Smithsonian

Contributions to Astrophysics

VOLUME 3, NUMBER 5

THE DOPPLER WIDTHS OF SOLAR

ABSORPTION LINES

By BARBARA BELL AND ALAN MELTZER

SMITHSONIAN INSTITUTION

Washington, D. C.

1959
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For sale by the Superintendent of Documents, U.S. Government Printing Office

Washington 25, D.O. - Price 20 cents
The Doppler Widths of Solar Absorption Lines

By BARBARA BELL1 and ALAN MELTZER2

The precise profiles of solar and stellar absorption lines depend upon many factors.

Among them are the mechanism of radiative

transfer, the form of the line absorption coefficient, atomic collision cross-sections, temperatures, densities, and their gradients in the solar

atmosphere. For weak and medium-weak

lines, the profiles are determined primarily by

the form of the absorption coefficient, which

depends in turn upon the mechanisms acting to

broaden the lines. Spectral lines are broadened

intrinsically by three processes: the Doppler

effect due to line-of-sight velocities of the radiating atoms; natural width due to the finite

width of the atomic energy levels; and external

effects due to perturbation of the radiating

atom by neighboring atoms and ions. In the

solar atmosphere, Doppler broadening and collision broadening are far more important than

natural width.

This paper deals chiefly with Doppler broadening. From observations of the continuous

spectrum, astronomers generally agree that the

continuum is formed in regions of the solar

atmosphere where the kinetic temperature cannot much exceed 5000° K. They also agree,

however, that solar absorption lines show a

Doppler width substantially in excess of that

given by 5000°. Since Doppler broadening

can result equally well from the random lineof-sight velocities of individual atoms, or from

mass motions of elements of gas, the concept

of turbulence, or mass motions of elements of

gas, has usually been invoked to explain the

extra width of the lines. Any broadening produced by turbulence must by definition be independent of atomic weight, while, according

1

 Harvard College Observatory, Cambridge, Mass.

1

 Formerly at Smithsonian Astrophyslcal Observatory; now at Rensselaer Polytechnic Institute, Troy, N. Y.

to kinetic theory, the mean square random

velocities of individual atoms will be proportional to the kinetic temperature and inversely

proportional to the atomic weight. Thus it

might appear relatively simple to distinguish

between these mechanisms by observing a few

well chosen lines. Since the Doppler widths

usually have been derived from metallic atoms

of nearly equal atomic weights, there has been

little evidence to test the correctness of the

turbulence hypothesis.

In recent years several studies (Bell, 1951;

Rogerson, 1957; Waddell, 1956, 1958) have

been made of the profiles of weak and mediumweak solar absorption lines. For the first of

these, the Utrecht Atlas (Minnaert et al.,

1940) provided extensive observational material, while the other two used photoelectric

profiles traced by the respective authors. Bell

and Rogerson each used the Voigt profile

method of analysis, which assumes in essence

that the shape of a weak line is the shape of its

absorption coefficient, and involves no assumptions about physical conditions in the solar

atmosphere. Waddell, on the other hand, used

a model atmosphere—with specific assumptions

about temperatures and densities in the regions

where his lines were formed—to compute

theoretical profiles to compare with those observed. The success of this method presupposes, of course, a reasonably correct idea of

physical conditions in the solar atmosphere.

These three studies give several contradictory

results that are independent of the method of

analysis.

Rogerson and Waddell each assumed kinetic

temperatures of the order of 5000° K, as indicated by continuum observations, and derived

turbulent velocities of 1.4 and 1.8 km/sec

respectively. Bell emphasized a comparison

39
40 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 8

of profiles from atoms of different atomic

weights, from carbon to iron, and concluded

that her data indicated a kinetic temperature

of 10,000° K and a turbulence of less than 0.5

km/sec for neutral lines of excitation potential

of 4 to 7 volts. Rogerson, however, found

that the atomic weight dependence of his profiles, from silicon to iron, was adequately accounted for by a kinetic temperature of 5000° K.

Furthermore, Bell found that the Doppler

widths of iron lines varied with excitation potential (EP) and hence with depth. In a later

study van Regemorter (in press) obtained similar results, while Rogerson finds no evidence in

his data for such a variation. Bell found the

damping factor in iron lines to depend markedly

on the parity—and hence on the binding

energy of the electron to the parent ion—and

very little on the excitation potential. Rogerson found the converse result, and has suggested

that some of the discrepancies between his

results and those of Bell may arise from the use

of different tables of the Voigt functions (Elste,

1953; van de Hulst and Reesinck, 1947), but

we have tried both tables on a few lines and

feel that this is not a probable explanation.

Further observational study is needed to resolve

these discrepancies.

In the present work we have investigated

the way in which the width of the line profiles

depends on the atomic weight of the atoms producing them.

The observational material was obtained at

the Sacramento Peak Observatory where the

authors were guest investigators—Meltzer during March and April 1957 and Bell from

September to November 1957.

We made photoelectric tracings of the line

profiles by means of a Lallamand cell and Brown

recorder attached to the large Littrow spectrograph. A 1200-line grating was used in the

second order, giving a dispersion of 4.45 mm/A.

A Jena OG-2 filter prevented the overlapping

of higher spectral orders. The entrance and

exit slits were kept at a width of 30 microns

and at a length of one inch. The scale of the

tracings was about 6 inches per A.

All tracings were made as near as practicable

to the center of the sun's disc. Because the

level of solar activity was high during 1957,

special care had to be taken to avoid plage and

spot areas.

The instrumental profile was studied from

tracings of the mercury 5461 line of isotope 198.

The half-width of the instrumental profile is

small, about 0.030A. The wings, unfortunately,

do not fit a Voigt profile. For this reason an

instrumental correction to the Voigt damping

parameter cannot be determined, and we have

not attempted to study the damping from our

observed line profiles. However, since the instrumental profile is completely independent of

atomic weight, the unconnected profiles should

suffice to give the kinetic temperature, and the

known half-width of the instrumental function

permits a reasonably good estimate of the turbulence.

We made at least six tracings of every line,

reversing the direction of scan after each trace.

For two reasons, we made additional tracings

for some of the lines. Because of the possibility of getting into a weak unnoticed plage

area, Bell traced the vital 5380 line of carbon

each day for comparison with other lines observed that day. Also, a random slippage in

the motion of the grating, and hence in the rate

of scan, introduced errors into the individual

tracings. Since we made two independent sets

of observations which give essentially the same

results, we feel justified in presenting our findings in spite of such errors in the individual

tracings.

We analyzed our lines by the Voigt profile

method. By definition, a Voigt function results from the superposition of a damping or

dispersion type function,

and a Gaussian probability function,

where eu c2, ft, and j82 are constants and x is the

distance from the line center. Thus Voigt functions are characterized by two parameters, ft

and /32, and the strength of their wings depends

on the ratio of /3,//32.

The line absorption coefficient similarly is

given by the superposition of a Maxwellian

velocity distribution function and a damping

function. The parameters ft and & can thus
NO. 5 SOLAR ABSORPTION LINES 41

readily be equated to factors in the absorption

coefficient, the first relating to the damping

half-width, the second to the Doppler halfwidth.

In an analysis by Voigt profiles, one assumes

that the profile of the observed line is the average of the absorption-coefficient profile appropriate to the regions of the solar atmosphere

over which the line is formed. Thus the

method can properly be applied only to comparison of lines that arise at the same average

depth in the solar atmosphere.

It is difficult to find suitable lines sufficiently

different in atomic weight and reasonably similar in excitation level. For this study we

selected lines of carbon, silicon, and iron having

excitation potentials of 7.6, 4.9, and 4 to 5 volts,

respectively, as shown in tables 1 and 2. Although the comparison of 7.6-volt carbon lines

with those of silicon and iron may be open to

criticism, we have included carbon because it

provides a long base line in atomic weight.

However, the greater emphasis probably should

be given to results arising from comparison of

iron and silicon lines, since these are quite

similar both in excitation and ionization

potential.

A Voigt profile is completely specified by

three quantities: AX, the width at half intensity,

generally called simply the half-width; e, the

central depth; and p, a function of fr/fo, determined by the width of the profile in the

wings relative to that at the half-intensity point

and varying from 1.06 for a pure Gaussian to

1.57 for a pure damping profile.

We measured the width of each trace at its

half-intensity point and at four points in the

wings, 0.1c, 0.15c, 0.2c, and 0.3c. The measures

for the individual tracings were combined to

give mean quantities for each line. Most of

the mean observed profiles showed a good fit

to a Voigt function. From Elste's (1953) tables

we obtained the Voigt parameters, p, bi, b\.

From the measured half-width, the more convenient quantity h=— 10* was obtained. We

A

then computed ft=bih and $=6|A,*. The ft and

/Si of the line, after correction for the respective

instrumental ft and /3£, should yield a good first

approximation to the damping constant and

the Doppler velocity, respectively. Our collection of lines is not suitable for testing the

parity effect; furthermore, the instrumental

ft is indeterminate, so we shall not further discuss the ft's here, except to note that they

suggest that damping is not negligible even for

weak lines.

The observational results are given in tables

1 and 2, where the data obtained by Meltzer

and by Bell are presented separately in order

to show clearly that, in spite of the grating

slippage, the independent sets of observations

gave results in close agreement.

Element

C

Si

Fe

TABLE 1.

Wavelength

5380. 32

•5665. 56

5772. 15

5793. 08

5386. 34

5441. 35

5752. 04

5793. 93

5852. 23

5856. 10

—Parameters of line profiles observed by Meltzer, April 1957

Excitation potential

7.65

4.90

5.06

4. 91

4. 15

4.35

4.59

4.24

4.59

4 28

Observed quantities

c

0. 12

.26

.32

.28

.26

.25

.41

.26

.30

.27

AX(A)

0. 142

. 118

. 130

. 126

.088

.092

. 106

. 100

. 108

. 103

h*

700

431

505

477

270

288

340

297

342

308

Voigt parameters

P

1. 18

1.25

1. 30

1.27

1.23

1.29

1.28

1.23

1.30

1.26

PI

185

91.2

89. 6

93. 5

60. 7

52.0

62.8

66.5

59.5

62.0

Number of

tracings

6

6

10

6

6

5

8

9

6

8

•Violet half only; red half blended.
42 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Parameters of line profiles observed by Bell, September-November 1957

VOL. S

Element

C

Si

Fe

Wavelength

5052. 16

5380. 32

*5665. 56

5690. 43

5701. 11

5772. 15

5793. 08

5293. 96

5295. 31

5386. 34

5395. 22

5401. 27

5441. 35

5464 29

5705. 48

5793. 93

5852. 23

5855. 09

5856. 10

5927. 80

6089. 58

Excitation

potential

7.65

7.65

4 90

4 91

4 91

5.06

4 91

4 12

4 35

4 15

4 35

4 35

4 35

4 12

4 24

4 24

4 59

4 59

4 28

4 59

5.00

Observed quantities

c

0.21

. 13

.26

.34

.26

.32

.27

.25

.24

.26

. 16

.20

.25

.31

. 29

. 26

.30

. 17

.26

.31

.29

AX(A)

0. 156

. 156

. 122

. 121

. 120

. 132

. 128

.092

.092

.095

.096

.096

. 101

.095

.099

.099

. 105

. 100

. 102

. 104

. 102

h

2

950

840

466

450

443

526

488

303

306

310

319

316

344

305

302

292

324

294

303

312

287

Voigt parameters

P

1.20

1.23

1.25

1.24

1.22

1.30

1.27

1.27

1.22

1.23

1.25

1.26

1.29

1.24

1.24

1.26

1.31

1.24

1. 25

1.29

1.28

A

235

190

98

96

102

89

96

58

70

70

68

64

62

67

64

58

52

64

63

56

54

Number of

tracings

12

22

6

6

7

11

13

8

8

18

7

6

8

6

6

13

10

11

11

6

4

•Violet half only.

The quantity (% is proportional to the Doppler width of the line. From the definition of

Voigt functions it can easily be shown that

(1)

where T is the kinetic temperature, vT is the

turbulent velocity, and /3f, is the instrumental

profile correction. The quantity in parentheses

is independent of n, the atomic weight. If this

term were zero, the /Sfs of the lines should be inversely proportional to the atomic weight of the

element producing the line. When this quantity is not zero, the quantity [#}— {1%+(&)]

should be inversely proportional to /*. Solving

equation (1) for the kinetic temperature, we

obtain

T=5.41 [^-(4+/^,.)]M . (2)

We computed a mean /3| for each element. By

trial and error we determined that a correction

of (flr+0«)=26 would yield the best inverse

relation between the quantity in square brackets

and the atomic weight, and the best agreeing

values of T for the three elements. The results

appear in table 3. We also solved equation (2)

for each pair of elements, with the results shown

in table 4.

We obtain a kinetic temperature of the order

of 10,000 to 11,000° K, in substantial agreement

with BeD's (1951) earlier work on comparable

lines.

If the entire quantity (vr+Pli) is due to

turbulence (i. e. if the instrumental /3|, is negligible), we obtain vT=l.Q km/sec. This is, of

course, an upper limit to the turbulence. The

maximum instrumental correction will be obtained if we assume the instrumental profile is a

Gaussian, so that its entire half-width goes into

/3|i- Such an assumption gives f%~\Q, and a

turbulence of 1.2 km/sec. However interpreted, our Doppler half-widths are somewhat

larger than those previously obtained. The

reason for this is unknown. If real, the effect

may be related to the remarkably high level of

general solar activity observed throughout 1957.

In addition to the profiles observed at the

center of the solar disc, in September we observed the profiles of 13 of these lines near the
NO. 6 SOLAR ABSORPTION LINES 43

north limb. The 1-inch long slit of the spectrograph was centered one inch from the limb, on a

10-inch image of the sun; thus, at r/R=0.8.

Table 5 gives the parameters of the lines,

while the third section of table 4 gives the indicated kinetic temperatures. The half-widths

of the lines increase markedly to the limb, but

the weighted mean temperature is 11,400°, only

slightly higher than that obtained at the center

of the disc. The turbulence increases to between

1.9 and 2.1 km/sec, which is 0.6 to 0.7 km/sec

greater than the center-of-disc values.

TABLE 3.—Determination of apparent kinetic temperature at center of disc

Observer

Meltzer

Bell

Element

C

Si

Fe

C

Si

Fe

Mean

ft

185

92

61

206

95

63

$-26

159

66

35

180

69

37

Ratio of

atomic

weights

(56/M)

4. 67

2.00

1. 00

4. 67

2.00

1. 00

Ratios of

($-26)

4.60

1.90

1.00

4.87

1.86

1.00

Temperature

10, 300° K

10,000

10, 500

10, 300 (mean)

11, 700

10, 400

11,200

11,000 (mean)

Weight

6

22

42

34

43

122

Any thorough study of center-to-limb changes

in the Doppler width of lines would of course

require observations at several points along the

radius. Until we obtain such data, we shall

not attempt to interpret the present north limb

observations. Our observations suggest, however, that the well-known increase in line halfwidth to the limb (see Allen, 1949) results

largely from increased turbulence rather than

from significantly higher kinetic temperatures.

Houtgast (1953) has criticized Bell's (1951)

work on the grounds that some of the lines she

compared (specifically, carbon and oxygen with

iron) differed in excitation potential and hence

must arise at different depths in the solar atmosphere. This argument may apply to the carbon lines, but it should not apply to the comparison of silicon with high excitation lines of

iron which should arise from the same average

level in the atmosphere. (Bell's determination

of the kinetic temperature depended as much

on a comparison of silicon and iron as on that

of iron with carbon and oxygen; also, only 4-5

volt lines of iron were used in these comparisons

precisely because of the difficulty mentioned by

Houtgast.)

A definitive analysis of a line profile cannot

be made without detailed consideration of the

processes of line formation and of the variation

of the absorption coefficient with depth in an

appropriate model atmosphere. The method

of this paper has been criticized as too simple

even for a first approximation. Therefore, to

examine the relationship between results obtained by this method and one using a model

atmosphere, we made a Voigt profile analysis

of a theoretical profile computed by Waddell

(1956) for the titanium line, X6126, from a

standard model atmosphere and Pecker's (1953)

method of weighting functions (see Waddell,

1958). We obtained a turbulence 0.2 km/sec

greater than Waddell put into his line.

As a second test, we made a Voigt analysis

of a pair of iron and silicon theoretical profiles,

computed by Doherty and Hazen (unpublished) from the Claas (1951) model of the

solar atmosphere, with the assumption that

scattering plays no part in the formation of the

lines. From comparison of their iron and silicon profiles, we obtained 7r

=6600°K, which is

the Claas temperature at the optical depth 1.2

in the continuum; a turbulent velocity of 2.1

km/sec, which is 0.35 above the assumed value

of 1.75 km/sec; and a damping of a=0.23,

slightly below the original 0.25.
44 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 3

From this analysis we conclude that the

single layer approximation, implicit in the

Voigt profile method, is not unrealistic as a

first approximation for elements such as iron

and silicon. Integration through an atmosphere does make the width of the lines moderately greater than the width of their absorption

coefficients, but when a Voigt analysis is used

this width appears in a spuriously large turbulence rather than in a spuriously high kinetic

temperature.

Our profiles have not been corrected for

instrumental scattered light. The Voigt

method is insensitive to this correction, however, so that its neglect results in only a minor

error at worst and cannot account for our high

temperatures. We tested this point by applying an arbitrary scattered-light correction of 10

percent to our mean observed silicon and iron

profiles. Voigt analysis of this pair of corrected profiles gave 7=12,000°, as compared

with 10,600° from the same pair of profiles

before correction. The correction decreased

the apparent turbulence by about 0.2 km/sec.

Hazen (private communication) has pointed

out that the Voigt profile method is very

sensitive to small changes in the assumed level

of the continuum, because the shape of the

wings is so important in determining the Voigt

parameters. If the continuum were drawn 1

or 2 percent higher, the two mean profiles would

give a temperature of 8,000 or 6,000°K respectively. In the spectral regions we studied, so

large a systematic error in drawing the continuum appears extremely unlikely. However, this sensitivity may account for much of

the scatter among individual tracings (and

individual lines in the Utrecht Atlas), and

indicates the importance of making several

tracings of each line. Moreover this source of

error would similarly distort the results from

more sophisticated methods of analysis, insofar

as they attempted to fit the damping wings.

One other comment may be made on the

Voigt profile method of analysis. Waddell, in

his model atmosphere analysis, assumed that

weak lines were undamped. In terms of Voigt

parameters, this implies that /3i=0 and p = 1.06.

Under the assumption of no damping, the entire

half-width is considered to result from temperature and turbulence, and the wing measures may be disregarded. When we applied

this assumption to our lines, Meltzer's observations yielded temperatures of about 11,000°

from carbon and iron and a substantially higher

temperature for silicon, as one might expect,

since its p's (Voigt parameters) are substantially

larger than those for carbon and iron. From

Bell's observations we can obtain good agreement among the three elements at around

17,000°K. We thus feel that the damping

cannot properly be ignored, and indeed any

attempt to do so only aggravates the problem

of high kinetic temperatures.

TABLE 4.—Apparent kinetic temperatures, determined

from comparison of Doppler half-widths of lines of

pairs of elements of different atomic weight

Observer

Meltzer

(center

of disc)

Bell (center

of disc)

Bell (0.2R

from

north

limb)

Elements

{paired)

C-Si

C-Fe

Si-Fe

C-Si

C-Fe

Si-Fe

C-Si

C-Fe

Si-Fe

Temperature

10, 600° K

10,300

9,400

10, 000 (mean)

12,600

11,900

9,800

11, 100 (mean)

12,800

11,800

10, 300

11, 400 (mean)

Weight

28

48

64

77

156

165

43

65

74

Waddell (1958) has pointed out a discrepancy

between observed and Voigt profiles in the far

wings, within about one percent of the continuum. But such a deviation is far smaller

than that between the observed profile and any

theoretical profile computed under the assumption of zero damping. While other interpretations of the line wings are conceivable, damping

is the most simple and straightforward. The

parity effect (Bell, 1951; Carter, 1949) would

appear to provide the best test of the correctness of this interpretation. According to

theory, the damping is proportional to the

binding energy of the electron to its parent term

of the ion. In iron these binding energies have

values that lead one to expect the damping

arising from odd terms to be about double that
NO. 5 SOLAR ABSORPTION LINES 45

arising from even terms of comparable excitation potential, although parity in itself has no

bearing on the problem (see Bell, 1951). We

hope to explore this question further with additional observations.

If we accept the hypothesis that the 22 lines—

or at least the 20 lines of silicon and iron—compared in this paper are formed through the

same average layer of the solar atmosphere, we

are faced with the conclusion that the atoms

possess a kinetic temperature of 10,000 to

11,000° K, although all continuum studies

indicate electron temperatures of the order of

5000° K.

TABLE 5.—Parameters of line profiles observed at 0.2 of the solar radius from the north limb, September 1957

Element

C

Si

Fe

Wavelength

5052. 16

5380. 32

5665. 56

5772. 15

5793. 08

5386. 34

5395. 22

5441. 35

5464.29

5793. 93

5852. 23

5855. 09

5856. 10

Excitation

potential

7.65

7.65

4.90

5.06

4.91

4. 15

4.35

4.35

4. 12

4.24

4. 59

4.59

4.28

Observed quantities

c

0. 17

. 10

.25

. 30

. 26

.26

. 16

.25

.30

. 25

.28

. 16

.25

AX (A)

0. 154

. 152

. 134

. 140

. 134

. 102

. 101

. 107

. 105

. Ill

. 116

. 109

. 115

h*

930

800

555

585

542

362

348

388

370

366

393

347

385

Voigt parameters

P

1. 17

1. 17

1.23

1.28

1.22

1. 18

1.26

1.24

1.25

1. 18

1.25

1.21

1. 19

ft

250

215

125

111

124

94

70

85

77

95

80

83

98

Number of

tracings

8

9

8

10

8

7

5

6

4

8

6

6

6

Three possible explanations for this discrepancy present themselves: (1) equipartition of energy between the atoms and electrons

does not occur; (2) the electrons actually have a

kinetic temperature of 10,000°; or (3) the continuous and the absorption-line spectra are

formed in significantly different regions of the

solar atmosphere. Because of the great frequency of atom-electron collisions, the first

hypothesis cannot be regarded seriously (see

Bhatnagar et al., 1955). With the second

hypothesis, the electrons would be much too

energetic for capture in sufficient numbers by

hydrogen to form H~, and it would seem

virtually impossible to account for the observed

continuum. Only the third hypothesis appears

to offer any possibility of a reasonable explanation.

If we postulate that the lower chromosphere

makes a substantial contribution to the absorption lines, while the continuous absorption

arises from photospheric levels, there is hope

that the temperature differences can be reconciled. Recent work by Zirker (1956, 1958)

on the metallic flash spectrum from the 1952

eclipse and by Pecker (1957) on the CH and

CN bands makes such a postulate appear more

tenable than it did a few years ago. The

similarity between the intensity and velocity

fluctuations in the strong magnesium X5167 line

and in medium-weak neighboring lines, observed with the vacuum spectrograph at the

McMath-Hulbert Observatory (McMath et al.,

1956), also suggests that the chromosphere may

make significant contributions to the cores of

at least medium-weak solar absorption lines.

The mere existence of such velocity shifts

makes it obvious that some form of macroturbulence must be broadening the profiles of

lines coming from an area of the sun large

enough to take in many granules. A complete

picture of velocities can, therefore, come only

from analysis of such detailed spectra.

As an alternative to chromospheric contributions, Pecker suggested (in conversation)

that inhomogeneities in the photosphere such

as described by the 3-stream model of Bohm

(1954) and Voigt (1956) might account for the
46 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS VOL. 3

apparent high kinetic temperature. By assuming values for the stream velocities, microturbulence, and stream temperatures, one could

compute profiles for two lines of different

atomic weight, analyze them by the method

used in this paper, and determine the apparent kinetic temperature for comparison with

observations. The 3-stream model as used

by Voigt, however, predicts that the violet

wings of profiles should be stronger than the

red wings. Our observations, as well as those

in the Utrecht Atlas, suggest that the red wings

are the stronger (i. e., more depressed).

To test any of these hypotheses, of course, we

should have to make detailed models, taking

account of the contributions of each layer—

photospheric as well as chromospheric—to the

line formation, and this has not yet been

attempted.

The work reported herein has been supported

in part by the Air Force Cambridge Research

Center, through Contract AF19 (604)-1394

with Harvard University; in part by the

Smithsonian Astrophysical Observatory, and

in part by a grant from the Research Grants

Committee of Rensselaer Polytechnic Institute.

We are indebted also to Dr. John W. Evans

and Dr. Henry Smith for their cooperation and

assistance in permitting us to use the facilities

at Sacramento Peak Observatory.

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Abstract

In an attempt to distinguish the contributions of turbulence and kinetic temperature to the half-widths of solar

absorption lines, photoelectric tracings where made of the profiles of 22 moderately weak lines of three elements

covering a wide range in atomic weight (/•): carbon (12), silicon (28), and iron (56). The tracings were analyzed by

the method of Voigt functions. In iron, to be as nearly comparable as possible with the available lines of silicon and

carbon, only lines of relatively high (>4.1 e. v.) excitation potential were used.

When the /i-dependent and the ^-independent parts of the Doppler half-widths were separated, a kinetic temperature of the order of 10,000° K was obtained. Temperatures of the same order, or somewhat higher, are indicated if

the damping is neglected and the entire half-width is assumed to arise from Doppler broadening.

U.S. GOVERNMENT PRINTING OFFICE: 1959