Distribution and Ages of

Magellanic Cepheids

Cecilia H. Payne-Gaposchkin

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SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS • NUMBER 16

Distribution and Ages of

Magellanic Cepheids

Cecilia H. Payne-Gaposchkin

SMITHSONIAN INSTITUTION PRESS

City of Washington

1974
ABSTRACT

Payne-Gaposchkin, Cecilia H. Distribution and Ages of Magellanic Cepheids.

Smithsonian Contributions to Astrophysics, number 16, 32 pages, 8 figures, 15

tables, 1974.—The distribution and ages of the Magellanic Cepheids are discussed under four major topics :

1. The Large Cloud is shown to contain components with a variety of ages.

A time scale is set up by means of the color-magnitude arrays of clusters, the

integrated colors of clusters, the luminosities of Wolf-Rayet stars, and the

periods of Cepheids. It is suggested that (unlike other components of the Large

Cloud) the red globular clusters may constitute a halo.

2. Changes of period for galactic and Magellanic Cepheids are used to test

the time scales derived for Cepheids. The computed time scales are seen to be

of the right order, and the actual time scales are similar for Cepheids in the

Galaxy and in the Clouds. If these time scales are sensitive to composition, the

changes of period furnish no evidence for differences of composition in the

three systems.

3. Evidence bearing on possible differences of composition is reviewed. So

far as Cepheid variables (and stars of similar age) are concerned, there is no

good evidence for differences of composition. This conclusion does not apply to

the globular clusters, and perhaps not to the intermediate-age clusters; those

in the Clouds are probably of similar composition to those of similar age in

the Galaxy.

4. The period-amplitude and period-frequency relations, and their differences, are shown to be compatible with differences in the time of formation of

stars that are now Cepheids in the two Clouds and in the Galaxy.

The discussion under these four topics suggests that the observed differences between the three systems can be interpreted in terms of differences in

the timetable of star formation, without the need to invoke initial differences

of composition.

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Distribution and ages of Magellanic Cepheids.

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Distribution and Ages of

Magellanic Cepheids

Cecilia H. Payne-Gaposchkin

A Time Scale for Clusters

and Cepheid Variables

The color-magnitude diagrams of open clusters

furnish a classical basis for a scale of ages. Table

1 contains data on (B —V)T5 the intrinsic color

at the turnoff, and on (B —V)o, the intrinsic integrated color, for clusters where both have been

determined. Successive columns give values of

(B-V) T published by Johnson et al. (1961),

Sandage (1963), Gray (1965), and an adopted

mean. The next two columns give the logarithm

of the age in years, taken from Sandage (1963)

for the clusters for which he published it, and

the logarithm of the ages of all the clusters in

the table, deduced from a smooth freehand curve

representing the data of the previous column.

The remaining columns give values of (B —V)o

as published by Sandage (1963), Arp (1964),

Buscombe (1964), and Gray (1965) and finally

an adopted mean. Data for a few clusters, denoted by asterisks in the final column, are from

Schmidt-Kaler (1967).

The age is determined from (B —V)T, which

sets a minimum for the cluster. The integrated

colors, which include measured values of

( B - V) o and summed values of (B-V) o , are less

accurate as criteria of age. They will be used

later in our discussion of the Large Magellanic

Cloud.

We now apply the cluster time scale to an examination of the ages of Cepheid variables. A

Cecilia H. Payne-Oapogchkin, Smithsonian Institution

Astrophyttical Observatory, Cambridge, Massachussets

02138. '

Cepheid that is a member of an open cluster

must of course conform to it in position and in

radial velocity. It should also have a similar

color excess when the latter is corrected for dependence of color excess on intrinsic color, as described, for example, by Wildey (1963) and Jung

(1970). The period of the Cepheid must also be

considered in assigning cluster membership.

It has long been recognized that there should

be a relationship between the age of a Cepheid

and its period. Young (1961) suggested (essentially on the basis of an assumed mass-luminosity

relation) a "semitheoretical formula":

log t 0.714 log P + 8.57, (1)

where "P is the period in days, and t, as before,

the age in years. Kippenhahn and Smith (1969)

have considered the ages of Cepheids on the

basis of the position of the Cepheid strip in the

evolutionary tracks of chosen models. By weighting the data given by Kippenhahn and Smith according to the duration of the Cepheid stage for

each star considered, Tammann (1969) has obtained a similar relation:

log t 0.651 log P + 8.16. (2)

Equations (1) and (2) differ principally in the

size of the constant that defines the time scale,

the ages deduced by Young's formula being

greater by a factor of about 2.5. We shall assume

that the Cepheids in clusters have the same age

as the clusters and, on this basis, deduce a time

scale for Cepheids.

Table 2 examines the credentials of a number

of Cepheids that lie near open clusters. Succes-
SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 1.—Colors of open clusters

Cluster

NGC 129

NGC 188

NGC 225

NGC 457

NGC 581

NGC 663

NGC 752

NGC 744

NGC 869

NGC 884

IC 1805

T r 2

NGC 1027

IC 1848

NGC 1245

Perseus

NGC 1342

Pleiades

NGC 1502

NGC 1528

NGC 1545

Hyades

NGC 1647

NGC 1662

NGC 1664

NGC 1778

NGC 1893

NGC 1907

NGC 1912

NGC 1960

NGC 2099

NGC 2158

NGC 2168

NGC 2169

NGC 2251

NGC 2264

NGC 2281

NGC 2287

NGC 2301

NGC 2323

NGC 2353

NGC 2362

NGC 2422

NGC 2539

NGC 2548

IC 2682

IC 2602

Johnson

-0.16

-0.11

-0.25

-0.21

-0.28

+0.35

-0.08

-0.28

-0.28

-0.32

-0.14

-0.02

-0.29

+0.16

-0.20

+0.05

-0.12

-0.29

-0.02

-0.08

+0.10

-0.09

-0.04

-0.10

-0.34

0.00

-0.09

-0.24

-0. 10

-0.17

-0.27

-0.16

-0.30

-0.20

-0.14

-0.19

-0.25

-0.28

-0. 18

+0.40

Sandage

+0.61

-0.20

-0.13

-0.28

-0.30

-0.30

-0.32

-0.14

-0.20

-0.33

-0.09

-0.07

-0.17

-0.24

-0.09

+0.30

+0.50

Gray

+0.65

-0.11

-0 97

-0.21

-0.24

+0.35

-0.07

-0.35

-0.14

-0.14

+0.16

-0.20

+0.05

-0.14

-0.03

-0.08

+0.10

-0.09

-0.04

-0.16

-0.09

-0.09

-0.06

-0.13

-0.17

-0.22

-0.20

-0.27

0.00

-0.20

-0.14

-0.24

-0.23

-0.29

-0.18

0.00

-0.05

-0.25

Adopted

-0.16

+0.63

-0.11

-0.24

-0.18

-0.27

+0.35

-0.08

-0.29

-0.29

-0.33

-0.14

-0.12

-0.29

+0.16

-0.20

+0.05

-0.13

-0.31

-0.05

-0.08

+0.10

-0.09

-0.05

-0.16

-0.10

-0.34

-0.04

-0.11

-0.24

-0.11

+0.30

-0.17

-0.24

-0.18

-0.28

0.00

-0.20

-0.14

-0.22

-0.24

-0.28

-0. 18

0.00

-0.05

+0.45

-0.25

logt

Sandage

10.08

7.10

7.95

6.60

6.50

6.50

6.30

7.75

7.10

6.00

8.12

8.20

7.35

6.87

8.12

9.40

9.87

Present

7.50

10.08

7.89

6.90

7.35

6.64

9.48

8.10

6.48

6.48

6.12

7.66

7.82

6.48

9.10

7.20

8.78

7.84

6.30

8.30

8.10

8.95

8.02

8.30

7.50

7.96

6.02

8.35

7.89

6.90

7.89

9.40

7.43

6.90

7.36

6.57

8.53

7.20

7.66

7.04

6.90

6.58

7.36

8.53

8.30

9.72

6.80

Sandage

+0.84:

+0.12

+0.05

-0.10

-0.15

+0.10

-0.27

+0.20

+0.13

-0.27

+0.08

+0.19

+0.10

-0.14

+0.26

+0.65:

+0.74

Arp

+0.61

+0.78

-0.18

-0.10

+0.40

+0.66

-0.18

-0.21

(B-V)o

Buscombe

+0.08

+0.02

-0.15:

-0.18

+0.06

-0.31

+0.06

+0.09

-0.31

+0.05

+0.15

+0.07

-0.16

+0.22

+0.69

Gray

+0.92

+0.11

+0.11

+0.01

-0.09

+0.63

+0.06

-0.33

+0.27

+0.13

+0.01

+0.02

+0.35

-0.13

+0.13

-0.21

+0.49

+0.07

+0.17

+0.13

+0.08

-0.16

+0.61

+0.07

+0.27

+0.03

-0.02

+0.13

-0.15

+0.56

+0.16

+0.23

+0.06

-0.12

-0.25

-0.06

+0.47

+0.26

-0.07

Adopted

+0.61

+0.85

+0.11

+0.11

+0.03

-0.11

+0.63

+0.06

-0.17

+0.08

-0.30

+0.14:

+0.12

-0.29

+0.01

+0.02

+0.35

-0.12

-0.29

+0.09

-6.21

+0.44

+0.07

+0.17

+0.13

+0.08

-0.16

+0.61

+0.08

-0.15

+0.25

+0.66

+0.03

-0.02

+0.13

-0.16

+0.56

+0.16

+0.23

+0.06

-0.12

-0.23

-0.06

+0.47

+0.26

+0.72

-0.07
NUMBER 16

TABLE 1.—Colors of open clusters—Continued

Cluster

NGC 3532

Coma

NGC 4755

NGC 6087

NGC 6231

NGC 6405

NGC 6475

NGC 6494

NGC 6531

NGC 6530

NGC 6633

IC 4725

IC 6709

NGC 6802

NGC 6866

NGC 6871

NGC 6940

NGC 7063

NGC 7092

NGC 7142

IC 5146

NGC 7160

NGC 7209

NGC 7261

NGC 7380

NGC 7789

NGC 7790

CepHI

Lac I

Orll

Johnson

+0.05

-0.20

-0.17:

-0.18

-0.10

-0.06

-0.30

-0.32

+0.15

-0.20

-0.16

-0.14

+0.06

-0.24

+0. 15

-0.10

-0.06

+0.38

-0.30

0.00

-0.10

-0.30

+0.30

-0.18

-0.25

-0.30

-0.32

(B-V)T

Sandage

-0.12

-0.14

+0.01

+0.10

-0.06

-0.05

-0.30

+0.32

-0.18

Gray

-0.04

+0.05

-0.20

-0.15

-0.12

-0.06

+0.05

-0.33

-0.33

-0.12

-0.20

-0.20

-0.13

+0.06

+0.16

-0.10

-0.12

+0.38

-0.27

-0.30

-0.06

-0.15

-0.33

-0.25

-0.30

-0.32

Adopted

-0.04

+0.05

-0.20

-0. 15

-0.30+

-0.15

-0.08

0.00:

-0.32

-0.32

-0.03:

-0.18

-0.18

-0. 14

+0.04

-0.24

+0.14

-0.10

-0.08

+0.38

-0.27

-0.30

-0.04

-0.12

-0.31

+0.31

-0.18

-0.25

-0.30

-0.32

logt

Sandage

7.95

7.75

8.45

9.17

8.30

8.30

6.50

9.48

7.35

Present

8.35

8.78

7.20

7.59

6.45

7.59

8.10

8.53

6.20

6.20

7.35

7.35

7.67

8.72

6.90

9.06

7.96

8.10

9.58

6.64

6.40

8.35

7.80

6.30

9.42

7.35

6.80

6.40

6.20

Sandage Arp

+0.22

+0.15

+0.13

+0.29

+0.35

-0.02

-0.21

+0.33

-0.19

+0.70 +0.62

+0.09

(B-V)o

Buscombe

+0.11

+0.21

+0.26

+0.48

+0.31

-0.03

+0.30

-0.22

+0.65

+0.04

Gray

+0.27

+0.19

-0.01

-0.15

+0.17

+0.15

+0.18

-0.16

-0.12

+0.12

+0.09

+0.21

+0.07

+0.41

+0.39

+0.23

+0.06

+0.60

+0.17

-0.25

+0.30

+0.19

-0.12

-0.36

+0.05

-0.12

Adopted

+0.27

+0.20

-0.01

-0.15

-0.24*

+0.17

+0.15

+0.18

-0.1

-0.12

+0.13

+0.14:

+0.21

+0.07

+0.32:

+0.48

+0.35

+0.23

0.00

+0.60

-0.02:

-0.25

+0.31

+0.19

-0.18

+0.66

+0.06

-0.36

+0.05

-0.12

sive columns give the cluster, the Cepheid, the

logarithm of its period, the observed color excess

of the Cepheid, the observed color excess of the

cluster, log t for the cluster (from Table 1), and

log t for the Cepheid, calculated from the formulas of Young (AY) and of Kippenhahn and

Smith (KS). Data for the Cepheid in NGC

6649 are taken from Tammann (1969), those of

S Nor from Breger (1970).

As suggested above, a Cepheid that is a cluster

member should have a color excess consistent

with that of the cluster, and its age should conform to that of the cluster. The stars whose color

excesses and/or ages do not conform to these criteria are placed in parentheses. We reject VY

Per, UY Per, SZ Cas, DF Cas, UX Car, and ER

Car on the basis of color excess, and VX Per,

YZ Car, CF Car, and AQ Pup on the basis of

age. The star CV Mon has not been included, because the cluster to which it was once assigned is

probably nonexistent. We note that the Cepheids

near the double cluster in Perseus, used by Sandage and Tammann (1968) in their calibration

of the zero point of the period-luminosity curve,

are all excluded on the basis of age, and nearly

all on the basis of color excess. As discussed elsewhere, the zero point determined with their aid

is nonetheless unaffected.

The acceptable Cepheids in Table 2 permit us

to conclude that the empirical determination of

cluster ages, based on Table 1 and the LimberSandage time scale, is in satisfactory agreement
SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

TABLE 2.—Classical Cepheids near open clusters

Cluster

NGC 129

NGC 869,884

NGC 1027

IC 2581

NGC 3496

NGC 3532

Tr 18

NGC 6087

IC 4725

NGC 6664

NGC 7790

Pup I

Vel m

NGC 6649

C epheid

DL Cas

(VX Per)

(VY Per)

OJY Per)

(DW Per)

(SZ Cas)

(DF Cas)

(UX Car)

(YZ Car)

(CF Car)

(ER Car)

(GH Car)

SNor

U Sgr

EV Set

CE Cas a

CE Cas b

CF Cas

<AQ Pup)

RS Pup

Anon

logP

0.903

1.040

0.743

0.730

0.562

1.134

0.583

0.566

1.259

0.740

0.888

0.758

0.989

0.829

0.490

0.711

0.651

0.688

1.475

1.617

0.709

Color

Cepheld

0.59

0.59

1.06

1.02

0.67

0.80

0.6-1

0. 13

0.37

0.2 4

0.36

0. 18

0.52

0.64

0.62

0.59

0.64

0.60

0.64

(1-24)

Excess

Cluster

0.58

0.56

0.56

0.56

0. 56

0.56

0.40

0.37

0.37

0.50

0.01

0. 37

0.20

0. 50

0.60

0.52

0.52

0.52

0. 54

0.62

1.24

log t

Cluster

7.50

6.55

6.55

6.55

6.55

6.55

7.75

(6. 30)

(6.30)

(8. 70)

8.35

(7.20)

7.59

7.75

7.96

7.35

7. 35

7.35

5.90

6.80

7.70

C

7.93

7.83

8.04

8.05

8.17

7.76

8.15

8.17

7.67

8.04

7.94

8.03

7.86

7.98

8.22

8.06

8. 11

8.08

7.52

7 . 4

H.06

epheid

KS"

7.57

7.48

7.68

7.68

7.79

7.42

7.78

7.79

7.34

7.68

7.58

7.67

7.52

7.62

7.84

7.70

7.74

7.71

7.2(1

7.11

7.70

with the time scale derived by Kippenhahn and

Smith on the basis of the theory of evolutionary

tracks. The time scale given by Young's approximate formula is too long. We shall accordingly

use the scale of ages based on Table 1 for the

clusters, and equation (2) for the Cepheids.

The relation between period and age for the

accepted Cepheids shows considerable scatter,

which might be ascribed to: (1) errors in the Cepheid periods; (2) dispersion in the physical

properties of the Cepheids; (3) uncertainty in

(B —V)T; and (4) dispersion in the properties of

the clusters.

1. Errors in the periods of the Cepheids used

can hardly affect the data, but the interpretation

of the periods may do so. If a star is pulsating

in an overtone, the period appropriate for age

determination will be longer, and the age accordingly smaller, with a difference in log P (for the

first overtone) of about —0.2. Possibly EV Set is

in overtone pulsation, but in that case the discrepancy would be even greater.

2. This possibility covers differences of composition and also mass loss (which might itself be a

function of luminosity and thus of mass). We

have no convincing spectroscopic evidence of differences of composition among classical Cepheids, although differences large enough to affect

the time scale might not be large enough to affect

the spectrum. Mass loss must certainly occur, but

the limits calculated by Kippenhahn and Smith

would account for only half the observed dispersion.

3. Kippenhahn and Smith (1969, Table 2)

used the luminosities of the stars at the turnoff

point to obtain cluster ages, and their material

was more heterogeneous than ours. We believe

that it is less circuitous to determine log t from

(B —V)T than from an absolute bolometric magnitude that involves a bolometric correction and

magnifies a possible error in color excess by a

factor of 3. The uncertainty in (B —V)T is certainly not greater than 0.m

10 for the clusters considered. This may still lead to an uncertainty in

log t of perhaps 0.5, since we are confined to the

region of negative (B — V)T.

4. The clusters, like the Cepheids, may differ

significantly in composition and also in other

properties, such as the presence of supergiants

and numerous red giants. It should be noted that
NUMBER 16

the most discrepant point in the KippenhahnSmith plot relates to the Cepheids in the Magellanic cluster NGC 1866, for which both the turnoff point and the modulus are uncertain. These

variables are not discussed in the present section,

but will be considered in our discussion of the

Large Magellanic Cloud.

Distribution and Affiliations of Large Cloud

Variables

Figures 1-4 illustrate the distribution of

several types of variable stars, and of Cepheids

of various periods and luminosities, within the

boundaries of the Large Cloud. The distributions

are neither uniform nor similar. Table 3 summarizes conditions in a number of areas, including

five sections of the bar, counted from south to

north. Column 6 refers to a small region around

the Tarantula Nebula 30 Dor. Column 7 gives

average values of the tabulated quantities for the

whole Cloud.

Successive lines of the table contain: (1) area

in square degrees; (2) median log P for the Cepheids in the area; (3) through (8) numbers of

Cepheids, irregular variables, long-period (including cyclic) variables, W Virginis stars,

Wolf-Rayet stars, and eclipsing stars, all per

square degree. Columns (9) through (13) give

the ratios of the number of stars of the indicated

types to the number of Cepheids in the area.

The periods of the Cepheids in the bar are

shortest in Area A and progressively longer toward Area E (south to north). The relative

numbers of irregular and long-period variables

tend to increase over the same interval. The 30

Dor region is exceptionally rich in irregular variables and Wolf-Rayet stars, whereas the northern end of the bar, rich in irregular variables, is

relatively poor in Wolf-Rayet stars.

Several compact blue clusters, notably NGC

1866, 2058, and 2065, seem to be associated with

knots of Cepheids, but with few if any variable

stars of other types. They will be discussed later.

Table 3 illustrates the variety of the Large

Cloud population, ranging from that of the 30

Dor region (poor in Cepheids and rich in

Wolf-Rayet stars, irregular variables, and eclipsing stars) through the bar (absolutely and relatively rich in Cepheids, and containing other

types of variable star) to the blue populous clusters (where Cepheids predominate). There are

also, as we shall see, compact red clusters that

contain RR Lyrae stars.

The difference in distribution for Cepheids of

different periods and its relation to that of other

objects to which ages can be assigned suggest

that the variety displayed by Table 3 may furnish a way of studying the timetable of star formation in various parts of the Cloud. Arp (1964:

227) has already remarked: "It would be important to pinpoint areas of present star formation

and try to discover differences between them and

the neighboring areas where star formation has

just ceased. . . . By studying color-magnitude

diagrams of various regions of the Cloud . . .

much can be learned about the age composition

of the stars in various regions within the Cloud.

In combination with the velocity data a beginning could be made on the problem of how the

locus of star formation has moved within the

system as a function of time." We explore these

possibilities by collecting data on variable stars

that appear to be associated with datable components of the Cloud.

The basis of our study is the time scale for

clusters (Table 1), which enables us to relate

(B —V)T and (B —V)o to age. We also make use

of equation (2), which expresses the age of a Cepheid as a function of period and which has been

shown to be compatible with the Limber-Sandage time scale that has been used for the clusters. We must be mindful of the possibility that

the physical properties of both Cepheids and

clusters may not be the same in the Cloud and

the Galaxy, but while this possible difference

might invalidate an absolute time scale, it seems

legitimate to expect that the times deduced for

the Cloud will be consistent for clusters and Cepheids.

Datable components are summarized in the following tables beginning with the youngest. Actually, the smallest ages that have been assigned

in the Cloud are those attributed by Westerlund

and Mathewson (1966) to three possible supernova remnants, 300 years for 132 D and 3000

years for N 49 and N 63. Neither variable stars

nor clusters can be associated with anything so

recent. These authors also suggest that Constellation III, and perhaps Constellation I, discussed
0.2 - 0.3 0.5-0.6

••"••I

0.3-0.4 0.6-0.7

. ". • •

0.4-0.5

J

0.7-0.8

FIGURE 1.—Large Cloud: Distribution of Cepheids with various values of log P. The

outline of the bar is indicated.
NUMBER 16

0.8-0.9 I.I— 1.2

0.9-1.0

1.0—I.I

1.2—1.4

.4-1.6 • 1.6-1.8 •

• •

FIGURE 2.—Large Cloud: Distribution of Cepheids with various values of log P.

534-240 O - 74 - 2
SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Jl 3 • 13-14

15.5-15.99

14.0-14.49- 14.5-14.99* 16.0-16.49

• • * * •* *

15.0 - 15.49

FIGUBE 3.—Large Cloud: Distribution of Cepheids with various apparent photographic

magnitudes, averaged to mean intensity and uncorrected for absorption.
LPV

. o

WOLF RAYET

AND Be

o

c

."o

W STARS NOVAE o RR

FIGURE 4.—Large Cloud: Distribution of long-period variables (LPV), irregular red variables (Ir). eclipsing variables (E), Wolf-Rayet stars (WR, dots) and Be stars (Be,

circles), W Virginis stars (W, dots) and novae (circles), and RR Lyrae stars (RR).

Foreground stars among the long-period and irregular variables are indicated by circles;

all the RR Lyrae stars are foreground.
10 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

by Shapley and Nail (1953), may "have had their

origin in "super-supernova" explosions about 106

yr ago. These constellations are associated with

the clusters NGC 1968-1974 and NGC

1962-1965-1966-1970 (see Table 4).

Data for very young clusters and associations

are collected in Table 4. Successive columns give:

(1) name of the group; (2) values of (B —V)o

published by van den Bergh and Hagen (1968)

or derived from the data of Bok and Bok

(1962), the latter denoted by asterisks; (3) to

(6) logarithms of ages, deduced, respectively,

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

Square degree

Median log P

(per square deg

Cepheids

Irregular

Long-period

W Virginis

Wolf-Rayet

Eclipsing ratio

to Cepheids:

Irregular

Long-period

W Virginis

Wolf-Rayet

Eclipsing

TABLE 3.—Typical

ree)

1

Bar A

0.586

0.552

73.4

5.1

1.7

1.7

0.07

0.02

0.02

2

Bar B 1

0.651

0.600

areas

3

3arC

0.759

0.677

130.6 156.5

9.2

4.6

4.6

0.07

0.03

0.03

26.4

5.3

1.3

5.3

0.17

0.03

0.01

0.03

in the Large

4

Bar D

0.690

0.662

111.6

27.6

4.3

5.5

4.3

0.25

0.04

0.05

0.04

5

Bar E

0.427

1.020

72.6

14.0

4.7

4.3

0.9

4.7

0. 19

0.06

0.06

0.01

0.06

Cloud

6

30 Dor Area

0.695

0.544

1.235

14.4

21.6

2.9

15. 0

10.0

1.50

0.20

1.07

0.71

7

LMC Average

39

0.630

20.4

5.9

1. 1

0.3

1.0

1.4

0.29

0.05

0.02

0.05

0.07

TABLE 4.—Very young clusters and associations

NGC

1810

1818

1929-1937

1955

1968-1974

1962-1970

1983

1984

2004

2070

2074

2081

2092

2100

Westerlund

Area "b"

(B-V)o

-0.07

-0.29*

-0.21*

-0.27*

-0.20'

-0.12*

-0. 19

-0.22

-0. 12

Logarithm

From C-M Array

Maximum Turnoff

6.30 6.56

6.50

6.34

6.36 6.68

6.56 6.78

7.00

6.45 6.84

of Age (yr)

£S>0

6.93

6.12

6.40

6.18

6.44

6.74

6.47

6.36

6.74

W Stars

6.57

6.43,6.68

6.39,6.67

6.69

6.77

Adopted

6.93

6.93

6.12

6.48

6. 18

6.53

6.72

6.60

6.47

6.37,6.67

6.67

6.78

7.26

6.78

6.0-7.0

Members:

Red

Supergiants

2

3

0

0

2

0

0

2

6

1

0

2

2

18

45

W Stars

0

0

0

1

0

2

0

0

0

10

2

2

0

0

0

HV

5495

2556

1017

2753

5993

6002

957

2565

2567

5870

Variable Stars

Type

Irregular

Irregular

Irregular

Irregular

Irregular

Irregular

Irregular

Irregular

Irregular

LP

Magnitude

10.95-11.87

14.84-16.35

15.30-15.95

15.30-16.70

15.30-16.25

16.18-17.65

13.87-14.84

13.43-14.43

14.44-15.15

14.30-17.09

Color

Blue

Red

Red

Red

Red

Red

Red

Red

Red

Red

Reference

Color-Magnitude Array

Woolley (1960)

Woolley (1960)

Bok (1964)

Bok, Bok, and Basinski (1962)

Bok, Bok, and Basinski (1962)

Westerlund (1961a)

Westerlund (1961a)

Westerlund (1961a)

Woolley (1960)

Westerlund (1961a)

Westerlund (1961a)

Westerlund (1961a)

Westerlund (1961a)

Westerlund (1961a)

Westerlund (1961a)
NUMBER 16 11

from the maximum and turnoff of the color-magnitude diagram by Westerlund (1961a), from

(B — V) o , and from the apparent magnitudes of

the Wolf-Rayet stars; (7) logarithm of an

adopted age; (8) number of red supergiants; (9)

number of Wolf-Rayet stars; (10-13) name, type,

and magnitude color of variable stars; and (14)

reference to the source of the color-magnitude

array. The ages derived from (B —V)o were deduced graphically from Table 1. Those in the

sixth column are deduced with the help of the

observation of Westerlund and Smith (1964)

that the brightness of a Wolf-Rayet star seems

to be related to its age, the youngest being the

brightest. Westerlund (1961a: 44) states: "It appears likely that the turnoff point gives a good

estimate of the age of a stellar group. . . . All

stars of type Wolf-Rayet found so far are situated at the turnoff point." All the Wolf-Rayet

stars in the clusters tabulated have composite

(W + O) spectra. The average (vo) magnitudes of

those in NGC 1962-1965-1966-1970, 2074, and

2081 are found from the work of Smith (1968)

to be 11.14:, 12.48, and 13.31, respectively. These,

with the ages of the relevant clusters, lead to the

relationship

log t = 0.10 Vo + 5.44.

The similarity of the color-magnitude arrays for

NGC 1810 and 1818 suggests similar ages, and

we have assumed them to be equal. Bok (1964)

assigns to NGC 1929-1937 an upper limit of 6.3

for log t. We defer discussion of the complex region surrounding NGC 2070.

The striking feature of Table 4 is the absence

of Cepheids, though it contains 10 irregular variables. In the Large Cloud as a whole, the number

of known irregular variables is 3% of the number of known Cepheids. The upper limit of age

for the clusters in Table 4 is about 107 yr, and

we infer that their members have not had time

to reach the Cepheid stage.

The red irregular variables (when present) are

brightest in the youngest clusters. The red supergiants (some of which are probably undetected

variables) show the same tendency. Their average B magnitudes in NGC 1984, 2081, and 2092

are, respectively, 14.71, 15.32, and 15.72; the corresponding adopted values of log t are 6.60, 6.79,

and 7.26. The older the cluster is, the fainter are

the evolved stars. An order-of-magnitude estimate of their luminosities, based on a true modulus 18.45, a color excess 0.m

06, and a color index

l.m6, gives -5.6, -5.0, and -4.6 for Mv of the

red supergiants in the three clusters.

No red semiregular variables are known in the

youngest clusters and associations. The bright irregular variable in NGC 1983 is a blue star, HV

5495 = HD 269582 (P Cyg spectrum). In NGC

2081, there are both Wolf-Rayet stars and red irregular variables, with B magnitudes 13.09 and

15.30 (max.), respectively, but since the W stars

are composite, the actual W component may not

be much brighter than the red variable. Westerlund's area "b" is a large association whose red

supergiants have a spread of 3 magnitudes. This

suggests that it contains stars with a variety of

ages, as already noted by Westerlund. One longperiod variable lies within its probable boundaries. The ages suggested by the brightness of the

red variables and supergiants range from about

106 to over 107 yr. These facts are in harmony

with the conclusion of Stothers (1969: 935) that

clusters containing supergiants show "decreasing

and increasing number of blue and red supergiants, respectively, with age."

Data for the region surrounding 30 Dor (NGC

2070) are given in Table 5. The corresponding

entry in Table 3 relates to Westerlund's sampling of stars in a smaller area. Table 5 embraces

an area of 0.695 square degree, which contains 15

irregular variables, 10 Cepheids, and 2 long-period variables. Evidently, the region is less homogeneous in population and age than those just

discussed. The Cepheids favor two periods; the

irregular and long-period variables have average

maximal photographic magnitudes 15.11 and

15.36 (corresponding roughly to Mv —5.1 and

— 4.9). We conclude that the irregular variables

point to a value of about 6.5 for log t, but the

presence of Cepheids suggests a value of at least

7.0.

The small region within 30 Dor itself (Table

6) suggests a smaller age. Data for the W stars

are from Smith (1968); those for the O to F supergiants, from Feast, Thackeray, and Wesselink

(1960); those for the red supergiant, from Westerlund (1961a). In obtaining a value of vo for R

134, 135, 139, and 140, we have adopted the

absorption used by Smith for HD 38268.
12 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Unlike the clusters previously noted, the group

within 30 Dor contains W stars with a large

range in magnitude, from 8.48 to 12.51. Both the

brightest (HD 38268) and the faintest (HD

269926) have composite spectra. Even if (as is

quite possible) HD 38268 is as multiple as the

Trapezium in Orion, there must still be a range

of at least 2 magnitudes among the W stars, and

HD 38268 would be as bright (and hence as

young) as any W star in the Large Cloud. The

W stars suggest values of log t from under 6.4 to

6.7, the irregular variables about 6.7, and the CeTABLE 5.— Variable ntars in the 30 Dor area (0.695 square, degree)

HV

5940

5930

2666

2616

2613

2620

2647

1006

1005

2749

Cephelds

logP

0. 3747

0.5376

0. 6124

0.6666

0.6681

0.6843

1.1519

1.1527

1.2721

1.3637

<»>o

16.78

16.55

15.52

15.92

15.96

16.00

15.63

15.04

14.50

15.12

Irregular Variables

HV

2626

2635

2649

2655

2669

2674

2679

2681

2728

2732

2740

2753

2761

12990

13044

Magnitude

15.35-16.25

14.50-15.50

13.91-15.09

15.75-16.78

14.35-15.30

15.55-16.35

14.53-15.21

15.26

15.33-16.00

15.00-15.75

16.00-17.00

15.30-16.70

15.20-16.22

15.72-17.25

14.91-15.64

Long-Period Variables

HV

2677

2763

Magnitude

15.26-17.62

15.40-17.64

TABLE 6.—Young stars in the SO Dor region

Star

HD 269891

HO 269926

HO 38282

HD 269928

HD 38344

R 134

R 135

HD 38268

R 139

R 140

R 131

R 132

R 133

R 137

R 138

R 141

R 142

R 143

Westerlund 8

Spectrum

OB +WN

WN4 + OB

WN7

WN 7

WN 6:+OB

(WN 7)

(WN7)

OB + WN

WN7:* OB:

WN 6

B9 I

B-A

O8

B0.5 Ia:

AO: I:

B0. 5:

B

F5-F8 la

v

0

10.55

12.51

10.79

11.24

12.10

(11.40)

(12.19)

8.48

(10.91)

(10.86)

13.47

<b-v)0

-0.21

-0.18

-0.20

-0.20

-0.17

-0.21

(+1.94)

Radial Velocity

(km/sec)

+269

+235

+263
NUMBER 16 13

pheids at least 7.0. Westerlund 8, in the compact

region, has an apparent B magnitude of 15.41

(unconnected for absorption) and thus falls in

the same age group as do the irregular variables.

The compact group contains no known Cepheids,

although R 143 may possibly be one, with an uncorrected B magnitude of 11.36.

These facts suggest a complex history of the

30 Dor region. Stars have been forming in the

surrounding area for at least 107 yr, but in the

compact center there is nothing with log t

greater than 6.7, and some of the stars must be

even younger. The association around NGC

1962-1965-1966-1970 seems to be similar to the

30 Dor cluster, and so is the association near

NGC 1955, described by Bok, Bok, and Basinski

(1962) as consisting primarily of blue-white supergiants and containing HD 36402, WC5 + OB,

vo= 11.38, which corresponds to log t = 6.58.

Neither of these associations contains any known

variable stars.

The young populous ("blue globular") clusters

that contain variable stars are given in Table 7.

Successive columns give the name of the cluster,

(B — V) o from van den Bergh and Hagen (1968),

ages estimated as described above from the color

TABLE 7.—Variable stars in and near young populous clusters

NGC

1850

1854

1856

1866

2058

2065

2136

2156

SL204

(B-V)o

0.07:

0. 13

0.26

0.20

0. 17

0. 17

0. 14

(0.05)

lO(

(B-V)o

7.45

7.70

8.18

7.95

7.85

7.85

7.72

7.47

ft (yr)

Cepheld

7.20

7.46

7.66

7.85

7.92

7.81

7.83

7.84

7.84

7.80

7.89

7.88

7.81

7.84

7.85

7.81

7.8.1

7.90

7.74

7.81

7.69

7.84

7.76

7.83

7.69

7.8 4

7.82

7.83

7.59

7.49

7.72

HV

904

9 0 5

2349

11985

12192

12193

12194

121%

12197

12199

12200

12201

12202

12203

12204

12205

1220(5

2706

2713

2714

2717

2720

5975

5976

13042

1008

1009

2868

12078

W 49

Variable Stars

Cepheids -

logP

1.483

1.073

? 0.763

0.483

0.366

0.540

0.506

0.493

0.498

0.422

0.435

0.537

0.492

0.470

0.536

0.506

0.399

0.646

0.538

0.728

0.499

0.615

0.502

0.729

0.487

0.534

0.513

0.883

1.029

0.677

Irregular

m0 HV

13.57

14.2a

5626 17.24-18.18

15.70 11988 17.93-<18

17.00 11989 17.59-18.22

15.99

16.54

lfi.40

16.36

16.69

16.89

16.71

16.35

16.80

16.93

15.89

K.. 10

16. 5M

15.49

16.43

15.61

16.53

15.29

16.47

16.01

15.34

15.31

15. U

15.29

15.22

16.03
SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

of the cluster and the periods of the Cepheids,

and data on the associated variable stars. A

query indicates that the variable is far from the

cluster and may not be a member. For NGC

1866, we include only stars within 10' of the

cluster center. All these stars are in the list of

Shapley and Xail (1951) ; we have determined a

period for HV 12192. Several of these stars have

also been studied by Arp and Thackeray (1967).

The integrated spectral class for NGC 2156 is

from the Henry Draper Extension. No integrated color has been published for this cluster,

and we have adopted a mean of the published

colors for three clusters also classed as A3 in the

Henry Draper Extension (NGC 1774, 0.00; XGC

2134,0.10; NGC 2136, 0.05). The star W49 was

discovered by Woolley and Epps (1963) in Cluster No. 204 of the list published by Shapley and

Lindsay (1963).

The clusters have a moderate range of ages,

log t ranging from 7.45 to 8.08. The ages deduced from the periods of the Cepheids are in

general agreement with those deduced from the

colors of the clusters, except for NGC 1856, for

which we note that the Cepheid membership is

doubtful on account of distance.

The known variables associated with "red

globular clusters" are collected in Table 8. Values of (B —V) are from van den Bergh and

Hagen (1968) ; the clusters for which no color is

given were taken from the list of Hodge (1959).

Most of the variables in the list were discussed

by Hodge and Wright (1963) in connection with

the clusters; they regarded those marked with

asterisks as probable members. Data for three

known globular clusters that contain RR Lyrae

stars (NGC 1466, 1978, and 2257) are not included.

The data of Table 8 are not readily understood

in terms of previous tables. Most of the stars are

Cepheids, and except for the one near NGC 1953,

they fall near the period-luminosity curve for

normal Cepheids in the Clouds. Hodge and

Wright discussed the possibility that these stars

are Population II Cepheids, in recognition of

their proximity to red globular clusters.

It is now known from the work of Gaposhkin

(1972) and Payne-Gaposchkin (1971) that the

TABLE 8.—Variable stars in red globular clusters

NGC

1751

1783*

1786

1846

1953

1978

2019

2121

SL 363

SI. 569

US 83

B-V

0.63

(0.67)

0.74

0.78

0.77

HV

12904

12910?

880

2315?

12905*

12911?

5910

12908*

12909*

12656?

2439*

12906

12907

13015

13016

Cepheids

logP

0.290

0.504

1.067

0.382

0.820

0.262

1.322:

0.402

0.756

(0. 344)

1. 127

0.682

0.242

(-0. 002)

-0. 178

-0.236

m

o

16.00

16.33

14.72

15.93

16.29

16.49

(15.8)

16.32

15.20

(16.81)

14.80

16.19

17.14

(17.5)

16.56

16.64:

Irregular

HV m

5 unnamed

12973: 17.95-

13017 15.75-16.33

NGC 1783: Three variables (two red, one blue) are recorded by Gascoigne (1962) and two more (both red) have

been noted In Harvard plates. The mean blue magnitude for Gascolgne's red variables is 17. 54. He suggests

that the blue variable may be an eclipsing star.

NGC 1973: The data are from Hodge (1960a). Four variables, two probably of RR Lyrae type, are mentioned

by Thackeray (1959).
NUMBER 16 15

Large Cloud does contain some Type II Cepheids about 2 magnitudes below the period-luminosity relation. In addition to 16 such stars in

the Large Cloud, there are 3 in the Small Cloud.

The likelihood that the Cepheids of Table 8 are

of Type II seems to be reduced. If these stars

are actually normal Cepheids, we shall have to

assume that their membership in the clusters

must be rejected on grounds of age (since log t

for all these clusters must be between 9 and 10).

However, it is hardly justifiable to assign Cepheids to blue clusters on the basis of proximity

and then rejecfc stars that lie equally close to

globular clusters. We must therefore examine the

possibility that they are actually associated with

the clusters.

Hitherto, we have treated all the Cepheids, the

young clusters, and the blue globular clusters as

though they were at the same distance from us,

although we should note that Arp (1967) considered it possible that NGC 1866 itself might lie as

much as 18 kpc beyond the center of the Large

Cloud.

The clusters of Table 8 were all given by

Hodge (1960b) in his list of red globular clusters, and his (uncalibrated) color-magnitude arrays for all (except HS 83, which he did not

study) show a strong red-giant branch. The detailed calibrated color-magnitude arrays for

NGC 1783 by Sandage and Eggen (1960) and by

Gascoigne (1962), for NGC 1846 by Hodge

(1960c), and for NGC 1978 by Hodge (1960a)

all display giant branches that contain their

brightest stars. Moreover, the colors of van den

Bergh and Hagen (1968) exclude the possibility

that the clusters they observed belong to the blue

group. However, they display enough variety to

suggest that they may not be identical in age, or

makeup, or both. The bluest in the table, NGC

1783, is described as "unclassifiable" by Gascoigne. It has some features in common with

NGC 361 and NGC 419 in the Small Cloud, and

these he regards as of "intermediate age." We

note that "intermediate age" is a somewhat loose

term and was applied, for example, to the considerably younger cluster SL 204 by Woolley and

Epps (1963).

Gascoigne (1966) considered that NGC 1466,

1841, and 2257 resemble galactic halo clusters;

they are distant from the Large Cloud and contain RR Lyrae stars. "In the absence of further

evidence," he says, they "must be considered old

and metal-poor." Some other clusters in the

Large Cloud, such as NGC 2209 and NGC 2231

(not in Table 8, since they contain no known

variable stars), have, according to Gascoigne

(1966: 80), "no galactic counterparts, and a

priori it is difficult even to say whether they are

young or old." If, as he points out, their blue

stars belong to the upper end of a main sequence,

their distance moduli would be 19.5, and NGC

2231 and Hodge 11 would be 25 kpc beyond the

Large Cloud. ". . . this hypothesis," he adds,

"seems unlikely, and we would need further evidence before accepting it."

There is, in fact, some evidence that the Large

Cloud has a halo of globular clusters. The three

that are known to contain RR Lyrae stars (NGC

1466, 1841, and 2257) are far from the Cloud;

NGC 1841 is 13 kpc from it, a third of the distance that separates the Large Cloud from the

Galaxy. If the Cepheids of Table 8 had the luminosities of W Virginis stars, then NGC 2121, SL

363, and SL 569 would be halfway between the

Cloud and the Galaxy. This suggestion could be

tested by a search for RR Lyrae stars in these

clusters, because most galactic globular clusters

that contain W Virginis stars contain RR Lyrae

stars too. The "mini-cluster" HS 83 does in fact

lie about halfway between the Galaxy and the

Large Cloud, as pointed out by Gaposhkin

(1967), who discovered two RR Lyrae stars connected with it.

The variable in NGC 1978, regarded by Hodge

(1960b) as a W Virginis star, would resemble the

galactic W Virginis stars in luminosity if it were

at the distance of the main body of the Cloud.

The irregular variables in NGC 1783 present no

anomalies; no Cepheids are known in that cluster.

The information contained in Tables 4 to 8 is

summarized in Table 9, which arranges the material in order of adopted age. The youngest objects are probably in the 30 Dor association.

Wolf-Rayet stars are found in the youngest

groups; the younger the group is, the brighter is

the Wolf-Rayet star. The same is true of the red

supergiants (which are not, however, found in

534-240 O - 74 - 3
16 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

the very youngest groups) and the red irregular

variables. Cepheids appear in clusters over 107 yr

old, their periods being on the average smaller

for older clusters. Data for the globular clusters

XGC 1466, 1841, and 2257, which contain RR

Lyrae stars, are from Gascoigne (1966).

Table 9 reinforces the belief expressed by Tifft

(1964: 349) : " . . . the relative numbers of stars

formed in the various stages of the history of the

systems [the Magellanic Clouds and the Galaxy]

have been quite dissimilar." Hodge (1960b, for

example) has repeatedly emphasized this point.

Woolley (1961) describes the Large Cloud as

composed of a mixture of an old population and

a new one. Tifft and Snell (1971) describe the

makeup of the "bar": ".. . a very strong old

component. Superimposed upon this is an irregular scattering of younger stars." In this region

they find no evidence of "a specific intermediate

age giant branch like that found by Arp in the

. . . SMC globular cluster NGC 419."

We can now apply our results to dating the

features on the face of the Large Cloud. We

compare first the distribution of Cepheid variables of different periods in the Large Cloud

(Figures 1 and 2). For stars with log P up to

0.8, corresponding to log t = 7.64, the area north

of the Bar, which we may call the "desert," is

nearly bare of Cepheids. We can infer either

that stars in this extensive region (which contains the dynamical center of the Cloud) are inhibited from Cepheid behavior or that potential

Cepheids in the area are too young or too old to

be in the Cepheid stage. The former alternative

seems unlikely. The second is made probable by

the distribution of the ages of the clusters,

TABLE 9.—Summary of clusters and associations, Large Cloud

Cluster

NGC 1929

NGC 1962- 1970

NGC 2004

NGC 1955

NGC 1984

NGC 2074

NGC 1983

NGC 2100

NGC 2081

NGC 1810

NGC 1818

NGC 2092

NGC 1850

NGC 2156

NGC 1854

NGC 2136

SL 204

NGC 2058

NGC 2065

NGC 1866

NGC 1856

HS 83

NGC 1466

NGC 1841

NGC 2257

30 Dor

Westerlund "b"

Adopted

6.12

6.44

6.47

6.48

6.60

6.67

6.74

6.74

6.79

6.93

6.93

7.26

7.47

7. 17

7.70

7.74

(8.06)

7.85

7.85

7.96

8. 19

>9

>9

>9

6.0-8.0

6.0-7.0

Wolf-Rayet

V

0

11. 14:

11.38

12.48

13.31

10. 5:-12. 5

Mean Magnitude

Red Supergiants

B

14.7

14.71

15.32

15.50

15.15

15.75

17.8

17.9

17.8

15.41

13.5-16.4

Red Irregular

Variables

mp g (max.,

14.84

15.30

16. 18

17.24

17.76

15. 75

15. 11

13.91

Cepheids

Mean log P

1.27

1.03

0.88

0.68

0.59

0.52

0.51

0.62::

-0.20

RR Lyrae

RR Lyrae

RR Lyrae

0.59-1.35
NUMBER 16 17

shown in Figure 5. The ages have been deduced

from the intrinsic colors published by van den

Bergh and Hagen (1968), including those of

some clusters not entered in our tables, because

they contain no variable stars. It is seen that

within the same roughly elliptical area avoided

by the Cepheids, there are no observed clusters

with values of log t greater than 7. Outside this

area, all the ages exceed this value. As we noted

earlier, the ages of Cepheids lie between 107 and

108 yr. We can then conclude that the potential

Cepheids in the "desert" area are too young to

have reached the Cepheid stage and that star

formation dates there from less than 107 yr ago.

There might, of course, have been another epoch

of star formation more than 108 yr ago whose

products are too old to be Cepheids now; but if

so, it has left no obvious relics in the shape of

intermediate-age clusters. When we look at the

distribution of Cepheids with longer periods, we

find them still sparsely represented in the "desert," and only for log P greater than 1.4, corresponding to log t = 7.25, do we find a good proportion of them encroaching on the region. On

the other hand, the bright irregular variables

(all very young, as shown by Table 4) and the

similarly young Wolf-Rayet stars are practically

confined to the area; the long-period variables

(also bright and very young) are well represented there, and so are the eclipsing stars, most

of which, as blue supergiants, also belong to the

very young population.

301-095

• 8.35

• 7.96

• 7.79

# 7.47

7.76

7.85* »7.74

• 7.66

7.38 •

•8.24

• 8.10

FIGURE 5.—Ages of clusters, expressed as log t in years. Circled dots denote globular

clusters.
18 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Along the northern edge of the region, there

are concentrations of Cepheids with log P between 0.4 and 0.7, corresponding to log t from

7.70 to 7.90. Such clusters as occur in the region

have similar ages. On the extreme northern edge

lies NGC 1866, the nucleus of a knot of Cepheids

of comparatively short period and an inferred

log t of 7.96.

The greatest concentration of Cepheids is in

the "bar" itself. As can be seen from Figure 1,

the highest density of Cepheids seems to move

up the bar from south to north with advancing

period; for log P 0.4 to 0.5, it is at the southern

end; for log P 0.7 to 0.8, it is in the center; and

for log P 1.2 to 1.4, it is concentrated at the

northern end. The progression is illustrated in

Table 10.

Data for the 30 Dor area are included in Table

10. The area of the Tarantula Nebula lies just

north of Area A and on the edge of the "desert."

We can infer a progression of star formation

along the bar from south to north, including the

contiguous 30 Dor area, beginning with log t =

7.81 and growing more recent as we proceed

northward along the bar. A second and much

more recent era of star formation is indicated

around 30 Dor and extends, as shown above,

through the desert region. A similar progression

can be noted in the ages of the star clusters in

and near the bar. As pointed out by Tifft and

Snell (1971), the bar has also been the seat of a

much earlier era of star formation, but we may

suppose that it is poor in components of ages 108

to 10» yr.

The very oldest stars evidently occupy extensive regions of the Large Cloud. Red globular

clusters are found as far as 25 kpc from it. In

fact, the situations of NGC 1466 and 1841 suggest that the two Clouds form an extensive binucleated system.

The evolutionary history of the Small Cloud

seems to have been quite different from that of

the Large Cloud. The youngest stars are found

in progressively more concentrated areas, and the

brightest Cepheids of longest period are almost

all found in the "axis," as shown by Payne-Gaposchkin and Gaposchkin (1966). All these stars

are probably still not far from their point of

birth. The axis of the Small Cloud seems to have

been producing stars continuously since about 4

X 108 yr ago, though not necessarily with a constant mass spectrum or at a constant rate. The

"wing" area of the Small Cloud has, however, a

different history from that of the body of the

system. It contains no Cepheids with log t

greater than about 7.5, and few with log t less

than about ,7.3; it also possesses many bright

blue stars that date back only about 10s yr. It is

in fact by far the youngest part of the Small

Cloud, as was pointed out by Westerlund (1961b).

It is interesting to compare these distributions

with the seemingly more orderly arrangement

that prevails in the spiral galaxy Messier 31 and

in our own system.

The work of Baade and Swope (1963, 1965)

and of Gaposchkin (1962) shows a progression

of properties in four areas. Table 11 feproduces

their results. The angular distances have been

converted to kiloparsecs with a distance of 674

kpc. The values of log t have been calculated as

before.

Our own Galaxy displays a similar progression,

as pointed out by van den Bergh (1958) and others. Table 12 represents the relation recently deduced by the writer from a rediscussion of all

available galactic Cepheids.

In both Messier 31 and our Galaxy, these numbers, taken at face value, indicate that the

youngest Cepheids are nearest to the center. In

the Small Cloud (except for the "wing"), we can

say with confidence that the oldest Cepheids are

at the edges. The Large Cloud is less simple. The

paucity of Cepheids near the dynamical center,

TABLE 10.—Ct-pheid variables in the bar

Median log P

Corresponding log t

0.552

7.80

0.600

7.77

0.677

7.72

0.662

7.73

1.020

7.50

0.544

7.81

1.235

7.3«
NUMBER 16 19

TABLE 11.—Cepheids in Messier SI

Region

Distance from nucleus

kpc

Medium log P

logt

I

15"

2.96

1.14

7.42

n

36'

7.01

0.85

7.61

m

50'

9.77

0.91

7.57

IV

96'

14.76

0.59

7.78

TABLE 12.—Galactic Cepheids

Distance from Galactic Center

(kpc)

6 - 7

7 - 8

8 - 9

9-10

10-11

11-12

12-13

13-14

14-15

15-16

16-17

Mean log P

1.334

1.158

0.956

0.842

0.877

0.799

0.780

0.728

0.643

0.691

0.671

Number of Stars

7

24

46

142

62

52

62

23

14

1

2

logt

7.29

7.41

7.54

7.61

7.59

7.64

7.65

7.69

7.74

7.71

7.72

and the fact that the youngest clusters are found

in that area, might be interpreted in the same

sense. But the youngest Cepheids in the Large

Cloud seem to concentrate toward the northeast

border.

From the distribution of Cepheids, we can evidently obtain some information about the history

of star formation in a galaxy, but this information pertains only to an interval from 107

 to 108

yr ago. Clusters do indeed provide data for times

before and after this interval, and it is encouraging to note that these data are not contradictory

for times where the scales overlap, at least in the

Large Cloud.

Evolutionary Patterns for Cepheid Variables

We consider that data presented in the preceding section establish that the stars in recognizable areas (clusters and associations) were formed

at different times. We suggest that the differences between the properties of the Cepheids in

various areas are results of these differences in

age, and that this conception can be extended to

areas of the Clouds and our own Galaxy that

have not been shown to contain otherwise datable

components. We further suggest that the differences between the variable stars of the Large and

Small Clouds, and of our own Galaxy, can be

similarly interpreted. We now examine the consequence of differences of age on the basis of current theory of evolutionary tracks to see whether

(or how far) they are adequate to produce the

observed differences in the properties of the variable stars in the systems considered. In the present section, we shall not consider the effects of

possible differences of composition, whose reality

we shall explore in a later section.

Recent work, notably of Hofmeister, Kippenhahn, and Weigert (1964a, b, c), Kippenhahn,

Thomas, and Weigert (1965), Iben (1966a, b, c),

and Hofmeister (1967a, b), has shown that an

evolving star becomes a Cepheid when its evolutionary track crosses a certain domain in the luminosity—effective-temperature plane. This domain, the "Cepheid gap," lies farthest to the red

for the stars of highest mass (and luminosity).

Tracks relevant to classical Cepheids are those

for masses between 3 and 9Q. The tracks may

cross the gap as many as five times, and on each

pass the star should be a Cepheid. The general

course of the tracks is well established, but as the

calculations are still subject to refinement, the results differ in numerical detail. Therefore, it

seems best to keep the argument qualitative as

far as possible. The theoretical results harmonize

qualitatively with the observed period-luminosity

and period-color relations. But the predicted

tracks are sensitive to composition, as well as to

the adopted physical parameters such as opacities and mixing lengths, so exact numerical comparison with observation seems premature.

Figure 6 shows schematically the theoretical

tracks for stars of masses 3, 5, 7, and 9Q in the

period-luminosity plane. A track labeled 7,1 de-
20 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

- 5

"pg - 2

1.6

FIGURE 6.—Passes in the period-luminosity plane for several solar masses. The parallel

lines indicate the approximate bounds of the instability strip. Each pass is identified by

two numbers, the first indicating the solar mass, and the second, the number of the pass.

For example, 7,1 indicates the first pass for a star of 7 solar masses. Arrows indicate

the direction of the pass. Ordinates are logarithms of period in days, and abscissae,

absolute photographic magnitudes.

notes pass no. 1 for mass 7£), and so forth. The

bounding lines are defined by the width, in effective temperature and color, of the Cepheid gap;

they define the limits of the period-luminosity

relation. The actual values are uncertain, since

they depend on the model chosen, but the general

picture is representative. It shows that there will

be a dispersion in luminosity for stars of a given

period, and a dispersion in period for stars of a

given luminosity. It also shows that stars of

given period and luminosity can have a variety

of masses.

Changes of period have been calculated by

Hofmeister (1967b) for various masses. They are

positive (period increasing) for passes 1, 3, and

5 and negative for passes 2 and 4. On account of

different rates of development during different

passes, the changes are smallest, in general, for

passes 2 and 3, larger for pass 4, and largest for

passes 1 and 5, for stars of a given mass. For the

same reason, the chance of observing a star of

given mass as a Cepheid is largest for passes 2

and 3, less for pass 4, and least for passes 1 and

5 (assuming, of course, that stars of this mass

have been supplied at a steady rate). Hofmeister's predictions show an order-of-magnitude

agreement with observation for some galactic Cepheids, as she herself has pointed out.

If there is a secular change in period, the period P can be expressed as

P - Po + x • PoB,

where Po is the period at an initial epoch, E the

number of epochs elapsed since the initial epoch,

and x a constant. After E epochs, the time at

which the star reaches a certain phase (e.g., max-
NUMBER 16

imum) will deviate by <x POEV2 from the time

predicted for constant Po .

Table 13 presents, for 23 galactic Cepheids,

data taken from the compilation by Parenago

(1958), from Walraven, Muller, and Oosterhoff

(1958), and from Oosterhoff (1960). The change

of period is expressed as the logarithm of the

change per century, in terms of the period, because Hofmeister expresses her results in this

form. The passes are tentatively identified. Table

14 gives similar data for 13 Magellanic Cepheids.

The expected change of period depends on the

following: (1) the mass of the star, being

greater for larger masses; (2) the pass being

traversed, as noted above; and (3) the composition. In Figure 7, we compare the observed values of AP/P per century with those predicted

for stars of initial masses 5, 7, and 9Q having

Hofmeister's "extreme" (= metal-rich) composition; the periods used are those she has calculated for maximum excitation at the respective

masses.

The observed changes of period are of the predicted order of magnitude, and there is no great

difference between the galactic and Magellanic

Cepheids. Of the 36 stars in the tables, only 3

are assigned to pass 1, which reflects the relative

brevity of that pass and the rarity of the stars

found to be performing it. For the Magellanic

Clouds, where over 2200 Cepheids have been

studied, only one can be assigned to pass 1.

The computed tracks suggest that at a given

period (mass loss being disregarded) a star

would become progressively brighter in going

from pass 1 to pass 5. A rough test for this tendency can be made by comparing values of mo +

2.5 log P (a measure of deviation from the period-luminosity relation) for the assigned passes.

The results are as follows for the Magellanic Cepheids :

Pass

1 (5)

2 (4)

3

m<, + 2.5 log P

17.61

17.49

17.37

No. of start

1

7

5

The number of stars is too small for conclusions;

if the passes are indeed 1, 2, and 3, the tendency

is in the direction expected.

Not all changes of period, however, are secular. Seventeen Cepheids in the Large Cloud and

two in the Small have shown discontinuous

changes of period, and with two exceptions, these

changes are increases, ranging from about 0.001

P at 3 days to nearly 0.01 P at about 100 days

and showing a rough correlation with period.

The fact that some stars show apparently secular changes of period, others show discontinuous

changes, and some show no changes at all disTABLE 13.—Changes of period of galactic Cepheids

Star

AXVel

WZ Pup

6Cep

i?Aql

£Gem

TWNor

SZ Cas

RWCaa

XX Car

YZCar

VYCar

RU Set

WZCar

SW Vel

XPup

T Man

ICar

EVAql

RS Pup

SV Vul

logP

0.41

0.70

0.73

0.86

1.01

1.03

1.13

1.17

1.20

1.26

1.28

1.29

1.36

1.37

1.41

1.43

1.55

1.60

1.62

1.65

Sign of x

+

-

+

-

+

+

-

-

+

-

+

-

+

+

+

-

log AP/P

per Century

-2.71

-2.14

-4.82

-4.47

-3.45

-2.32

-1.78

-3.11

-2.41

-2.66

-1.70

-2.36

-1.70

-1.53

-1.40

-3.19

-2.09

-0.62

-2.62

-1.97

Pass

1

1

2

3

2

1?

1

2

2?

3

4?

3

1

1

1

3

3

1

3

2

TABLE 14.—Secular changes of period for Magellanic

Cepheids

HV

12697

12534

2795

2584

1695

1003

902

2251

1002

909

2257

834

829

System

LMC

LMC

LMC

LMC

SMC

LMC

LMC

LMC

LMC

LMC

LMC

SMC

SMC

logP

0.388

0.464

0.592

0.670

1.164

1.388

1.421

1.447

1.484

1.575

1.594

1.867

1.947

log AP/P

Sign of x per Century

+ -3.81

-3.32

-3.84

+ -2.40

-2. 95

-2.38

-2.45

-2.30

• -2.61

+ -2.49

+ -2.77

+ -2.30

-1.26

P u s

3

4

4

1

2

2

2

2

3

3

3

3

2
22 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

turbs the clarity of the picture. Perhaps we

should consider that all changes are discontinuous : the star maintains a constant period for a

time and then changes more or less abruptly to

another period. If such changes are frequent and

observation is intermittent, the impression of a

secular change is produced. If they occur at long

intervals, a discontinuous change is inferred. If

these intervals are comparable to the baseline of

observation, the period appears to be constant.

Apparently, secular changes show increases and

decreases in roughly equal numbers, but discontinuous changes are almost all increases.

Table 15 summarizes change of period of all

types for Magellanic Cepheids. The percentage

of stars with observably variable periods increases almost uniformly from short to long periods, despite the fact that the number of elapsed

epochs in a given time interval (over 50 yr for

the Harvard material on the Magellanic Clouds)

is greater for a star of short period.

Our study of period changes permits four conclusions: (1) the observed secular changes are of

the order predicted by Hofmeister; (2) they do

not differ appreciably between the Magellanic

Clouds and the Galaxy; (3) some stars show secular changes of period, others show discontinuous changes, and others (in the same period

range) show none; and (4) the percentage of

stars with inconstant periods increases with period.

The most realistic statement is probably that

the theoretical changes of period (predicted at

maximum excitation for the relevant masses) coincide roughly with the upper limit of the observed changes of period. But (as illustrated in

detail later) stars of a given mass should theoretically show a variety of periods, and stars of

a given period should accordingly possess a variety of masses. The rate of development and

hence the rate of change of period are very sensitive to mass. The stars that show the largest

changes of period will be those of the largest

mass in the range of period considered. From

this point of view, we should expect to find what

is actually observed: upper limits to the rate of

change at any one period, corresponding to the

stars of highest mass. On any probable assumpFIGURE 7.—Change of period, in logarithms of AP/P per century, plotted against log P,

for galactic and Magellanic Cepheids. Triangles refer to galactic stars, circles with dots to

Large Cloud stars, and dots to Small Cloud stars. The + and - signs beside the symbols

indicate whether the period is increasing or decreasing. Theoretical lines calculated by

Hofmeister are shown for passes 1, 2, and 3, and a possible course for pass 5 is indicated.

On passes 1, 3, and 5, the period is increasing; on passes 2 and 4, it is decreasing.
NUMBER 16 23

TABLE 15.—Changes of period for Magellanic Cepheids

logP

-0.1 -0.099

0.10-0.299

0.30-0.499

0.50-0.699

0.70-0.899

0. 90-1.099

1.10-1.299

1.30-1.499

1.50-1.699

1. 70-1. 899

1.90-2.099

2. 10-2.299

Increase

2

1

5

4

5

1

1

Large Cloud

Decrease Erratic

1

2

1

3

1

1

Cepheids

0

19

233

485

169

92

57

36

13

2

2

1

Small Cloud

Increase Decrease

1

1

1

Erratic

1

1

1

Cepheids

39

293

321

248

116

57

46

16

12

3

2

1

%

0

0

0.6

0.3

0

1.3

7.7

13.4

24.0

40.0

75.0

0

Combined

Cepheids

39

312

554

733

285

149

103

52

25

5

4

2

tion as to the mass-frequency function, such stars

would be a minority. We therefore feel justified

inYegarding the rough correspondence between

theory and observation, for stars whose changes

of period have been observed, as evidence that

the time scales that have emerged from the calculations are of the right order.

We are not yet in a position to anticipate what

effect composition will have on the rate of

change of period. The most we can say is that if

composition has an appreciable effect, the similarity of the changes of period for galactic and

Magellanic Cepheids does not point to an appreciable difference of composition.

The computed times derived from the tracks of

Hofmeister (1967b) and of Iben (1966a, b, c) are

not identical. The Iben time scale would lead to

log t = 8.34 - 0.717 log P,

and the Hofmeister time scale to about

log t = 8.14 - 0.717 log P,

a formula that would give results very little different from those deduced from Tammann's formula (equation (3)).

The predicted position and width of the

Cepheid strip are compatible with the observed

dispersion of the period-luminosity relation. As

pointed out by Payne-Gaposchkin and Gaposchkin (1966), 50% of the Cepheids in the Small

Cloud lie within O.m22 (photographic) of the line

defined by a linear least-squares solution for the

period-luminosity relation. Sandage and Tammann (1968) admit a total spread of ±0.m

6 at

any one period. Figure 7 suggests ±0.m5.

The slope of the period-luminosity relation

also seems to agree fairly well with prediction.

The values deduced from Hofmeister's maximum-excitation points and expressed for photographic magnitudes give

Mpg = - 0.96 - 2.44 log P,

if a linear relation is assumed. This relation falls

within the limits of the nonlinear relation favored by Sandage and Tammann (1968).

In summary, the theoretical tracks conform

reasonably well with observation, and their form

will therefore be accepted in principle.

Evidence Bearing on Composition

In the preceding sections, we have attributed

the differences between the two Clouds, and between the Clouds and the Galaxy, to differences

in history. We must now examine the evidence

for another widely acclaimed source of difference

—chemical composition. It seems, from the evidence that has been presented, that differences of

age and history are inescapable. Is there also evidence as to differences of composition?

Within our Galaxy, the recognized differences

of composition embrace the extreme metal poverty of some members of the halo population and

the metal richness of the young Population I
24 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

stars. The range is illustrated by an excerpt from

the compilation of Aller (1961: 203).

Population Halo Intermediate Disk Old Young

II II II

Fraction of

heavy 0.003 0.01 0.02 0.03 0.04

elements by

weight

Age (10s yr) 6000 5000 to 1500 to 100 to under

6000 5000 1500 100

From Table 9 we see that the oldest variable

stars that we have studied in the Clouds have

ages of about 108 yr; thus, they fall within the

age limits of young galactic Population I stars,

or exceed it only slightly. The globular clusters

associated with the Large Cloud, some of which

contain RR Lyrae stars, must of course be older,

and Walker (1972) has shown that NGC 2257 is

either of "extremely low metal content like M 92

but with an abnormally low red-giant branch,"

or a cluster of intermediate metal deficiency like

M 3 or M 13.

We are concerned, however, with differences

between the LMC, the SMC, and the Galaxy that

depend on studies of variable stars and young

clusters, and if differences between these are results of composition, we must suppose that the

material that was available in the Clouds for

star formation 108 yr ago was of different atomic

makeup from the contemporaneous material in

our Galaxy. We can test this possibility only by

examining the current composition of young

stars and nebulae in the Clouds.

Several sources of information are available:

(1) direct analysis of stellar spectra; (2) direct

analysis of nebular spectra; (3) UBV photometry of stars; (4) ubvy photometry of stars; (5)

color-magnitude arrays of clusters; (6) colors of

Cepheid variables; and (7) period frequency of

Cepheids. Conclusions based on (1), (2), (3),

(4), (5), (6), and (7) are progressively less direct.

1. There are no obvious differences between the

spectra of luminous Magellanic and galactic

stars. Code and Houck (1956, 1958) found the

stars they examined in the Large Cloud "essentially similar to the OB stars of our own Galaxy." Studies by Feast et al. (1958, 1960) were

based on direct spectroscopic comparison, on

comparison of H-R diagrams, and on UBV

photometry. They stated that "We have found

no evidence . . . that there is a difference in

chemical composition," and further that "Peculiarities have been found in certain stars, most of

which can certainly be attributed to causes other

than metal-poorness." A more detailed result is

the coarse analysis of the spectrum of HD 33579

in the Large Cloud by Przybylski (1965), who

found the value of log (metals/H) smaller in

HD 33579 by -0.2 ± 0.2. Feast (1964) found no

evidence of metal weakness in his study of the

SMC cluster NGC 330.

2. The He/H ratio has been studied for 30

Dor by Hugh Johnson (1959) and by Faulkner

(1964). The former derived a ratio 0.13, nearly

the same as for the Orion Nebula. The latter

gives the values 0.074 for 30 Dor, 0.117 for the

Orion Nebula, and 0.114 for the Eta Carinae Nebula, and O/H ratios of 2.5 X 104

 for 30 Dor

and 3.4 X 10* for the Orion Nebula; the differences seem marginally significant. The He/H

ratio for NGC 346 (Small Cloud) was found by

Aller and Faulkner (1962) to be 0.11.

3. The application of UBV photometry to the

blue supergiants in the Clouds is complicated by

the difficulty of determining the intrinsic colors.

Not only are the intrinsic colors given by Johnson (1963) for luminosity classes la and Ib in

the Galaxy too red, as shown by Serkowski

(1963) and tabulated by Schmidt-Kaler (1965:

297), but also they are functions of luminosity,

as could be deduced from the work of Mendoza

(1971) and as specifically pointed out by the

Walravens (1971). We note, however, that Dachs

(1972) does not take account of this effect. It

seems that, except for the excessive luminosities

of some Cloud supergiants, the conclusions of the

Walravens (1964: 328) still stand: ". . . no real

difference can be detected between the Galaxy

and the Magellanic Clouds." Insofar as intrinsic

color is an index of composition, we conclude

that no real difference in the latter is established

by these data.

4. Using four-color intermediate-band photometry, Williams (1961) reached the conclusion

that the metal/H ratios "do not differ by a large

factor, if at all," between the Clouds and the

Galaxy, at least for the long-period Cepheids to

which the study was confined.
NUMBER 16 25

5. The color-luminosity arrays of clusters have

received conflicting interpretations. From his

careful photometry of cluster stars in the Small

Cloud, Arp (1958a, b, 1959a, b) has argued that

the clusters considered are metal poor. Feast

(1960) considers that the same data do not require metal poverty. These clusters fall into the

group described by Gascoigne (1966: 81) as of

"intermediate age," unlike the true globular clusters such as NGC 2257, which have been shown

by Walker (1972) to be metal poor. These intermediate-age clusters are certainly older than any

of the variable stars with which we have been

concerned.

6. The colors of the Magellanic Cepheids have

been extensively discussed, and I shall not here

deal with the subject in detail, as I have treated

it elsewhere (Smithsonian Contributions to Astrophysics, no. 17). Here I will state the bare outline: the difference in color between the LMC

Cepheids and those of the Galaxy is barely significant. When light amplitude is taken into account, there is a definite difference in color at

minimum between galactic Cepheids and those of

the Small Cloud; at maximum the colors do not

differ sensibly. At minimum the difference is

about 0.ml, which seems significant. However, it

is found primarily for the Cepheids of shortest

period and faintest magnitude and may be an effect of background light on the B magnitudes. It

is not certain, even if the difference in color at

minimum is real, that it points to metal poverty

for Magellanic Cepheids. Why is it inconspicuous or absent for the maximal colors?

7. The argument based on differences of period

frequency is even less direct. In the next section,

we shall examine the effects of age on the period-frequency and period-amplitude relations. If

the differences can be attributed to age alone, it

would seem unnecessary to invoke differences of

composition in interpreting them, unless this has

been rendered inescapable by more direct arguments.

In summary, our discussion of evidences for

composition differences suggests that these data

do not compel us to conclude that such differences exist between the young stars and clusters

of the Clouds and our Galaxy. A similar view is

expressed by G. Burbidge (1971): ". . . the bulk

of the matter which is easily studied in the Magellanic Clouds . . . contains elements with similar total and relative abundance to that in the

disk of our Galaxy." He adds that "there may

very well be a range of element abundances in

the Magellanic Clouds similar to that in our Galaxy."

The Period-Frequency and Period-Amplitude

Relations

In examining the effects of the age of a stellar

group on the period-frequency function and the

period-amplitude relation of the associated Cepheids, we find the crucial consideration is that

the time taken for a star of given composition to

reach the Cepheid stage is exceedingly sensitive

to mass. Hofmeister (1967b) has tabulated the

times spent on the main sequence and in the Cepheid stage for stars of masses 5, 7, and 9Q« The

transition from main-sequence to Cepheid stage

is so rapid that the time spent on the main sequence is approximately equal to the whole age

of a star that has become a Cepheid. Therefore,

the ratio of these times gives a measure of the

fraction of its lifetime that a star spends as a

Cepheid. We select for comparison the "extreme"

composition (X = 0.602, Z = 0.044), since "normal" composition seems ruled out by the observed changes of period. Extreme and normal

compositions differ both in H/He ratio (greater

for normal) and in metals/He ratio (greater for

extreme). Kippenhahn (1965: 14) has remarked:

"It seems clear that the appearance or disappearance of the loops depends on the ratio of the

speed of the helium burning phase to some kind

of adjustment time of the outer layers. . . . Although we do not yet understand what actually

caused the disappearance of the loops [for normal composition], it seems empirically that the

loops are a good indication for chemical composition."

The times given by Hofmeister, and their ratios, are as follows:

Mass (©) 5 7 9

Time on main sequence

(yr) 5.07 X10T 2.61 X107 1.66X107

Cepheid stage (all passes)

(yr) 2.82X106 5.4X10* 2.1X10*

Ratio 0.0555 0.0218 0.0013

Accordingly, in a group of stars that are similar in age but different in mass, those that are
26 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

Cepheids at any one time will have an extremely

small range in mass. Coeval stars whose masses

differ by more than a few percent cannot be Cepheids at the same time. But stars with this very

limited range of mass will, if of the same age,

display a considerable range of period, depending on their current position in the Cepheid

strip.

Hofmeister has calculated "stability coefficients" for all five passes of a star of mass 9.

Maximum value of the stability coefficient rj is

associated with the model of maximum pulsational excitation for the corresponding mass. It

seems reasonable to suppose that this model will

correspond to maximum light amplitude and

that amplitude will be related in some way to 17.

Figure 8 shows the values of 77 for the five passes of a star of mass 9. A coeval group of stars

with masses very close to 9© will display a variety of periods. The amplitudes should be small

for the shortest of these periods, should rise to a

maximum for log P rather greater than the average, and should fall more abruptly on the longperiod side. This would follow even if the expected amplitudes were weighted in inverse

proportion to the speed at which stars traverse

the strip at the corresponding pass (greatest

weight to passes 2, 3, 4, less to pass 5, and least

to pass 1).

If stars of other masses have a similar relationship between 77 and period at the various passes, a similar result would be valid for each

log P

1.4

1.2

O"Z x1. 0

0.8

0.6

0.4

0.2

0

1.0 I.I

i i

I

f

1.2 1.3 1.4

1 i •

V

4

I

J

1.5

\

>

\

\

\

\

\

\

\

1.6

\

\

\

\

\

\

2

i

1.7

-

-

-

-

i

4

i

FIGURE 8.—Hofmeister's "stability coefficient" y plotted against log P for all five passes

of a Cepheid of 9 solar masses. The number of the pass is indicated at the right-hand end

of the line; arrows on the line show the direction in which the period is changing.

Vertical arrows indicate the point of maximum stability. The relative durations of passes

1 to 5 are, respectively, 10, 55, 97, 37, and 11.
NUMBER 16 27

mass. Each coeval group would show its own period-amplitude function over a limited range of

periods.

If the stars in a system are not coeval but are

being produced continuously, their period-amplitude functions will be superimposed. The lower

limit of period will be set by the interval since

the oldest stars that have reached the Cepheid

strip were produced; these will be the Cepheids

of lowest mass, which develop the most slowly.

At a given time, these stars will be joined by

more massive stars, born more recently, that have

reached the Cepheid strip. These stars will have

a period-frequency function that produces maximum amplitude at a somewhat longer period

than the oldest group. At the same time, stars

still more massive will contribute period-amplitude functions with maximum amplitudes at still

longer periods. A group in which stars are being

continuously supplied will show a period-amplitude function that is the sum of the period-amplitude functions of all the stars massive enough

to have reached the Cepheid strip. One can see

that this function will reach a plateau at the period corresponding to the period of maximum

excitation of the least massive stars that have

reached the Cepheid stage. This would be true

(on account of the different rate of development

of stars of different masses) even if stars of all

masses were produced in equal numbers; actually, the less massive stars are probably always

the most numerous, and the maximum will be accentuated.

In the Small Cloud, the Large Cloud, and the

Galaxy, there is a close relationship between the

period-amplitude and the period-frequency relations: they tend to peak at the same period. The

foregoing suggestion is in harmony with this

fact. At the long-period side of the frequency

distribution, the overlapping stability coefficients

would lead to a rather abrupt fall in the period

frequency and a concomitant diminution in amplitude ; this also is observed.

An alternative interpretation of the differences

of period frequency rests on the possibility that

within the Cepheid strip the situation of the

loops in the evolutionary tracks may differ from

star to star, perhaps as a consequence of composition. Hofmeister's "normal" calculations (relatively poor both in helium and in metals) show

almost complete suppression of the loops, so that

the Cepheid stage would be confined to pass 1. If

this result is valid, a population of "normal"

composition would contain less than 1% as many

Cepheids as an "extreme" population with the

same distribution of masses and the same history.

If the Small Cloud is metal or helium poor

compared to the Galaxy, it should be far poorer

in Cepheids, whereas it appears to be far richer.

Thus, even if the difference between the Galactic

and Magellanic Cepheids is a result of composition, this argument cannot be used to show that

the Clouds are poorer in metals.

A period-frequency function has been predicted by Smak (1962) with simplified assumptions: (1) Cepheids originate from an initial

main sequence that has the Salpeter initial luminosity function; (2) the Cepheid stage follows

closely after the main-sequence stage at the same

(visual) absolute magnitude; (3) the Cepheid

lifetime is proportional to mass/luminosity. The

frequency function thus predicted falls sharply

with increasing period and thus agrees (at least

qualitatively) with the observed period-frequency functions of the Galaxy and the Clouds

for periods greater than that corresponding to

the maximum frequency. But the deficiency of

short periods is not predicted; Smak inclines to

attribute it to observational incompleteness, a

consequence of small amplitudes at short periods.

However, as shown by the writer (1971), it is

undoubtedly real.

Hofmeister (1967b) refines the approach. Assumption (1) is retained, (2) is somewhat modified, and (3) is replaced by the lifetimes cited

earlier, which deviate greatly from Smak's assumption. The resulting function shows an abrupt rise to maximum and a slower fall toward

long periods, numerical agreement being best for

the Small Cloud. She attributes the differences

between systems to slight differences in the location of the loops within the Cepheid strip: ". . .

we may suspect that different metal-to-helium ratios in the Galaxy and the Small Cloud might

lead to a shift of maximum."

The alternative interpretation now put forward is that the supply of stars has not been

continuous and that star formation (producing

stars that are now Cepheids) became important
28 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

at different times in different systems—earliest in

the Small Cloud, later in the Large, and latest in

the part of the Galaxy with which we have compared these systems. It has also differed in different parts of the same system, as the distribution of Cepheids of different periods in the

Cloud, the galaxy, and Messier 31 seems to

show. If the difference of period frequency between the center and the edge of Messier 31 were

a result of differences in composition in different

regions of that galaxy, a much larger range in

composition would be required than would be

needed to account for the differences between the

Magellanic Clouds and our Galaxy. The same is

true of the difference of period within our own

system (Table 12). This statement is independent

of any numerical estimate of composition in any

of the four systems: if period frequency is an

index of composition, the range of composition

within our own Galaxy and Messier 31 is greater

than the difference of composition between the

solar neighborhood and either of the Clouds.

We shall recall that all attempts to predict a

period-frequency function have assumed that

there has been a continuous supply of stars, and

that their masses are distributed according to the

Salpeter function. From what has been said

above, we have little reason to feel confident

about the former assumption.

Another uncertainty is introduced by the tacit

assumption that the stars have developed at constant mass. Mass loss, however, is almost certainly taking place. Christy (1967) suggested

that fi Dor has sustained mass loss during the

red-giant stage on the basis of his calculations of

velocity and light curves for a star of this period. If mass loss takes place, a Cepheid reaches

passes 2 and 3 (the slowest, and those with

which most Cepheids must accordingly be associated) with a lower mass than at pass 1. Mass loss

would, qualitatively, have two effects. The period-luminosity relation would become less steep,

and the frequency of long periods would be increased. All the attempts to predict a period-frequency function have resulted in fewer long periods than are observed. This discrepancy might

be removed, or at least reduced, by considering

mass loss; however, it could also be removed by a

modification of the assumption that the stars

have been produced at a constant rate.

The conclusions that we have reached are supported by the opinion of Thackeray (1971): ". . .

the predominance of 2-day Cepheids in the SMC

. . . very probably points to some difference from

LMC and galaxy in its stage of evolutionary development. . . . The whole picture of the LMC

suggests to us that the system is one of very active star formation, while in the SMC apart

from the wing there appears to have been a decline in star formation." We also quote the evaluation of E. M. Burbidge (1971): "The Clouds

may owe their barred and asymmetrical distribution, including departure of the centre of rotation from the geometrical centre, to local fluctuations in H I density and rate of star formation

at different epochs."

References and Bibliography

Aller, L. H.

1961. The Abundance of the Elements. New York:

Interscience Publishers, Inc.

Aller, L. H., and J. D. Faulkner

1962. The Helium to Hydrogen Ratio in the Small

Magellanic Cloud. Publications of the Astronomical Society of the Pacific, 74:219-222.

Arp, H. C.

1968a. Southern Hemisphere Photometry. HI: The

Color-Magnitude Diagram of NGC 419 and the

Adjoining Field in the Small Magellanic Cloud.

Astronomical Journal, 63:273-282.

1968b. Southern Hemisphere Photometry, V: The Color-Magnitude Diagram of NGC 361 and the Adjoining Field of the Small Magellanic Cloud.

Astronomical Journal, 63:487-491.

1959a. Southern Hemisphere Photometry, VI: The Col- .

or-Magnitude Diagram of NGC 458 and the Adjoining Region of the Small Magellanic Cloud.

Astronomical Journal, 64:175-182.

1959b. Southern Hemisphere Photometry, VII: The

Color-Magnitude Diagram of NGC 330 and the

Adjoining Region of the Small Magellanic

Cloud. Astronomical Journal, 64:254-258.

1960. Southern Hemisphere Photometry, VIII: Cepheids in the Small Magellanic Cloud. Astro-,

nomical Journal, 65:404-444.

1964. The Role of the Magellanic Clouds in the Understanding of Galaxies. Pages 219-227 in F. J.

Kerr and A. W. Rodgers, editors, The Galaxy

and the Magellanic Clouds (International Astronomical Union-International Scientific Radio
NUMBER 16 29

Union Symposium No. 20). Canberra, Australia:

Australian Academy of Sciences.

1967. Analysis of Stellar Content and Cepheid Evolution in NGC 1866. Astrophysical Journal,

149:91-106.

Arp, H. C, and A. D. Thackeray

1967. The Star Cluster NGC 1866 and Its Cepheids.

Astrophysical Journal, 149:73-89.

Baade. W., and H. H. Swope

1963. Variable Star Field 96' South Preceding the

Nucleus of the Andromeda Galaxy. Astronomical Journal, 68 AS5-4&9.

1965. Variables in the Andromeda Galaxy—Fields I

and III. Astronomical Journal, 70:212-268.

Bok, B. J.

1964. A Young Association in the Large Magellanic

Cloud. Pages 335-341 in F. J. Kerr and A. W.

Rodgers, editors, The Galaxy and the Magellanic Clouds (International Astronomical Union-International Scientific Radio Union Symposium No. 20). Canberra, Australia:

Australian Academy of Sciences.

1966. Magellanic Clouds. Annual Review of Astronomy and Astrophysics, 4:95-144.

Bok, B. J., and P. F. Bok

1962. Integrated Magnitudes and Colours of Young

Associations in the Large Magellanic Cloud.

Monthly Notices of the Royal Astronomical Society (London), 124:435-444.

Bok, B. J., P. F. Bok, and J. M. Basinski

1962. Colour Magnitude Arrays for Two Associations

in the Large Magellanic Cloud. Monthly Notices

of the Royal Astronomical Society (London),

123:487-^96.

Breger, M.

1970. Pulsation and the Radius of the Southern Cepheid S. Normae. Astronomical Journal,

75:239-243.

Burbidge, E. M.

1971. Importance of Magellanic Cloud Studies for Extra-Galactic Work. Pages 163-168 in A. B.

Muller, editor, The Magellanic Clouds (Proceedings of the European Southern Observatory

Symposium on The Magellanic Clouds). Dordrecht, Holland: D. Reidel Publishing Co.

Burbidge, G.

1971. Nucleosynthesis in the Magellanic Clouds and

the Galaxy. Pages 156-162 in A. B. Muller, editor, The Magellanic Clouds (Proceedings of the

European Southern Observatory Symposium on

The Magellanic Clouds). Dordrecht, Holland:

D. Reidel Publishing Co.

Buscombe, W.

1964. The Total Brightness of Galactic Clusters.

Pages 24-29 in F. J. Kerr and A. W. Rodgers,

editors, The Galaxy and the Magellanic Clouds

(International Astronomical Union-International

Scientific Radio Union Symposium No. 20).

Canberra, Australia: Australian Academy of

Sciences.

Christy, R. F.

1966. Pulsation Theory. Annual Review of Astronomy

and Astrophysics, 4:353-392.

1967. Non-Linear Calculations of Cepheid Models.

Publications of the Astronomical Society of the

Pacific, 79:429-430.

1968. The Theory of Cepheid Variability. Quarterly

Journal of the Royal Astronomical Society

(London), 9:13-39.

Code, A. D., and T. E. Houck

1956. Observations of Early Type Stars in Extragalactic Nebulae. Astronomical Journal, 61:173.

1958. A Superluminous B-Type Star in the Large Magellanic Cloud, and Its Galactic Counterpart.

Publications of the Astronomical Society of the

Pacific, 70:261-266.

Dachs, J.

1972. Photometry of Bright Stars in the Large Magellanic Cloud. Astronomy and Astrophysics,

18:271-286.

Dickens, R. J.

1966. Two Colour Photometry of Cepheids in the

Large Magellanic Cloud. The Observatory,

86:18-24.

Faulkner, D. J.

1964. A Comparison of the 30 Doradus and Eta Carinae Nebulae. Pages 310-316 in F. J. Kerr and

A. W. Rodgers, editors, The Galaxy and the

Magellanic Clouds (International Astronomical

Union-International Scientific Radio Union

Symposium No. 20). Canberra, Australia: Australian Academy of Sciences.

Feast, M. W.

1960. Note on the Interpretation of Color Magnitude

Diagrams in the Small Magellanic Cloud. The

Observatory, 80:104-106.

1964. Spectroscopic Work on the Magellanic Clouds;

NGC 330 in the Small Magellanic Cloud. Pages

330-334 in F. J. Kerr and A. W. Rodgers, editors, The Galaxy and the Magellanic Clouds

(International Astronomical Union-International

Scientific Radio Union Symposium No. 20).

Canberra, Australia: Australian Academy of

Sciences.

Feast, M. W., A. D. Thackeray, and A. J. Wesselink

1958. The Magellanic Clouds—Spectra and Photometry of Bright Stars. The Observatory,

78:156-165.

1960. The Brightest Stars in the Magellanic Clouds.

Monthly Notices of the Royal Astronomical Society (London), 121:337-385.

Gaposchkin, S.

1962. 223 Variables in the Andromeda Nebula. Astronomical Journal, 67:334-362.

Gaposhkin, S.

1967. Undecoded Variable and a Strange Cluster in

the Large Magellanic Cloud Together with Its

Topography. Publications of the Astronomical

Society of the Pacific, 79:432-433.
30 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

1972. The Large Magellanic Cloud: Its Topography

of 1830 Variable Stars. Smithsonian Astrophysical Observatory Special Report No. 310, 52

pages + figures.

Gaseoigne, S. C. B.

1962. NGC 1783, a Cluster in the Large Magellanic

Cloud. Monthly Notices of the Royal Astronomical Society (London), 124:201-219.

1966. Color-Magnitude Diagrams for 9 Globular-like

Clusters in the Magellanic Clouds. Monthly Notices of the Royal Astronomical Society (London), 134:59-82.

Gaseoigne, S. C. B., and G. Kron

1965. Photoelectric Observations of Magellanic Cloud

Cepheids. Monthly Notices of the Royal Astronomical Society (London), 130:333-360.

Gray, D. F.

1965. Integrated Colors and Magnitudes of Open

Clusters. Astronomical Journal, 70:362-367.

Henize, K. G.

1956. Catalogues of Ha-Emission Stars and Nebulae

in the Magellanic Clouds. Astrophysical Journal

Supplement, 2:315-344.

Hodge, P. W.

1959. Globular Clusters of the Large Magellanic

Cloud [abstract]. Astronomical Journal, 64:335.

1960a. Studies of the Large Magellanic Cloud, III:

The Globular Cluster NGC 1978. Astrophysical

Journal, 132:346-350.

1960b. Studies of the Large Magellanic Cloud. Doctoral Thesis, Harvard University.

1960c. Studies of the Large Magellanic Cloud, II: The

Globular Cluster NGC 1846. Astrophysical Journal, 132:341-345.

1961. Studies of the Large Magellanic Cloud, VI:

Properties of 1057 Field Stars. Astrophysical

Journal Supplement, 6:235-252.

Hodge, P. W., and F. W. Wright

1963. Studies of the Large Magellanic Cloud, IX:

Globular Cluster Cepheids. Astrophysical Journal, 138:366-374.

1968. Studies of the Large Magellanic Cloud, X: Photometry of Variable Stars. Astrophysical Journal Supplement, 17:467-490.

Hofmeister, E.

1967a. Sternentwicklung, VII: Zur Entwicklung von

Sternen mit 5 und 9 Sonnenmassen. Zeitschrift

fur Astrophysik, 65:164-184.

1967b. Delta-Cephei-Sterue vom Standpunkt der Sternentwicklung. Zeitschrift fiir Astrophysik, 65:

194-225.

Hofmeister, E., R. Kippenhahn, and A. Weigert

1964a. Sterneutwicklung, I: Ein Programm zur Losung der Zeitabhangigen Aufbaugleichungen.

Zeitschrift fiir Astrophysik, 59:215-241.

1964b. Sternentwicklung, II: Wasserstoff-Brennende

Phase eines Sterns von 7.0 Sonnenmassen. Zeitschrift fiir Astrophysik, 59:242-260.

1964c. Sternentwicklung, III: Die Helium Brennende

Phase und die Cepheidenstadien eines Sterns

von 7,0 Sonnenmassen. Zeitschrift fur Astrophysik, 60:57-75.

Iben, I., Jr.

1964. The Surface Ratio of N14 to C12 during Helium

Burning. Astrophysical Journal, 140:1631-1633.

1966a. Stellar Evolution, III: The Evolution of a 5

Mo Star from the Main Sequence through Core

Helium Burning. Astrophysical Journal,

143:483-504.

1966b. Stellar Evaluation, IV: The Evolution of a 9 Mo

Star from the Main Sequence through Core

Helium Burning. Astrophysical Journal,

143:505-515.

1966c. Stellar Evolution, V: The Evolution of a 15 Mo

Star from the Main Sequence through Core

Helium Burning. Astrophysical Journal,

143:516-526.

Johnson, H. L.

1963. Photometric Systems. Pages 204-24 in K. Aa.

Strand, editor, Basic Astronomical Data. Chicago : University of Chicago Press.

Johnson, H. L., A. A. Hoag, B. Iriarte, R. I. Mitchell,

and K. L. Hallam

1961. Galactic Clusters as Indicators of Stellar Evolution and Galactic Structure. Lowell Observatory Bulletin, 5(8) : 133-147.

Johnson, Hugh

1959. The Spectrum and Mass of the 30 Doradus Nebula. Publications of the Astronomical Society

of the Pacific, 71:425-^34.

Jung, J.

1970. On the Distance Scale of Nearby Cepheids. Astronomy and Astrophysics, 6:130-137.

Kippenhahn, R.

1965. Stellar Evolution and Variability. Kleine

Veroffentlichungen der Remeis-Sternwarte zu

Bamberg, 4:7-16.

Kippenhahn, R., and L. Smith

1969. On the Ages of 8 Cephei Stars. Astronomy and

Astrophysics, 1:142-146.

Kippenhahn, R., H.-C. Thomas, and A. Weigert

1965. Sternentwicklung, IV: Zentrales Wasserstoffund Heliumbrennung bei einem Stern von 5

Sonnenmassen. Zeitschrift fiir Astrophysik, 61:

241-267.

Kukarkin, B. W.

1954. Erforschung der Struktur und Entwicklung der

Sternsysteme auf der Orundlage des Studiums

Verdndcrlicher Sterne. 133 pages. Berlin:

Akademie Verlag. [German translation; see especially pages 38-39.]

Limber, D. N.

1960. The Universality of the Initial Luminosity

Function. Astrophysical Journal, 131:168-201.

Mendoza. E. E.

1971. Intermediate Band Photometry of the Brightest

Stars in the Magellanic Clouds. Pages 69-73 in

A. B. Muller, editor, The Magellanic Clouds

(Proceedings of the European Southern Obser-
NUMBER 16 31

vatory Symposium on The Magellanic Clouds).

Dordrecht, Holland: D. Reidel Publishing Co.

Mitchell, R. I., B. Iriarte, D. Steinmetz, and H. L. Johnson

1964. Photoelectric Photometry of Cepheid Variable

Stars. Boletin de los Observatorios Tonantzintla

y Tacubaya, 3 :153-304.

Oosterhoff, P. Th.

1960. Three-Color Photometry in the U, B, V System

of 51 Northern Cepheids. Bulletin of the Astronomical Institutes of the Netherlands, 15:

199-228.

Parenago, P. P.

1958. On Period Changes of Long Period Cepheids.

Variable Stars, 11:236-267.

Payne-Gaposchkin, C.

1971. The Variable Stars of the Large Magellanic

Cloud. Smithsonian Contributions to Astrophysics, 13: 41 pages.

Payne-Gaposchkin, C, and S. Gaposchkin

1966. Variable Stars in the Small Magellanic Cloud.

Smithsonian Contributions to Astrophysics, 9:

203 pages.

Przybylski, A.

1965. Abundance Analysis of a Supergiant in the

Large Magellanic Cloud. Nature, 205 :163.

Sandage, A.

1963. Photoelectric Observations of the Interacting

Galaxies VV 117 and VV 123 Related to the

Time of Formation of Their Satellites. Astrophysical Journal, 138:863-872.

Sandage, A., and O. J. Eggen

1960. Photometry in the Magellanic Clouds. Ill :

The Cluster NGC 1783. Monthly Notices of

the Royal Astronomical Society (London),

121:232-237.

Sandage, A., and G. A. Tammann

1968. A Composite Period-Luminosity Relation for

Cepheids at Mean and Maximum Light. Astrophysical Journal, 151:531-545.

Schmidt-Kaler, Th.

1965. Physical Parameters and Two-Parameter Diagrams of the Stars. Pages 284-315 in Group

VI, volume I, H. H. Vogt, editor, Landolt-Bornstein. New York : Springer-Verlag.

1967. Reddening and Distance of M 33 and M 31 as

Derived from Open Clusters. Astronomical

Journal, 72 :526-531.

Serkowski, K.

1963. Slopes of the Reddening Trajectories and Intrinsic Colors of Early-Type Stars. Astrophysical Journal, 138:1035-1049.

Shapley, H., and E. M. Lindsay

1963. A Catalogue of Clusters in the Large Magellanic Cloud. Irish Astronomical Journal,

6:74-91.

Shapley, H., and V. McKibben

1940. Galactic and Extragalactic Studies, V : The Period Frequency of Classical Cepheids in the

Magellanic Clouds. Proceedings of the National

Academy of Sciences, U.S.A., 26:105-115.

Shapley, H., and V. McKibben Nail

1951. NGC 1866 and the Magellanic Cloud Variables.

Astronomical Journal, 55 :249-251.

1953. Magellanic Clouds, VII: Star Colors and Luminosities in Five Constellations. Proceedings of

the National Academy of Sciences, U.S.A.,

39:349-362.

1955. Magellanic Clouds, XVII: Seven Notes on the

Cepheid Variables. Proceedings of the National

Academy of Sciences, U.S.A., 41:829-836.

Smak, J.

1962. A Theoretical Period Frequency Function

for Classical Cepheids. Ada Astronomica,

12:93-101.

Smith, L. F.

1968. Absolute Magnitudes and Intrinsic Colors

of Wolf Rayet Stars. Monthly Notices of

the Royal Astronomical Society (London),

140 :409-433.

Stothers, R.

1969. Red Supergiants and Neutrino Emission. Astrophysical Journal, 155 :935-956.

Tammann, G. A.

1969. Die Lichtelemente eines Anonymen Cepheiden

und iiber Seine Wahrscheinliche Zugehorigkeit

zu den Offenen Sternhaufen NGC 6649. Astronomy and Astrophysics, 3 :308-315.

Thackeray, A. D.

1959. Comparision of Globular Clusters in the Galaxy

and the Magellanic Clouds. Astronomical Journal, 64:437-441.

1971. Survey of Principal Characteristics of the Magellanic Clouds. Pages 3-8 in A. B. Muller,

editor, The Magellanic Clouds (Proceedings of

the European Southern Observatory Symposium

on The Magellanic Clouds). Dordrecht, Holland : I). Reidel Publishing Co.

Tifft, W. G.

1964. Old and Intermediate Populations in the Magellanic Clouds. Pages 349-353 in F. J. Kerr and

A. W. Rodgers, editors, The Galaxy and the

Magellanic Clouds (International Astronomical

Union-International Scientific Radio Union

Symposium No. 20). Canberra, Australia: Australian Academy of Sciences.

Tifft, \V. G., and C. M. Snell

1971. Magellanic Cloud Investigations, III: The

LMC Bar. Monthly Notices of the Royal Astronomical Society (London), 151:365-384.

van den Bergh, S.

1958. Cepheids and Galactic Structure. Astronomical

Journal. 63 :492-496.

van den Bergh. S., and G. L. Hagen

1968. I'BV Photometry of Star Clusters in the Magellanic Clouds. Astronomical Journal. 73:569-578.

Vogt, N.

1971. rntersuchung des Doppel-Sternhaufens h und

chi Persei auf Grund einer Dreifarben-Photo-
32 SMITHSONIAN CONTRIBUTIONS TO ASTROPHYSICS

metrie. Astronomy and Astrophysics,

11:359-376.

Walker, M. F.

1972. Electronographic Photometry of Star Clusters

in the Magellanic Clouds, III: The Color-Magnitude Diagram of NGC 2257. Monthly Notices

of the Royal Astronomical Society (London),

156 :459-469.

Walraven, Th., A. B. Muller, and P. Th. Oosterhoff

1958. Photoelectric Magnitudes and Colours at Maximum for Cepheids. Bulletin of the Astronomical

Institutes of the Netherlands, 14 :81-129.

Walraven, Th., and J. H. Walraven

1964. Supergiants in the Magellanic Clouds and in

the Galaxy. Pages 321-328 in F. J. Kerr and

A. W. Rodgers, editors, The Galaxy and the

Magellanic Clouds (International Astronomical

Union-International Scientific Radio Union

Symposium No. 20). Canberra, Australia: Australian Academy of Sciences.

1971. Physical Parameters of Supergiants in the Magellanic Clouds. Pages 117-135 in A. B. Muller,

editor, The Magellanic Clouds (Proceedings

of the European Southern Observatory Symposium on The Magellanic Clouds). Dordrecht,

Holland: D. Reidel Publishing Co.

Westerlund, B.

1961a. Population I in the Large Magellanic Cloud.

Uppsala Astronomiska Observatoriums Annaler,

5(1) :3-58.

1961b. The Distribution of Stars in an Outlying Part

of the Large Magellanic Cloud. Uppsala Astronomiska Observatoriums Annaler, 5(2) :2—17.

Westerlund, B. E., and D. S. Mathewson

1966. Supernova Remnants in the Large Magellanic

Cloud. Monthly Notices of the Royal Astronomical Society (London), 131:371-381.

Westerlund, B. E., and L. F. Smith

1964. Wolf Rayet Stars in the Large Magellanic

Cloud. Monthly Notices of the Royal Astronomical Society (London), 128:311-325.

Wildey, R. L.

1963. Optimum Use of Interstellar Reddening Data

to Obtain Intrinsic Stellar Luminosities and

Colors. Astronomical Journal, 68 :190-194.

Williams, J. A.

1961. Metal-to-Hydrogen Ratios in the Magellanic

Clouds. Astronomical Journal, 71:186-187.

Woolley, R. v. d. R.

1960. Photometry in the Magellanic Clouds, II: Some

Colour Magnitude Arrays. Monthly Notices of

the Royal Astronomical Society (London),

120:214-219.

1961. A Survey of Observational Problems of Stellar

Evolution. Proceedings of the Royal Society of

London, 260:189-201.

Woolley, R. v. d. R.

1963. Studies in the Magellanic Clouds, V : An Open

Cluster of Intermediate Age in the Large Magellanic Cloud. Royal Observatory Bulletin,

65 :251-260.

Woolley, R.v.d.R., A. R. Sandage, O. J. Eggen, J. B. Alexander, L. Mather, E. Epps, and S. Jones

1962. Studies in the Magellanic Clouds, IV: Photometry of Cepheids in Variable Field I, Large Magellanic Cloud. Royal Observatory Bulletin, 58:

57 pages.

Young, A. T.

1961. Stellar Kinematics and Spiral Arms. 93 pages,

Doctoral Thesis, Harvard University.


Publications of the Smithsonian Institution Astrophyaical Observatory

This series, Smithsonian Contributions to Astrophysics, was inaugurated in 1966 to

provide a proper communication for the results conducted at the Astrophysical Observatory of the Smithsonian Institution. Its purpose is the "increase and diffusion of knowledge" in the field of astrophysics, with particular emphasis on problems of the sun, the

earth, and the solar system. Its pages are open to a limited number of papers by other

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Another series, Annals of the Astrophysical Observatory, was started in 1900 by the

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These quarto volumes, some of which are still available, record the history of the Observatory's researches and activities. The last volume (vol. 7) appeared in 1964.

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to them are available on request from the Publications Division, Smithsonian Institution

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OEOBOE B. FIELD, Director

Smithsonian Institution

Astrophysical Observatory

Cambridge, Massachusetts