider other intensity ratios. One set of

lines that could be used is X4068 and X4076, the ratio

between their sum and that of X6716 and X6730 being

sensitive to Te . However, there is an observational

-problem in that the X4068 and X4076 lines are blended

with those of Hg, so that they cannot always be used.

However, X4068 is often sufficiently free from Hg con-

- tamination that an estimate of the line intensity can

be made, and the ratio

r 2 = I (X4068)

KX6716) + KX6730)

is generally used. But the intensity of the \4068 line

157
-2.0 -1.0 0 I

log X

Figure 2. Theoretical curves for the intensity ratio, i 158
weak and therefore much less accurately measured

pn those in r 2

. This leads to results that can be

consistent. Consider again NGC 7662. If one takes

i measured value of r 2 and uses the theoretical

eves r 2 vs. log x (Figure 3) to obtain x for values

Te in the range 7500° < Te

< 15,000° , and if one

^n uses this value of x with the value of Ne obtained

bm r 1 to find Te , one finds that this Te is nowhere

|r the Te of the curve in Figure 3, regardless of

Lch curve is used. The difference may be as much as

159
an order of magnitude. Or, if one computes Te by usi

a different ion, as for example the [OIII] ratio

I(X4363)/I(N 1 +N 2

) and uses r 2 to obtain Ne , the resul

ing value of Ne will usually be higher than that

obtained from r x

. The difference may be as much as a factor of 1.5 to 2.

IV. CONCLUSION

Today, while we have certain spectroscopic data

(mostly in the blue region) , it is quite apparent th;

additional data in the visual and infrared regions a: required. The discrepancies in Ne and Te as deterrai:

by the r 2 and r 2 ratios confirm this, While the A40': and A4076 values in ISIIJ are highly desirable in ou calculations, the mercury contamination (blending)

number of instances precludes their use. It is also

necessary to get additional data for other lines,

namely, those of [C&III] , [ArlV] , and other 2p3 and

3p3 (q = 2,3,4) ions. With accurate intensity , ratio

and atomic parameters, the study of the structure an ionization distribution can be carried out in greate

detail and with greater confidence.

REFERENCES

Bowen, I.S. 1934, P. A.S. P., 46_, 146.

Menzel, D.H. 1962, Selected Papers on Physical

Processes in Ionized Plasmas (New York: Dover)

Weedman, D.W. 1968, Ap . J., 153, 49.

160
CHEMICAL COMPOSITION OF TYPICAL PLANETARY NEBULAE

Lawrence H. Aller

University of California 3 Los Angeles

When we attempt to determine the chemical composi-

)n of a gaseous nebula from its bright-line spectrum,

know at the outset that there exist tremendous devia

Ins from local thermodynamic equilibrium, and that we

It invoke the detailed mechanism appropriate to the

(citation of each line. In fact, the prime objective

the original program embodied in the series on kysical Processes in Gaseous Nebulae" was the quanti-

:ive interpretation of the spectra of these objects;

I last paper (Menzel and Aller 1945) was an attempt

assess their chemical compositions.

If we grant that the physical mechanisms of

[ictral-line and continuum excitation are understood,

have the following tasks:

|l. Calculation of accurate atomic parameters,

notably the Einstein A values and the collision

strengths Q (Hebb and Menzel 1940) . Czyzak has

mentioned this problem in the preceding paper.

2. Accurate measurement of line intensities and con tinuum data.

3. Allowance for the distribution of atoms of a given element among different ionization stages.

I cannot overemphasize the importance of a photometric calibration of line intensities measured by

j>tographic photometry. We have tried to do this for

! . the nebulae discussed in a series of papers

^ectrophotometric Studies of Gaseous Nebulae" . Early

)tographic work had suggested a deviation of the

.mer decrement from theoretical predictions; later

isurements showed a preponderance of Balmer decreets that tended to agree with theory. Joseph Miller

•71) has found a decrement for NGC 7027 that agrees

:h theory, and indeed a new series of spectrograms of

-s object with improved calibrations confirms this

161
result; so great care must be used in the measurement

of weak lines.

Although "photoelectric accuracy" is the envy of

all of us who work with the photographic plate, we muj

realize that there are certain tasks that can be done

only by combinations of photographic and photoelectric

photometry. A typical photoelectric measurement of a nebular spectrum line embodies an integration over th< entire disk of the nebula - or a sizable region there<

Thus

I PEP I(x,y)dA

while a photographic observation gives us

I ptg (x ' Y) AxAy

y+^Ay

y-^Ay

x+^Ax

I (x ,y) dxdy

x-^Ax

Here Ax and Ay depend on the resolution of the photographic plate, the seeing, and the microphotometer s]

employed. Further,

Kx,y) E (x ,y , z) dz

—oo

where dz is the element of integration along the ,lin<

of sight, whereas theoretical considerations always

give us E(Ne ,T e ), which can vary from point to point

x,y,z, within the nebula.

Consider, for example, the isophotic contours f NGC 6818, as shown in Figure 1. Photoelectric measu

ments would give the integrated intensity over the s face; photographic measurements would give intensiti

corresponding to a small area or a series of small areas taken along a line across the nebula. The ide

solution would be to use the photoelectric measureme

in conjunction with the isophotic contours to interp

the photographic intensity measurements.

So far we have not had sufficiently detailed in)

mation on isophotic contours of different ions to ap

this technique to any complex nebula. At this pointW

need a large body of monochromatic photographs of

162
s

Figure 1. Isophotic contours of A5007 [OIII] in NGC

6818. These contours were traced with, the Michigan Isophotometer by Mrs. Nancy Boggess from a plate secured

at the coude focus of the 100 -inch telescope of the

Hale Observatories. The approximate scale is indicated

at the left. The numbers, 1.0, 0.95, 0.9, etc. give

the logarithm of the intensity (surface brightness of

the nebula) . Loss of resolution is produced mostly by

seeing and guiding errors.

nebulae, such as those obtained by Kent Ford and Vera

Rubin (1971) and by M. F. Walker and G. E. Kron (1971).

At the present time there are two ways one can proceed. One is to concentrate attention on selected

knots or filaments and analyze these in great detail.

This procedure requires much observing time with a large telescope, but it may prove necessary for objects

such as NGC 6 54 3 or NGC 2392.

An alternate procedure, which has been applied by

Peimbert and Costero (1969) to the Orion nebula, is to

take the variations of density and temperature into

account in a statistical sense. For example, different

'values of the electron temperature may be found from an analysis of the radio-frequency-continuum data (Mills

and Shaver 1967) than from the forbidden lines of

163
[OIII]. A comparison of the Balmer jump with high mem- bers of the Balmer series may give another estimate,

and so forth. These temperature differences represent

a different weighting of different regions in the

nebula, depending on the mechanism of emission involved

In an extended object such as Orion, one has little

choice, but in a planetary nebula where individual

knots and filaments can be recognized, it is to be

hoped that one may have regions of fairly constant temperature and density.

Nevertheless, we cannot overemphasize the importance of these fluctuations, which Peimbert has clearly

demonstrated must be taken into account. We must still

face up to the problem of why these temperature fluctuations are so large. In a given nebula, they may

range from 6000°K to 10,000°K.

Density fluctuations are also spectacular and

occur in many planetaries. Some seventeen years ago

(Aller 19 54) , I suggested that the observed spectrum of

NGC 7027 ...can be understood in terms of a nebula con- sisting of numerous filaments, knots, and tenuous

regions, such that the density may range from perhaps less than 10,000 ions/cm to perhaps some- thing like 200,000 ions/cm 3 ... Such large densities seemed unusual in planetaries

(other than IC 4997) at that time, but Goldberg has

presented a similar conclusion for NGC 7027 at this

symposium.

A second problem is how to allow for the distribution of atoms among different ionization stages. Three

procedures have been proposed:

1. Construction of empirical ionization curves

2. Allowance for a domination of the ionization of

many ions by the ionized helium radiation field,

and other empirical considerations

3. Detailed construction of models for nebulae

In the first method, originally employed by Bowen

and Wyse (19 39) , one compares the ratios of ionic con- centrations of various elements, e.g., employing the

lines of [Nelll] and [NelV] , or [Oil] and [OIII], or

[Arlll] and [ArlV] , and so forth. That is, one assume c that the degree of ionization depends only on the

ionization potential and neglects the detailed deformations of the radiation field.

When this procedure is applied, one finds, for

example, that the [NelV] and [NeV] lines must be produced in much hotter regions than the [OIII] lines;

otherwise one finds a strange dependence of chemical

composition on excitation.

16 4
Seaton (1968) pointed out that one should employ a alation of the type

N(HeII) + N(Hel)

N(Hel) N(OII) + N(OIII)

N(0)

ince the ionization of oxygen is influenced by that of

elium. That is, the second ionization potential of

elium falls near the third ionization potential of

xygen, so unless Hell is present, there should not be

xygen/hydrogen abundance ratio against the excitation

lass of the nebula (Aller 1956) , there is a large

batter but a very distinct relation between the maxijum 0/H ratio and the nebular excitation, in the sense hat only high-excitation nebulae have large 0/H

atios. That is to say, the 0/H ratio depends on the

Ixcitation class. In these calculations we have

ssumed that the electron temperature is that given by

tie usual [OIII] line ratios. One suspects that the

iopted model is oversimplified, and I have accepted

ne larger values of the 0/H ratio as being more meaningful.

Of course there probably exists a large variation

h the elemental abundance ratios, as indicated for

Sample by the work of Kaler (1970). One is, however,

aspicious of a dependence on excitation class,

learly, one must employ models with appropriate temperture and density variations, as Peimbert and Costero

ave done for the Orion nebula.

By using the data published in the nebular photometry series, I find for helium

I

ith a spread of about 0.1. This value is deduced from

le A4686 line of ionized helium and the A4471 and

4026 lines of Hel, interpreted with the aid of the

leory developed by Robbins (196 8)

.

The CII X4267 doublet is observed in a large num-

|pr of nebulae. If we assume that this line is proiced by recombination only, we may deduce the

(C++)/N(H+) ratio from the expression

Log N (He) = A (He) = 11.09

(C++) 0.256 1(4267)

I (4861) ' (H+) = 0.0060 T 6300°K < T < e 20,000°K

165
derived from the calculations by Bednarek and Clarke

(1971). For A(C) = 8.7, 1(4267) < 0.8. Indeed, since

the A4267 line appears to be stronger than this in a number of nebulae, it must, as pointed out by Kaler

(1971) , be excited by line emission rather than by

pure recombination.

There are a number of nebulae, among them NGC

7009, where the line is considerably weaker, and here

it may actually be excited by recombination. For the

time being, we adopt A(C) = 8.7 with the understanding

that this is the roughest kind of guess rather than a determination

The nitrogen abundance is difficult to estimate.

The NIII lines cannot be used since they are excited b}

the Bowen fluorescent mechanism, and the Nil lines are weak. A theory similar to that developed for CII mighi

be employed, but here again we might be dealing with

excitation by radiation from the central star. One cai

employ the ionization curve method or, what amounts to

very nearly the same thing, assume N(N+)/N(N) = N(0+)/N(0). The objection to this procedure is that o] the photographs obtained with the best definition,

filaments observed in [Nil] tend to be "harder" in

appearance than those observed in [Oil] . If we apply

this simplified procedure, restricting it to the lower

excitation objects or to objects that show strong

[Nil] or [NI] lines even though they may show numerous

high-excitation lines, we obtain

A (N) = 8.12 ±0.12;

but there is a big spread among the nebulae. For a single nebula, the dispersion a = 0.37.

To estimate the oxygen abundance, I have favored

the higher excitation objects, where the temperature

derived from the [OIII] line ratios probably agrees

more closely with that from the hydrogen spectrum. Tl: average value is thus found to be

A(O) = 8.85 ±0.15.

The ionization pattern of neon probably mimics

that of oxygen, whether one draws an ionization curve

or employs Seaton's argument. Thus I compare neon ami

oxygen directly to find A (Ne) = A(O) - 0.63. Hence,

166
A (Ne) =» 8.2 ±0.1.

I would be quite willing to agree with Kaler that

planetaries probably show a large range in chemical

composition, although these approximate methods probably do not give good estimates for the heavier elements in any one nebula.

For fluorine, sodium, and others, I still recommend, as working estimates, the figures given at the

Tatranska Lomnica Symposium (Aller and Czyzak 1968) s A (F) = 4.9 A(S) = 7.9 A (Ar ) = 7.0 A(Ca) - 6.4

A(Na)= 6.6 A(C1)=6.9 A (K) = 5.7 .

All these approximations suffer from the fact that no proper account is taken of the modification of the

radiation field by the nebular gases and of the consequent change of ionization with distance from the cen- tral star. One must construct a model for the nebula,

in which the transfer equation and the equations of

statistical equilibrium are solved throughout the

nebular shell. At each point, then, the electron temperature and radiation field are obtained.

Such calculations have been undertaken by Williams

(1968), by Flower (1968, 1969) and by Harrington (1969).

It is, however, necessary to consider the inhomogeneities. A refined treatment in which account is also

taken of the rarer elements, fluorine, sodium, sulfur,

chlorine, argon, and others, is being developed by

Mrs. Buerger at Ohio State University and will be

applied to a number of nebulae.

ACKNOWLEDGMENT

This program was supported by the National Science

Foundation Grant No. GP23, 460.

167
REFERENCES

Aller, L.H. 1954, Ap . J. , 120_, 401.

Aller, L.H. 1956, Gaseous Nebulae, (London: Chapman & Hall) , 66.

Aller, L.H., and Czyzak, S.J. 1968, Planetary Nebulae,

I.A.U. Symposium 34, eds . D. Osterbrock and C.R.

O'Dell (Dordrecht, Holland: Reidel Publishing

Co.) , 209.

Bednarck, T.A. and Clarke, W. 1971 in press.

Bowen, I.S. and Wyse, A.B. 1939, Lick Obs. Bull., 19,

Flower, D.R. 1968, Planetary Nebulae, I.A.U. Symposium

34, eds. D. Osterbrock and C.R. O'Dell (Dordrecht

Holland: Reidel Publishing Co.), 205.

Flower, D.R. 1969 , M.N.R.A.S., 146, 171, 243.

Ford, K. and Rubin, V. 1971 in press.

Harrington, J. P. 1969, Ap. J., 156_, 903.

Hebb, M.H. and Menzel, D.H. 1940, Ap . J., 92, 408.

Kaler, J.B. 1970 , Ap. J., 160_, 887.

Kaler, J.B. 1971 in press.

Menzel, D.H. and Aller, L.H. 1945, Ap . J., 102 , 239.

Miller, J.S. 1971, Ap . J. Letters in press.

Mills, B.Y. and Shaver, P. 1967, Australian Journal

Physics , 2_1, 95.

Peimbert, M. and Costero, R. 1969, Boletin No. 31 Obs.

Tonantzintla, Taoubaya (Mexico)

Robbins, R.R. 1968, Ap . J., 151, 497.

Seaton, M.J. 1968, M.N.R.A.S., 139_, 129.

Walker, M.F. and Kron, G.E. 1971, quoted in Planetary

Nebulae, by L.H. Aller (Cambridge, Mass.: Sky

Publishing Corp.), Chap. 5.

Williams, R.E. 1968, Planetary Nebulae, I.A.U.

Symposium 34, eds. D. Osterbrock and C.R. O'Dell

(Dordrecht, Holland: Reidel Publishing Co.), 190.

168
RADIO RECOMBINATION LINES

Leo Goldberg

Harvard College Observatory

J. P. Wild (1952) pointed out that transitions

between levels of high quantum number in hydrogen would

occur at radio frequencies, although he assumed they

would overlap to form a continuum and would not therefore be observed as lines. In the solar flash spectrum,

for example, Stark broadening at chromospheric densities terminates the Balmer series at about n = 30. In

H II regions, however, where the density is about

10 ** cm , Stark broadening is relatively insignificant

for n < 200, and the line shapes are almost entirely

determined by Doppler broadening.

A few years later, Kardashev (1959) calculated the

theoretical intensities of- hydrogen recombination lines

with An = 1 and predicted that they ought to be observable in H II regions. Kardashev used a simple equation

expressing the ratio of the central line temperature to

the brightness temperature of the free-free continuum

as a function of electron temperature and line

frequency:

6.5 10

6" v (1)

For T = 10,000°K, this expression predicts intensity ratios varying from 1% at 1500 MHz to 20% at

30,000 MHz. Kardashev also suggested that similar

recombination lines of helium might be observed, but

displaced toward higher frequencies by 123 km/sec as required by the slight difference in Rydberg constants.

In 1964, Kardashev 1 s prediction was confirmee;

observation, first in the USSR (Dravskikh and Dravskikh

1964) and shortly thereafter in the USA (Hoglund and

Mezger 1965) . The first lines detected corresponded to

transitions with An = 1 . Such transitions from n + 1

169
to n are called na lines, and by analogy with optical

series, transitions from n + 2, n + 3, n+ 4, n + 5 ... to the same lower level n are called n3, ny , n6 , ne ... lines. na lines have now been observed in a large num- ber of H II regions over a wide range of frequencies

corresponding to principal quantum numbers as small as

n = 56 and as large as n = 253. Transitions with

An = 2 or more have also been detected. The corresponding helium lines have also been detected in many

of these objects as well as another set of lines, which

are almost certainly due to neutral carbon.

The intensities of radio recombination lines

depend on the level populations, and therefore the

departure coefficients bR for the high levels are of

interest. Since the bn values must approach unity

near the series limit, Kardashev argued that the level

populations could be calculated from the Saha-Boltzmann

equation. When the Kardashev equation is used for the

determination of temperature, however, the values

derived from the a-lines tend to be 30-40% smaller than

optical determinations, for example from the ratio of

forbidden line intensities. On the other hand, the 3 and higher-order lines yield temperatures more nearly

in accord with optical values. Three possible explanations of the discrepancy have been debated among radio

astronomers and theorists (Dupree and Goldberg 19 70)

(1) The assumption of thermodynamic equilibrium (TE) in

the calculation of level populations is incorrect. (2)

The optical determinations of electron temperature are

in error, possibly due to inaccurate cross sections for

the collisional excitation of forbidden lines. This

explanation implies that the electron temperatures of

H II regions are lower than previously assumed, by

30-40%, and also that some unexplained physical process

is attenuating the intensities of the higher order

lines. (3) The discrepancy is caused by inhomogeneities in the temperature and density of H II regions.

It now seems reasonably certain that the observations can be explained by a combination of departures

from TE and density inhomogeneities . In H II regions,

it is indeed true that the bn values of high atomic

levels are nearly unity, for example, bioo = 0.99 32 for

Te = 10 ,to K, ne = lO^cm" 3 (Brocklehurst 1970). However,

the most interesting consequence of departures from

thermodynamic equilibrium is not the slight reduction

in the absolute population of the levels, but the even

smaller deviation of the ratio of populations from

unity and its effect on the amount of stimulated emission, or negative absorption as I prefer to think of it.

In his first paper in the famous series on physical

170
rocesses in gaseous nebulae, Professor Menzel (1937)

Dinted out that in gaseous nebulae, negative absorption reduced the line absorption coefficient not by the

actor

B N

i _ mn m - i _ hv/kT

B N

1 e nm n

t by

v/kT

lere Bmn and Bnm are the Einstein coefficients of

bgative and positive absorption, respectively, and

here m is the upper and n the lower level of the tranjjLtion. In H II regions, hv is always << kT throughout

le radio frequency spectrum, and therefore the factor

lay be written

Bmn N (bm

- b ) bm hv

-, mn m _ m n_ _m , 9

, B N b b kT ' {Z) nm n n n

d In b b hv

n An + m

dn b kT

n

L en n is very large, v is proportional to An and

;nce we can put An = 1 and v = v a

. Before discussing

te significance of this expression, I would like to

.ow in Figure 1 how bn

is expected to vary with n, :cording to theoretical calculations by Brocklehurst

970) . Such calculations for high levels with n > 40

;re first made by Seaton (1964) to demonstrate the

feet of electron collisions on the populations of

gh levels. The rate at which electron collisions

ansfer atoms from one level with principal quantum

mber n to adjacent levels increases as n

1*. For the

nge of electron densities shown in Figure 1, collions are unimportant in populating levels with n < 20,

id the b^ values are accordingly independent of elecon density. As n increases, collisions become effecve at some value of n which depends on the electron

171
I I I I I I L I I

i i i i 60 100 140 180 220 260

n Figure 1. Departure coefficients bn

as a function of

principal quantum number n for T = 10,00Q°K and N =

10, 10% 10 3

, 10 h and 10 5 cnT 3

.

density, after which the bn values increase rapidly

towards unity.

Seaton (196 4) pointed out that the intensity per

unit frequency longward of the series limit, in the

region where the high series members overlap to form z continuum, is proportional to bn

, and that intensity

measurements near the Balmer and Paschen limits in th<

spectra of gaseous nebulae might give important information on physical processes. Coincidentaily , Seaton

calculations were published at about the time radio 1 recombination lines were first being observed and so '\ had an entirely different and unintended application.

The original calculations have since been superseded >

a whole series of more accurate ones, the latest of

which are by Brocklehurst (19 70)

Recently, we have used these calculations in con junction with measurements of the spectra of Orion A i and NGC 7027 obtained by J. L. Greenstein and I. S. j;I Bowen with the 200-inch telescope (Goad, Goldberg, an Greenstein 19 71) to derive values of the electron den,1 sity in the two objects. The points plotted in Figur

172
Figure 2. Experimental determination of departure coefficients b from intensity measurements near the Balmer

limit in tne spectra of NGC 7027 (open triangles) and

NGC 1976 (Orion A) (filled circles) . The curves are theoretical predictions for T = 10,000°K, Ne =

4 x 10 5 cm" 3 (NGC 7027) and for T = 10 f 000°K, Ne =

1 x lO^cm" 3 (NGC 1976). (Goad, Goldberg and Greenstein

1971) .

2 are the empirical values of bn derived from the spectra, whereas the curves are predicted from theory. For

Orion A, the best fit is obtained with T = 10,000°K and

N

e = 1 x I0 k cm"" 3 and for NGC 7027, T = 10 ,000°K and

Ne = 4 x io 5 cm

-3

. The curves are relatively insensitive to temperature. The electron densities are in

I fairly good agreement with values derived by other

i methods (Saraph and Seaton 1970; Hjellming and Davies

II 1970).

173
As shown in Figure 3, d In bn/dn is always positive and larger than hv/kT over a large range of n. Accordingly, the line absorption coefficient is negative. As n increases, d In b /dn passes through a max'

imum at some value of n depending on the electron density and then gradually decreases toward 0, For a given value of Ne

, there is always a value of the prin^

cipal quantum number, say n 0

, at which the d In b^/dn

and hv a/kT curves intersect and which increases with

decreasing electron density. At this point, the populations of the upper and lower levels of the transitioi

are equal; positive and negative absorption exactly

balance, and the gas is optically thin to the line

radiation, no matter how great the optical depth in tlu

continuum. In Figure 1, the intersection occurs at

n = 130 for N = 10 5 cm" 3

, and at n = 210 for N =

174
10 h cm

-3

. To the left of the intersection point, the

level populations are inverted and the line intensities

may be amplified above their LTE intensities by partial

maser action. The degree of amplification depends not

only on the electron temperature and density but also

on the optical depth in the continuum and therefore on the emission measure, but in the limit of very large

optical depth, the intensity is independent of 1

1

emission measure (Dupree and Goldberg 1970). To the

right of the intersection, the level populations are no longer inverted and approach their equilibrium values

jas n increases. Since the absorption is now positive,

(large optical depth in the continuum causes the lines

to vanish.

Physically, the effect of inverting the level populations is to decrease the total absorption coefficient in the line plus continuum and thereby to

decrease the optical depth and increase the source

function. The theory has been well worked out, and

extensive and detailed numerical calculations have been

performed (Hjellming et al. 1969; Andrews and Hjellming

1969) for a, 3, y , 6, and z lines in the range of quantum numbers from 40 to 220 and for a variety of combinations of temperature, electron density and emission

measure. To be successful, the theory has to explain

two anomalies that arose earlier in the interpretation

'of the data by TE theory. The first is that the a-line

intensities are generally higher than predicted with

optically determined temperatures, and the second is

that the intensities of higher order lines were usually

found to be weaker than expected relative to a-lines

observed at nearly the same frequency. Qualitatively,

both discrepancies could be explained by the non-LTE

theory because higher order lines are amplified less

than a-lines. The difficulty was that the required

degree of amplification demanded somewhat higher electron densities and considerably higher emission measures for objects like Orion A than would have been

expected from other types of optical and radio measurements . Hjellming and Churchwell (1969) seem to have

explained this anomaly, however, by postulating that

[most of the recombination line radiation originates in

! small clumps of relatively high density. Since the

'intensity is weighted by the square of the electron density, the emission comes mostly from the clumps of hi N

g and high emission measure. Various methods have

been devised for the estimation of mean values of the

nebular parameters by comparisons between theory and

Observation (Hjellming and Churchwell 1969; Goldberg

and Cesarsky 1970; Hjellming and Gordon 1971).

175
TABLE 1 PARAMETERS OF H II REGIONS DERIVED FROM

RADIO RECOMBINATION LINES

Object T(°K) N (cm" 3

) E(pc cm"" 6

) Orion A

M17

W3 (IC 1795)

10,000

8,000

11,000

2.5 x 10"

3.8 x 10 4 7.7 x 10 4 1.26 x 10 7 1.0 x 10 7 4 x 10 7 ~6 x 10 6 ~5 x 10 6 <2 x 10 6 W43

M16

5900-8000

NGC 2024

-7250

-7500

From R.M. Hjellming and R.D. Davies , 1970, Astron. and

Ap . , 5_, 53 . Table 1 shows mean values of the three parameters

derived by Hjellming and Davies (1970) for a number of

H II regions.

Helium recombination lines have now been observed

in more than fifteen H II regions, their radial velocities indicating they are formed in the same region as the hydrogen lines. The relative widths of the hydrogen and helium lines are a measure of the election

temperature, and their relative intensities may provide

one of the best indicators of the helium abundance in

the Galaxy. The ratio of intensities is in fact identical with the ratio of abundances if ionized hydrogen

and singly-ionized helium occupy the same volume, since

recombination theory predicts that departures from TE

in the level populations will be the same for both

hydrogen and helium. A recent summary by Churchwell

(1970) classifies northern H II regions in three group.,

according to their ionized helium abundances as shown

in Table 2. Optical determinations of ionized helium

abundances in Group I objects, when they are available,

agree with the radio results, but they also suggest

that neutral helium adds 1-3% so that the total abundance ratio is about 10% by number. Theoretical calcu

lations also suggest that the sizes of H+ and He+

regions are the same if the density is uniform and the

ionizing stars are of sufficiently early type.

Clumping of the gas, which has been inferred from the

interpretation of the hydrogen lines, would increase

HELIUM LINES

176
TABLE 2 ABUNDANCE RATIO IONIZED HELIUM TO IONIZED HYDROGEN

DERIVED FROM RADIO RECOMBINATION LINES IN H II REGIONS

Source N(He+)/N(H+)

GROUP I IC 1795 0 .077 + 0.013

)rion A 0.083 ± 0.005

*CW 38 0.140 + 0.030

:arina I 0.088 + 0.042

ICVI 57 I 0.088 + 0.025

RCW 57 II 0.130 + 0.034

>KS 1549-54 0.116 ± 0.057

>KS 1618-50 0.099 ± 0.038

6357 0.083 ± 0.012

18 0.093 ± 0.037

117 0.091 + 0.008

151 0.085 + 0.010

GROUP II

GC 6334 0.059 ± 0.020

|IGC 6357 0.054 ± 0.014

tf43 0.057 ± 0.012

749 0 .061 ± 0.012

GROUP III

5gr < 0.019

5gr < 0.041

Sgr < 0.021

IGC 7538 < 0.060

)R 21 < 0.111

iJGC 2024 < 0.02

rom E. Churchill, 1970, Thesis, University of Indiana

:he proportion of neutral helium, and therefore 10% is

:onsidered to be a lower limit. The ionizing stars

relieved to be associated with most of the Group II

objects are very hot, and therefore it is conjectured

-hat the Group II objects may exhibit an unusually high

degree of clumping.

Among the Group III objects, NGC 2024 is known to

177
be a low excitation object. Recently, the helium lines

85a and 109a have been detected by Cesarsky (1971) who

finds an abundance ratio to hydrogen of 0.017 - 0.020,

which is within the upper limit given by Churchwell.

Of the remaining objects, both DR 21 and NGC 7538 may

have considerable He++, but the small lower limits

shown by the three galactic center sources have not

been explained and may imply a real deficiency in the

helium abundance toward the galactic center.

CARBON LINES

In addition to the hydrogen and helium lines,

recombination lines of an element of higher atomic

weight have been detected in seven H II regions at sev- eral frequencies from 1425 MHz to 10,527 MHz. There

are three reasons why the element can probably be identified as carbon in a region in which the hydrogen is

predominantly neutral:

(1) If the line is assumed to be carbon, the

radial velocity frequently differs from that of the

companion hydrogen line but is in much closer agreement

with available measurements of the 21-cm absorption

line.

(2) Carbon is the most abundant element with an ; ionization potential less than that of hydrogen.

(3) The central intensity of the carbon line in

NGC 2024 is stronger relative to hydrogen than in any

other H II region. Last year we observed the hydrogen

166a line with unusually high spectral resolution (Bal.

et al. 19 70) and found a narrow component superposed o|

the profile but displaced from the line center by +5.0

km/sec, which agrees with the relative displacement of;

the carbon line to well within the experimental error.

In other words, the separation of this line component

from the carbon line is exactly the amount expected

from the difference in Rydberg constants. L Recently, a similar component of the hydrogen lin

has been observed at three other frequencies in the J same object, by Chaisson (1971) at 8 GHz (9 4a) and by „ Cesarsky (1971) at 10 GHz (85a) and 3*2 GHz (I37a)

The observations are summarized in Table 3. The radial

velocities derived for both the hydrogen and carbon

lines at the four frequencies are in good agreement.

If we assume that the carbon is fully ionized and that

its abundance relative to hydrogen is 4 x 1G~ 4

, we car infer the fractional ionization of hydrogen in the H J region. The derived value of 2 x 10" ^ is in satisfactory agreement with theoretical calculations on the

178
TABLE 3 C (H I) , H (H I) AND II (H II)

LINE PARAMETERS IN NGC 2024

Line T

L VLSR (km/sec) n( H+)/n(C+)

H T T 1 J. 0.70 ± 0.01 C C. 4- 1 H I 85a 0.03 ± 0.01 9.5 ± 1 0 . 3 ± 0.25

C I 85a 0 . 11 ± 0.01 10.0 ± 1 H

T T y 4 a 0.42 ± 0.01 c n + U . Z H I 94a 0 . 024± 0.01 9. 1 ± 1.5 0 . 8 ± 0.6

C I 94a 0 . 049± 0.01 9.3 ± 0.7

H

T T iu y a 0.67 ± 0.01 r tr _i_ 1 H

TJ. < 0

.

04

c I 109a 0.11 ± 0 .02 10.4 ± 1 H II 137a 0.39 ± 0.05 5.1 ± 1 H I 137a 0.07 ± 0.05 9.4 ± 3 0. 56± 0.5

C I 137a 0.18 ± 0.05 10.3 ± 0.7

H II 157a 0.16 ± 0.03 3.2 ± 1

H I 157a 0.075± 0.04 8.2 ± 1 0. 68± 0.5

C I 157a 0.168± 0.05 8.8 ± 3 ^Sources are given in the text.

ionization of H I clouds by low energy cosmic rays

J (Field et al. 1969) . It seems highly probable that the carbon lines are formed in cool, dense clouds or condensations in which

'the hydrogen is mostly neutral. The clouds also seem

[to be close to or embedded in H II regions. For example, no lines have been observed in non-thermal sources.

But the exact physical parameters of the clouds are

(jstill unknown and the subject is controversial. The

j one thing that seems certain is that the lines are not

formed in TE , because they appear in emission even when

the brightness temperature of the background H II con- tinuum is as high as several thousand degrees, despite

Jthe fact that the temperature of the line forming

region is probably less than 100°K. Following a suggestion by Zuckerman and Palmer (1968), Mezger,

jChurchwell and Hjellming (Churchwell 19 70) have proposed that the lines are formed in dense, cold condensations, which they identify with prestellar objects in

179
which Te = 12 °K and - 10 6 cm" 3

. The high density is

needed to keep the hydrogen neutral against the ionizing radiation field. In TE, the optical depths at

the line center are >> unity (on the order of 10 3

) and

would produce strongly saturated absorption lines. If

TE is not assumed, the optical depth in the line may be

expressed as t = bn

3x L

* (Goldberg 196 8) where xL

* is

the optical depth the line would have in TE and

In the Mezger-Churchwell-Hjellming model, bn

$ must take

on small positive values, in order to reduce the line

absorption coefficient and thereby increase the source

function so that the lines can appear in emission

against the continuum of the background H II region.

Churchwell (19 70) has shown that in condensations

dense enough to maintain neutral hydrogen, the carbon

will nevertheless be completely singly-ionized, but a more detailed treatment by Werner (19 70) of the absorbing effects of dust shows that the carbon will remain

neutral for hydrogen densities greater than about

10 3 cm" 3

. However, the line might still be emitted

from the outer periphery of the condensation.

Our own explanation of the carbon line (Dupree and

Goldberg 1969) is based on the following argument.

Strong 21-cm absorption is frequently observed against

the background continuum of H II regions, and agreement

in radial velocity and line width suggests that the

carbon line is formed in the same region as the 21-cm

line. Neutral hydrogen densities derived by Clark

(196 5) from Orion A observations of the 21-cm line are on the order of 100 cm" 3

, which would correspond to an electron density of about 0.1 cm" 3 at most. At such

densities, level populations should be strongly

inverted at quantum numbers of about 100, and only a slight amplification of the background H II continuum,

by as little as 0.1%, would be sufficient to account

for the observed line intensities. It must be realized

however, that the number density is derived from the

column density by assuming the cloud is roughly spherical. The true densities could be much greater if the

cloud is highly flattened along the line of sight.

Theoretical calculations of departure coefficients

(3)

180
under conditions found in H I regions and high resolution mapping of the emitting sources are needed to

clarify the mechanism of the carbon line emission.

REFERENCES

Andrews, M.H. , Hjellming, R.M. 1969, Ap. Lett., 4, 159.

Ball, J. A. , Cesarsky, D. , Dupree, A.K. , Goldberg, L.

,

and Lilley, A.E. 1970, Ap. J. , 162, L25.

Brocklehurst, M. 1970, M.N.R.A.S. , 14_8, 417.

Cesarsky, D. 1971, in preparation.

Chaisson, E. 1971, in preparation.

Churchwell, E. 1970, Thesis, University of Indiana.

Clark, B.G. 1965, Ap. J., 142, 1398.

Dravskikh, A.F. and Dravskikh, Z.V. 1964, Astron.

Tsirk. , 282 , 2.

Dupree, A.K. and Goldberg, L. 1969, Ap. J., 158 , L49

.

Dupree, A.K. and Goldberg, L. 1970, Ann. Rev. Astron.

and Ap. , 8, 231.

Field, G. , Goldsmith, D.W. and Habing, H.J. 1969,

Ap. J. , 155, L49.

Goad, L., Goldberg, L. and Greenstein, J.L. 1971, paper

presented at 134th Meeting Amer. Astr. Soc.

,

Baton Rouge, La.

Goldberg, L. 1968, Interstellar Ionized Hydrogen , ed.

Y. Terzian (New York: W.A. Benjamin, Inc.).

Goldberg, L. and Cesarsky, D. 1970 , Ap . Lett., 6_, 93.

Hjellming, R.M. , Andrews, M.H. and Sejnowski, T.J. 1969,

Ap. Lett. , 3, 111.

Hjellming, R.M. and Churchwell, E. 1969 , Ap. Lett., 4_, 165.

Hjellming, R.M. and Davies, R.D. 1970, Astron. and Ap .

,

5, 53.

Hjellming, R.M. and Gordon, M.A. 1971, Ap. J., 164, 47.

Hoglund, B. and Mezger, P.G. 1965, Science, 150 , 339.

Kardashev, N.S. 1959, Astron. Zh. , 36./ 838 - Menzel, D.H. 1937, Ap. J., 8J5, 330 . Saraph, H.E. and Seaton, M.J. 1970, M.N.R.A.S. , 148 , 367.

Seaton, M.J. 1964, M.N.R.A.S. , 127 , 177.

Werner, N.W. 1970, Ap. Lett., 6, 81.

Wild, J. P. 1952, Ap. J., 115, 206.

Zuckerman, B. and Palmer, P. 1968, Ap . J., 153 , L145.

181
INTERNAL MOTIONS AND KINEMATICS OF

PLANETARY NEBULAE

William Liller

Harvard College Observatory

The earliest astronomical reference to Donald

Howard Menzel appears in Harvard Bulletin 113, written

almost 50 years ago:

"Mr. D. H. Menzel has recently found approximately

two thousand nebulae on ninety photographs made at

Arequipa, with the 24-inch Bruce telescope. . .nearly

20,000 nebulae are now recorded. approximately twentyfive per cent have been found at the Harvard Observatory, (signed) H. Shapley, August 1, 1922."*

According to Harvard Bulletin 111, five of the new

nebulae were in fact planetary nebulae, although actually only three were new. These are listed in the

Perek-Kohoutek Catalogue of Galactic Planetary Nebulae

as 322-2°l, 329-2°2, and 331-1°1. We feel it appropriate to show, in Figure 1, a reproduction of the first

planetary discovered by young Mr. Menzel.

In a review article written only four years later,

Menzel (1926) brashly attributed "the curious doubled

lines" seen in the spectra of many planetary nebulae to

the Doppler effect. Because he was the first to do so publicly, it is particularly fitting to review at this

time the state of our knowledge of the internal motions

and kinematics of planetary nebulae.

At the outset, we stress that 9 8 per cent of the mass in a planetary nebulae is contained in hydrogen

and helium. Thus through collisions, heavier elements

*It should be noted that Professor Menzel frequently wrote popular articles on science (and science

fiction) under various pseudonyms such as Don Home,

Charles Howard, and Charles Bahama. Possibly, earlier

papers exist but it would seem unlikely since neither

Professor Menzel nor his secretary for more than 20

years, Miss Beaudoin, could recall such literary offerings .

182
Figure 1. Mz 1 alias 322-2 a l, the first planetary nebula discovered by D. H. Menzel. Pencil drawing made

from the photograph that appears in the Perek-Kohoutek

Catalogue of Galactic Planetary Nebulae.

183
must quickly absorb the momentum carried by these two

constituents and assume a velocity close to that of the

surrounding atoms and ions. Different velocities

derived from the radiation of different ions therefore

reflect the stratification of these ions within the

nebula and the dependence in some way of the velocity

on distance from the central star.

Secondly, apparent outward (or inward) angular

motion of the nebular edge may result from increased

(or decreased) excitation and ionization. In the formula for the radius of the ionization or Stromgren

sphere, we find such factors as the temperature and

luminosity of the exciting star, and the density and

composition of the intervening gas. Thus a nebula that

grows steadily in angular extent may in fact be much

larger than observed and may be undergoing internal

changes that have nothing to do with the gas motions

Basically, two techniques are available for investigating the kinematical structure of a planetary

nebula: spectrography and astrometry. Each will be

discussed now in some detail.

At a temperature of 10,000°K, the root-mean-square

velocity of an oxygen atom is 3.2 km/s; for hydrogen it

is 4 times greater. A high resolution optical spectrograph can reach these velocities and resolve lines separated by even smaller amounts. The pioneering work of

Campbell and Moore (1918) and the later work of 0. C.

Wilson (1950) and of Osterbrock and his associates

(1966) have fully exploited the attainable photographic

resolution. Increased efficiencies have come through

the multi-slit technique used well on planetaries by

Wilson (19 58) and by G. Munch (19 68) . Fabry-Perot

interferometry makes possible the precise measurement

of numerous local velocities from one photographic

plate, since wavelength shifts corresponding to around

1 km/s cause detectable distortions in the circular pat

tern produced by constructive interference at different

orders. Some of the earliest experiments of Fabry

(Fabry and Buisson 1911) used gaseous nebulae for study

subjects. More recently Ring and his colleagues

(Davies, Ring, and Selby 1964), Vaughan (1967), Courtes

(1960) , and Picmic (19 71) have carried experimentation

with interferometers to a high degree of sophistication

Measurements of the increase in angular size of

planetary nebulae have been made successfully by

Latypov (1957), Liller (1957), Liller, Welther, and

Liller (1966), and Chudovicheva (1964). Probably the

best photographic material has been only partly

reported (Liller and Liller 1968) , and the final

results are in preparation. In every instance, the pro

184
cedure involved detailed comparison of old and m

plates taken with the same instrument. Intervals between plates ranged up to 62 years (Crossley reflector,

Lick Observatory) at plate scales as high as 5 .

0

seconds/mm (Mount Wilson 100-inch Cassegrain) . The

final mean errors attainable amount to a few tenths of an arc second per century, with the results never being

larger than ten times this amount. While routine astro

metric procedures are usually followed in the reduction

the plates have inherently several unique error sources Included among these is the "spiky" distribution of

energy in planetaries and the happenstance that singly

ionized oxygen has a strong pair of lines in the near ultraviolet (3726, 3729 A), and doubly ionized oxygen

has a strong pair of lines in the green (4959 , 5007 K) . Differing spectral response, caused by the conversion

around 19 30 from silver to aluminum for mirror coatings

and the improved emulsion sensitivity in the green, can affect the importance of these radiations and confuse

the results. Fortunately, many discrete features such

as sharp knots and filaments exist in planetaries, and

the green nebular lines so dominate their spectra that

they are monochromatic for all practical purposes.

O. C. Wilson's classic work (1950) reveals outward

expansions of up to 57 km/s (NGC 2392) , but even in

this planetary zero velocities occur for quadruplyionized neon, which is found only in the inner regions

of the nebula. In general one finds a good linear cor- relation between outward velocity and monochromatic

image diameter for radiations of differing levels of

excitation and ionization, leading us to conclude that

on the whole particles move outward with speeds that

increase in proportion to distance from the center.

The results for hydrogen are somewhat less well determined since these spectral lines are not as sharp as those from heavier ions. Such a phenomenon would be

expected since the root-mean-square kinetic velocities

of hydrogen atoms are always a sizeable fraction of the

expansion velocities. The detailed line-shape studies

of Osterbrock and his associates (Osterbrock, Miller,

and Weedman 19 6 6; Weedman 19 68) reveal that lines of H,

He II, [0 III], and [N II] are wider than the expected

thermal Doppler widths and therefore establish that

significant mass motions exist within planetary nebulae

Moreover, these authors find that the distribution of

emission with radial velocity has a rather well-defined

peak, which suggests that the heavier ions make excellent markers in the general nebular wind.

Multi-slit observations have permitted Wilson

(1958) and G. Munch (1968) to derive models for specifi

185
nebulae; Wilson for NGC 7662 and Munch for NGC 6543.

The latter nebula appears to consist of two spiral filaments, which are placed like opposing corkscrews ema- nating along the line of sight from the central star.

To reach nebulae of low surface brightness such as NGC 6853 (the "Dumbbell"), Bohuski, Smith, and Weedman

(19 70) employed a pressure-scanned Fabry-Perot interferometer tuned to Ha and to singly ionized nitrogen at

A6584. While the width of each of the nitrogen components averaged 14.5 km/s , comparable to the spectrographs results of Osterbrock et al. (1966) , Bohuski et

al. found the hydrogen line at the center of the nebula

to present a broad profile of half width 75 km/s. They

conclude that the hydrogen emission is spread throughout much of the nebula while the [N II] emission is

restricted to a thin spherical shell.

A similar approach by Carranza,, Courtes , and

Louise (1968) to NGC 7293 (the "Helix") shows it to

have a radial expansion velocity of 37.4 km/s in the

light of [N II]. However, they were unable to fit a regular helical pattern to the observations.

The first apparently successful measurement of the

increase in angular size of a planetary nebula was by

Latypov, who found from astrograph plates (60 "/mm plate

scale) that the Ring Nebula (NGC 67 20) expands at a rate of 0'.'9 ± 0 71 per century. However, Liller,

Welther, and Liller (1966) , using Crossley reflector

plates (387 7/mm) taken over a 6 2 year base line, were

unable to confirm this result. More recent results by

the Lillers (see Figure 2) give insight into the disagreement. The points plotted here were derived from

Mount Wilson plates taken at the Cassegrain focus of

the 60-inch and the Newtonian focus of the 100 -inch

telescopes, most of which show greater filamentary

detail than do the Crossley photographs and presumably

those taken with the Soviet astrograph. As might be

expected, edges present complications in both the measurement and the analysis. The difficulty of measuring

a diffuse edge is far greater than locating a diffuse

filament, simply because of the asymmetry involved.

Furthermore, seeing problems, changes in emulsion contrast, and possibly sensitivity differences can all add

uncertainties that are difficult to evaluate. With the

high plate scale and good seeing available with the

Mount Wilson photographs, we find the new filament measures definitely superior to any other results. Expansion data for NGC 2392, 6818, and 7662 have already

been published (Liller and Liller 196 8) ; other results

will appear soon in Publications of the Astronomical

Society of the Pacific. In all, some 22 planetaries

186
EDGES

FILAMENTS

I

20 40

Figure 2. Radial expansion rate in arc seconds per cen- tury as a function of radius for NGC 6720 (the Ring Nebula) . The error bars are twice the mean error in

length; the x's mark the weighted means of filament and

edge measures. From Mount Wilson photographs.

have now been studied with Mount Wilson plates by Mrs.

Liller and myself.

From a comparison of the spectrographic and astrometric results, one can draw limited conclusions about

the distances of planetary nebulae, since for a spherically symmetric object the distance

d = 100 V,

4.74 0 parsecs

where VR

is the outward velocity of the gas and 8 is

the angular motion nerpendicular to the line of sight

measured in arc seconds/century. The problem is in

identifying the appropriate 9 and VR since both usually

have a spread of values, which depend on the distance

from the central star. Another possible source of error is an asymmetry, which would cause the gas in one plane of the nebula to move outwards with a velocity

different from that of the gas in another plane.

Liller, Welther, and Liller (1966) have, nonetheless,

187
made a general analysis of distance scales and find

that for optically thin nebulae, Shklovsky's (1956) dis

tance scale appears most reliable, while for all other

planetaries the Minkowski (1965) distance scale is best

These results have recently received confirmation from

Heywood Smith Jr. (1971).

Another valuable use for the results of motion

studies is to test and evaluate models of planetary

nebulae such as those described by Mathews (1966)

,

Turoff (196 5) , and others. For example, Mathews has

pointed out that both angular velocity data and com- puter models occasionally yield inward motions, especially at the inner edge of a ring. (Note Figure 2!)

Finally, there exist a number of planetaries that

present special problems of interest. The conspicuous

ansae of NGC 7009 (the "Saturn" nebula) move outward at

a velocity close to the value one would predict from a linear extrapolation of the inner region velocities.

The "rim" of certain planetaries near the galactic

plane moves outwards at a lower velocity than one might

predict by linear extrapolation, suggesting that the

rim is caused by a piling up of material resulting from

the interaction of the expanding nebula with the interstellar medium.

Lastly we mention the comet-like condensations on

the inner edge of the Helix nebula, NGC 729 3. The

three brightest condensations move outwards with a velocity of 0V88 ± 0 V 44/century , and if we take the dis

tance of the nebula to be 100 pc, as the parallax data

suggest, this angular velocity corresponds to a linear

velocity of only 4.2 ± 2.1 km/s . Recently, VorontsovVelyaminov (196 8) predicted that the outward velocities

of these knots, accelerated by the stellar wind, should

be high, perhaps close to 100 km/s. Such a velocity is

clearly far too large for consideration.

In the following paper, Professor Menzel will com- ment further on these interesting features in NGC 729 3.

188
REFERENCES

Bohuski, T.J., Smith, M.G., and Weedman, D.W. 1970, Ap.

J. , 162_, 27.

Campbell, W. , and Moore, J.H. 1918, Pub. Lick Obs. Bull

13, 75.

Carranza, G. , Courtes, G. and Louise, R. 1968, in

Planetary Nebulae , ed. D.E. Osterbrock and C.R.

O'Dell (New York: Springer Verlag) , p. 249.

Chudovicheva, O.N. 1964 , Izv. Pulkovo Obs., 23_, 154.

Courtes, G. 1960 , Ann. Astrophys., 23_, 155.

Davies, L.B., Ring, J. and Selby, M.J. 1964, M.N. , 128 , 399.

Fabry, C. and Buisson, H. 1911, Ap . J., 33, 406.

Latypov, A. A. 1957, Pub. Astron. Obs. Tashkent (2), 5,

31.

Liller, M. and Liller, W. 1968, in Planetary Nebulae,

ed. D.E. Osterbrock and C.R. O'Dell (New York:

Springer Verlag), p. 38.

Liller, M.H., Welther, B.L. and Liller, W. 1966, Ap . J. 144 , 280.

Liller, W. 1957, P.A.S.P., 69_, 511.

Mathews, W.G. 1966, Ap. J., 1£3, 173.

Menzel, D.H. 1926 , P.A.S.P., 38_, 295.

Minkowski, R. 1965, Numerical Data and Functional Relationships in Science and Technology , ed. H.H.

Voigt (Berlin: Springer Verlag) Group VI, 1, 566.

Munch, G. 1968, in Planetary Nebulae, ed. D.E.

Osterbrock and C.R. O'Dell (New York: Springer

Verlag) , p. 259

.

Osterbrock, D.E., Miller, J.S. and Weedman, D.W. 1966,

Ap. J. , 145, 697.

Picmis, P. 1971, private communication.

Shklovsky, I.S. 1956 , A. J. (U.S.S.R.), 33_, 222 , 315.

Smith, Haywood, Jr. 1971, Astron. J. , 76_, 193.

Turoff, M. 1965, A Computer Model for Planetary Nebulae

(Ph. D. Thesis, Brandeis University).

Vaughan, A.H., Jr. 1967, Ann. Rev. of Astr. and Ap . , 5, 139.

Vorontsov-Velyaminov , B.A. 196 8, in Planetary Nebulae,

ed. D.E. Osterbrock and C.R. O'Dell (New York:

Springer Verlag), p. 256.

Weedman, D.W. 1968, Ap . J., 153 , 49.

Wilson, O.C. 1950, Ap . J., Ill, 279.

Wilson, O.C. 1958, Rev. Mod. Phys., 30, 1025.

189
FILAMENTARY STRUCTURE OF PLANETARY NEBULAE

Donald H. Menzel

Harvard College Observatory

The largest and presumably the nearest of all

planetary nebulae is NGC 7293, often referred to as the

Helical Nebula in Aquarius. Various determinations

have been made of its distance. I shall adopt the

value of 60 parsecs as representative. The observed

angular radius of the outer ring, 400", thus leads to a value of 24,000 Astronomical Units or 3.6 x 10 1

cm for

the true radius.

A remarkable feature of this nebula (see Figure 1)

,

first discovered by Walter Baade, is the filamentary

structure of the inner portion (see Sky and Telescope , 13 , 302, 1954). These filaments are cometary in

appearance, each with a well-defined "head" and with a "tail" stretching radially away from the nuclear star.

B. A. Vorontsov-Velyaminov (1967) and G. A.

Gurzadian (1967) have both briefly discussed this filamentary structure. They have also noted the existence

of condensations or "clots" on the inner end of the

radial filament. Gurzadian points out a possible analogy between the nebular structure and the interaction

of the solar wind with the heads of comets.

In most models of planetary nebulae, the gaseous

envelope is regarded as a uniform, continuous shell,

presumably ejected from the star by some type of nova

action. The shell, expanding indefinitely, eventually

dissipates into space and vanishes.

Alternatively, in this paper I plan to investigate

various properties of a model planetary composed of some large number, N, of orbiting structures resembling

comets, whose tails are responsible for the filamentary

structure. The orbits, I shall suppose, are elliptical

The periods would be of the order 4 x 10 6 years. I further assume that this shell probably originated long

ago, perhaps as condensations from nova ejecta. Alternatively, the structures may simply be debris left over from the original contraction of a large mass of gas

into a star.

190
Figure 1. NGC 7293 planetary nebula in Aquarius.

Photographed in red light; 200-inch photograph. (Hale

Observatories)

I am fully aware that C. T. Daub (1963), G. B.

'Field (1965) , and S. Sofia (1966) have concluded that

such condensations cannot form. Since the observations

speak for themselves, I feel that some special conditions, not envisaged in the assumed initial conditions,

are able to produce condensations. Magnetic fields may

well be the missing link in the evolutionary process.

Certain data relating to the nebula and nucleus

are relevant. For the hotter range of nuclear stars,

application of the Zanstra-Menzel theory gives a mini-

: mum surface temperature for the nuclear star. Most of

the stellar radiation lies in the far ultraviolet,

; where it can ionize hydrogen atoms. Of this energy,

one-fourth can appear as radiation in the visible spec-

| tral range. The remainder goes to produce Lyman a. -The total energy of the nebula, in the visible region,

therefore will be

T

k B = AG -— (1) n 4

191
where T is the surface temperature and A the area of

the star. The apparent brightness of the nuclear star

will be, by Planck's law,

B = A

s

2irh v dv

hv/kT

e ' -1

(2)

ro A

2-rrkT v

2 dv = A2 TrckT [ — J

where X

1 and X

2 represent the wavelengths of the shortand long-wave limits of plate sensitivity. The approximation is valid because hv/kT << 1 for the photovisual region. Let mn and ms be the observed apparent

magnitude of "nebula and star. Then the ratio of brightnesses

B /B

n' s (2.512)

m - m

s n

(3)

Let

1.5 x 10 1 3 (4)

for A

1 = 3500& and X2 = 5000A.

The foregoing equations thus lead to

n , t-. m - m

T

3 =

irrk£F (2-512) s

m - m

12/ ^ s n 9.2 x 10 1Z (2.512)

192
por NGC 7293, mn

= 7.5 and ms = 13.5. Hence we obtain,

as the stellar temperature, the value of

T = 6 icr °k (6)

This figure is a minimum; it will be greater if the

nebula does not completely absorb the radiation beyond

the Lyman limit.

The absolute magnitude of the nuclear star is

about 9.6. Elementary calculations show that the

buclear star is very small, perhaps even smaller than

the Earth. This means that despite the star's high

surface temperature, the effective temperature of the

burrounding nebula cannot be raised by direct absorption of its radiation. The effective black-body temperature that a star can produce varies inversely as

{the square root of the distance from its center. Hence

Ithe effective T of the Sun at a distance of 1 A.U. is

about 425°K. At a distance of only 1000 A.U., a small

fraction of the diameter attributed to NGC 729 3, the

['effective temperature would be only 13°K, a value far

too small to melt or vaporize the icy structure of an ordinary comet. For the nuclear star of NGC 7 293, this

figure would increase by perhaps a factor of 10. But

again, it appears that the ' comet- like structures cannot

pe ordinary comets of the solar-system variety.

To estimate the density of NGC 7293, let us com- pare it with NGC 766 2, for which the data are well

<nown (Table 1) . The quantity Am/sq min represents the

(quantity applied to mn to give the surface brightness

l n , in magnitudes per square minute of arc:

nd

Am/sq min = 2.5 log it + 5 log A"/60 (7

H = m + Am/sq min . (8) n n TABLE 1

(NGC R" Rxl0~ 17 cm dist,pc m

n Am/sq min H

n 7662 8 1.43 1200 8.7 -3,11 5.6

7293 400 3.6 60 7.5 +5.4 12.9

19 3
The difference of 7.3 magnitudes in surface brightness

between NGC 7662 and NGC 729 3 corresponds to a ratio of

832, which agrees well with the value of 600, determined observationally by H, D. Curtis (1918)

Let us determine the electron density of the

nebula from equation (13) given by Menzel and Aller

(1941)

N = 1.84 x 10"T 3/4 exp(-X /2) (2.512)~H

3 /2 (Rb) 1/2

(9) e f h wherein T now represents the electron temperature,

the surface brightness of the nebula in the light of

the second member of the Balmer series, h h the dimensionless factor describing departure of the gas from

thermodynamic equilibrium at temperature T (Menzel

1937) , and

x^ = hv^AT = 9.8 x 10 3 /T . (10)

From comparison with other nebulae, we may set

* 0.16 and T = 10 lfo K. Also let

H„ = H + AH (11

Again, from other nebulae, we may take AHo = 1.6, so that Hg = 14.5. With R = 3.6 x 10 17

cm, we thus obtain

for the electron density of the nebula, Ne = 60/cm 3

. This figure is based on the assumption that the

nebula is a homogeneous sphere. However NGC 729 3 is

clearly far from homogeneous. It seems to possess an outer shell consisting of two intertwined loops, in

addition to the cometary condensations previously discussed. If only a fraction, , of the spherical voluircontains an appreciable amount of matter, we must

increase the previously-calculated electron density byj a factor of $>~^.

I have estimated the apparent magnitude of the

typical filament at about 16.5. Since the nebula is

about nine magnitudes fainter than the filament, we should need about 4000 such filaments, if all were of

the same brightness, to account for the nebular luminosity. Their dimensions on the photograph appear to]

be about 2" x 2" x 20", corresponding to a volume of some 80 sec 3

. The corresponding volume of the nebula

19 4
is about 2.7 x 10 8 sec 3

. The volume of the 4000 filaments would be only 3 x 10 5

, so that the ratio, <j)

,

would be about 1/900. The mean density of the filaments would be about 30 times greater than the mean

density previously calculated, or Ne ^ 1800/cm 3

. This

figure does not appear to be extreme or excessive. It

is in line with or even slightly smaller than the mean

electron densities for many other brighter planetaries

(Menzel and Aller 1941; Liller and Aller 1954).

We have seen that radiation from the central star

cannot produce appreciable heating of the nucleus of

the filament. One can also show that the heating

effect of the hot, tenuous electron gas is likewise negligible. The equilibrium temperature of the radiating

surface will be only a few tenths of a degree absolute.

How, then, are we to explain the observed filamentary

structure of the nebula? Gurzadian has suggested a corpuscular stream analogous to the solar wind, but

this factor, too, seems to be quantitatively insufficient.

My estimates lead to the volume of filament about

6 x 10 cm 3

. With 1800 atoms of hydrogen per cm 3

, the

total mass comes out to be some 3 x I0 26

g, a figure

that agrees roughly with the slightly smaller value of

5 x 10 g suggested by Vorontsov-Velyaminov , who

further argues that the forces forming the radial filament must somehow derive from the nuclear star. He

favors the view that the filaments represent matter

ejected from the central Wolf-Rayet star. The energy

source, in his opinion, lies in the original hot,

expanding material.

I tend to favor a somewhat different view. If - as seems not unlikely - the total mass of the nebula

greatly exceeds that of the nuclear star, the gravitational collapse of a shell consisting of gas and dust

grains would also be approximately radial. The process

would probably take place in the manner discussed by

J Prentice and ter Haar (1971) , who consider the interU action of a gas cloud containing dust grains. They

show how the dust grains in a fragment might fall

toward the center of that fragment. The result would

be a number of large condensations.

The inner edge of the luminous ring of NGC 729 3 presents a peculiar appearance that has not, to my

knowledge, been previously described. Ample evidence

exists for the radial filamentary structure. However,

- the "comet heads" are no longer star like. They look

ij more like the heads of ordinary comets, with sharply

defined, curved, inner edges, sweeping outward into

[ hazy, stubby tails.

19 5
Could these peculiar formations, which number into

the hundreds, possibly be the progenitors of the

sharply defined filaments nearer the center? Might not

the "tails" be the result of the well-known "tunneling

effect" , caused by gravitational focusing of a body

falling in toward the center of the planetary? Not all

of the tails are precisely radial. Some have considerable inclination with respect to the nuclear star, and

the mass of the gravitating body could well be of the

order of those of solar planets.

If one assumes that the planetary has a mass about

that of the Sun, with 4000 "comets", the individual

masses could prove to be 5 x 10 29

g. The figures are uncertain and speculative, but they do at least suggest

that here we may have a true planetary nebula, a solar

system in the making.

In passing one may note that the nebulosity probably does not contain any large quantities of dust,

since several external galaxies are clearly visible

through it, especially near the cuter boundary.

On the hypothesis that NGC 7293 may consist of

large numbers of orbiting filamentary objects I have

calculated the distribution of intensity from a large

number, N, of such bodies randomly distributed between

periastron and apastron in elliptical orbits of semimajor axis a and semi -mi nor axis b.

From the vis viva integral we have the equation

defining the radial velocity (dr/dt) and tangential

velocity r(d<|)/dt) of an orbiting comet:

(£) * •'$) - =»(§

- 1)

for a body at radius r; G is the gravitational constant

and M the mass of the central star. Kepler's second

law prescribes that the areal velocity be constant, so that

1 2 4 _ frab n r

2 r dt " P

'

where P is the period. Kepler's third law provides th*. relation, for elliptical orbits, of

P

2 = (2tt) 2 a

3 /GM . (14

196
Then the radial velocity will be

2 \ ^

(15)

It is more convenient to express r in units of the

semi-major axis, a. Also let the ellipticity, r\, be

n = b/a . (16)

Then equation (15) becomes:

dt " la'/

^ r *J

'

During the interval dt, the body will have moved through

the fraction 2 dt/P of the half period.

r dr

= p dr , (18)

it ( 2r - r

2 - n

2 )^

where p is the probability of finding the comet between

r and r + dr. The factor of two enters because the

comet may attain the same radius vector on either an inward or outward portion of the orbit.

Over the orbit, r ranges from rmax to rm^ n

, where

rmax

= !+(!- , rmin = 1 - (1 - n

2 )^. (19)

The probability p becomes infinite for both the extreme

I values of r. These correspond to the two turn-around

points in the radius. The infinity for apastron

J exceeds that for periastron by the ratio rraax /rmi n

.

197
Despite these infinities, the integral of the probability remains finite,

•rmax

p dr (20)

mm

as required, since the comet must lie somewhere between

the two extremes

Consider N comets distributed randomly with

respect to spherical polar coordinates 6 and <(), but

with the radial distribution as defined by equation

(18) . Then the average number n of comets in the

volume element,

dx sinG dr d0 d< (21)

will be

n dx = Nr 2 sine dr d8 d^>

4tt

2 r(2r - r n2

) (22)

whose integral over the ranges of the variables is, as required,

n dx = N . (23)

We suppose that the brightness of an individual

object varies as Cr"^. For convenience in calculation,

we adopt the value k = 4 , usually employed for solarsystem comets. The total brightness, B, of the shell

follows from the integral

nC dx NC(3 - n

2

) 2n 5 (24)

19 8
Spherical coordinates are inconvenient for

expressing the apparent distribution over the plane of

the sky. Cartesian or cylindrical coordinates may be

used, with the z-axis directed along the line of sight.

We therefore replace the spherical volume element by:

dx = r

2 sine dr d0 d<() = dx dy dz = p dp dip dz , (25)

for cylindrical coordinates p, \\> , z. We must also make

the substitution

I r

2 = x2 + y

2 + z

2 = p2 + z

2

. (26)

As before, the units of length are expressed in terms

of a. The surface brightness H depends on an integration

along the z coordinate.

dz

(p2+z2) (k+L)/2|-2(p2+z2)

^

(p2+z2) .n2]^

(27)

Since the integrand is an even function of z, we introduce a factor of 2 and integrate over only positive

values of z. Let

p

2 + z

2 - u) 2

. (28)

ri 5 B

TT 2 (3-r, 2

)

Then the integral becomes

H = n

5 B

TT 2 (3- n

2

)

max

mm

dw

(29)

199
with

max

= 1 + /l - n

2 = a (30)

and

{

P

1 - /l - n

2 = 3. min whichever is greater. (31)

The quantities a and 3 are respectively the apastron

and periastron distances.

I have not been able to find a general expression

for the integral (29) . However, a satisfactory approximation can be developed. First of all, factor the

radicals in the denominator to obtain

which has two singularities, one at w = a, the upper

limit, and the second at either 3 or p, by (31). This

confluence of roots introduces a difficulty, although

the integrals for p = 0 and p >> B are easily obtained.

To derive an approximate expression, we proceed as follows

whose singularity at p + 3 we now adopt for the lower

limit. We may then write the integral (29) in the

approximate form:

(oo + p) (a) - p) (u) - 3) (ot - 03) (32)

(oi - p) (to - 3) = oo 2 - (p + 3)w + 3p

(33)

H = 3+P

(34)

200
For the factor in brackets, we adopt a mean value, F(p)

,

taken over the range from p to a, as follows:

F(p) =

a

doo

P r—jH—t

Loo + pj

•a dw

P

/a 2 + pa + /2p + pln[/p(/2 + l)/(/a + p + /a) ) (a - p)

(35;

This is a slowly changing function of p. One readily

finds, by the standard method of removing indeterminacy,

that

F(0) = 1, and F(a) = 1//2 (36)

„ _ n

5 BF(p) 35 (2+p) tt - 12 0 (2+p) 2 (n 2 +a p) + 48(n 2 + ap) 2 « - (3-n 2

) 128 (n

2 +ap) ?

(37)

From this equation we may calculate the distribution of surface brightness as a function of p (see

Table 2) . The details depend markedly on our choice of

n . The smaller the ellipticity, the greater will be

the theoretical increase of brightness toward the

center of the nebula, marked by the nuclear star.

This increase, however, results from the assumption that the brightness of the individual comets

201
o LO ro o o a> 1 1 1 1 1 1 CM CN CN

00 r00 CN 00 rH 1 1 rH LO ro ro ro 1 1

ro CN LT> CN CN o o 00 rH 1 rH LO ro in 1

ro CO W CN in 00 o 11 ^ rH rH r- LO VD D i—

PQWZ

00 CN <o

>H CN CN o CN m 11 < rH rH <Ti r- CO

Eh CN rH H§ O ro ro CO rH rH

cu 1 H 00 i—

ro o o 1 fa ro CN rH rH rH o

ee 00 00 00 G\ LO ro

enCO o CN 1—

VD CO

PQ s

CT> CN rH rH ro

Eh id

EEO 00 O CN in H • • • • • <o cr> in CN

PQ o O CN ro CN ro ro rH HU

ro in CN • • • ED o CN ro in rH rH

CO ro rH in in o 00 LO CN H

rH

LAI H • o o O 00

CN o ro 00 • 00 o rH ro rH O

ro

IT) rH o O o 00 o o O 00 CN 1 CN CN 00 in rH

II 1 ID ro CN

Q_ VO CN

CN \£> 00 o o O o O o rH
varies as r~\ One would expect the orbiting media to

become highly ionized toward the central star. The gas

would then be expected to radiate in entirely different

wavelengths

.

It is tempting to suggest that the broad emission

bands of Wolf-Rayet stars, many of which comprise

planetary nuclei, arise from comets near perihelion

passage. The broadening would then result from the

high orbital velocities at that position.

One may readily extend the elementary comet-shell

model developed in this paper to cover a range of

orbits of different semi-major axes and eccentricities.

I would not go so far as to argue that the comet shell

postulated by Oort is analogous to those in the planetary nebulae. But the postulated radii are not very

different

.

I wish to acknowledge the help and suggestions

generously given by W. Liller and F. L. Whipple.

REFERENCES

Curtis, H.D. 1918, Pub. Lick. Obs., 13, 55.

Daub, C.T. 1963, Ap. J., 137 , 185.

Field, G.B. 1965, Ap. J., 142, 531.

Gurzadian, G.A. 1967, Planetary Nebulae, I.A.U. Symposium 34, eds. D. Osterbrock and C.R. O'Dell

(Dordrecht, Holland: Reidel Publishing Co.),

p. 450.

Liller, W. and Aller, L.K. 1954, Ap . J., 120 , 48.

Menzel, D.H. 1937 , Ap . J. , 85_, 330.

Menzel, D.H. and Aller, L.H. 1941, Ap. J., 93_, 195.

Prentice, A.J.R. and ter Haar , D. 1971, M.N.R.A.S.

,

151 , 177.

Sofia, S. 1966, Ap . J., 145 , 84.

Vorontsov-Velyaminov , B.A. 1967 , Soviet Astronc^r, , 12, 389.

203