40
SOME OBSERVATIONAL ASPECTS OF STELLAR EVOLUTIONl By OLIN J. EGGEN Royal Greenwh Observatory The interplay between theory and observation in astronomy has no- where been more successful than in the field of stellar evolution. Modern theories of stellar evolution have been, in outline, firmly fixed for more than ten years, and the observations upon which they were based, as well as some derivative observations and suggested alterations in the theories, have been described in detail by Sandage (1) and Burbidge (2). The general ideas are so well entrenched that any dis crepant result of a f undamental kind must stand the most careful scrutiny. Because the field of stellar evolution is too large to cover completely in a short article, only a few topics of current inter- est to the writer are discussed. ZERO-AGE MAIN SEQUENCE One of the serious obstacles in the mating of theory and observation is in equating temperatures and bolo metric luminosities derived for stellar models with observed, narrow and wide band magnitudes and colours. The responsi- bility for the conversions might best be assumed by those who compute the stellar models, since to obtain the luminosities at selected wavelengths would require small effort in the computer programmes. The available data have been gathered in Table I and are based on the following: (a) Zero-age main sequence; (Mv,B- . The main sequence, at the onset of hydrogen burning, is given in Table I for stars with a chemical composition similar to that of the Hyades and Pleiades stars. For stars redder than B -V = +04 this is the main sequence of the Hyades cluster and group (3), and for bluer stars it is based on the Pleiades and other young clusters (4) . (b) The bolometric corrections for stars of type later than about AS are based on the infrared observations by Johnson (5) with the zero-point ad- justed to give a correction of -007 for the Sun. The corrections for the hot- ter stars are entirely uncertain because of the inaccessibility of that part of the spectrum ( <3300 A) where the flux is a maximum. The values obtained from stellar models that fit the observed part of the spectrum are given in Table I I (6). 1 The survey of literature for this review was concluded in December 1964. 235 Annu. Rev. Astro. Astrophys. 1965.3:235-274. Downloaded from www.annualreviews.org by University of Central Florida on 10/05/13. For personal use only.

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Page 1: Some Observational Aspects of Stellar Evolution

SOME OBSERVATIONAL ASPECTS OF STELLAR EVOLUTIONl

By OLIN J. EGGEN Royal Greenwich Observatory

The interplay between theory and observation in astronomy has no­where been more successful than in the field of stellar evolution. Modern theories of stellar evolution have been, in outline, firmly fixed for more than ten years, and the observations upon which they were based, as well as some derivative observations and suggested alterations in the theories, have been described in detail by Sandage (1) and Burbidge (2) . The general ideas are so well entrenched that any discrepant result of a fundamental kind must stand the most careful scrutiny. Because the field of stellar evolution is too large to cover completely in a short article, only a few topics of current inter­est to the writer are discussed.

ZERO-AGE MAIN SEQUENCE

One of the serious obstacles in the mating of theory and observation is in equating temperatures and bolo metric luminosities derived for stellar models with observed, narrow and wide band magnitudes and colours. The responsi­bility for the conversions might best be assumed by those who compute the stellar models, since to obtain the luminosities at selected wavelengths would require small effort in the computer programmes. The available data have been gathered in Table I and are based on the following:

(a) Zero-age main sequence ; (Mv,B- V).

The main sequence, at the onset of hydrogen burning, is given in Table I for stars with a chemical composition similar to that of the Hyades and Pleiades stars. For stars redder than B - V = +0'!'4 this is the main sequence of the Hyades cluster and group (3) , and for bluer stars it is based on the Pleiades and other young clusters (4) .

(b) The bolometric corrections for stars of type later than about AS are based on the infrared observations by Johnson (5) with the zero-point ad­justed to give a correction of - 0'!'07 for the Sun. The corrections for the hot­ter stars are entirely uncertain because of the inaccessibility of that part of the spectrum ( <3300 A) where the flux is a maximum. The values obtained from stellar models that fit the observed part of the spectrum are given in Table II (6).

1 The survey of literature for this review was concluded in December 1964.

235

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236 EGGEN

TABLE I

ZERO-AGE MAIN SEQUENCE

B- V U-B Mv MB Log T,

-0.25 -0. 90 -2.0: (-3.5 ) (4.40) -0. 20 -0.68 -1.2: ( -2.1) 4.25 : -0.15 -0. 46 -0.5 ( -1. 1) 4. 13: -0.10 -0.25 +0. 5 (+0.1) 4. 04: -0. 05 -0.09 +1. 0 (+0.8) 4.01:

0.00 +0. 01 +1.5 5 +1. 4 3.98: +0. 05 +0.07 +1. 9 +1. 8 3.965 : +0.10 +0.09 +2. 1 +2.0 3.95 : +0.15 +0. 12 +2. 3 +2. 2 3. 93: +0.20 +0. 13 +2.5 +2.4 3.915 : +0.25 +0.11 +2.7 +2.6 3.90: +0. 30 +0.07 +2.9 +2. 9 3. 88 +0.35 +0. 03 +3.10 +3.10 3.86 +0.40 +0.01 +3.42 +3.42 3.845 +0. 45 0.00 +3. 78 +3.77 3. 83 +0. 5 0 +0.03 +4. 10 +4. 08 3. 815 +0.5 5 +0.08 +4.45 +4.40 3.80 +0.60 +0.13 +4.78 +4. 70 3. 785 +0.65 +0.19 +5 .02 +4.93 3.77 +0.70 +0.25 +5.32 +5 . 21 3.75 5 +0. 75 +0. 34 +5.60 +5 .45 3. 74 +0. 80 +0. 43 +5.85 +5 .67 3. 72 +0.85 +0.5 4 +6.10 +5.88 3. 705 +0.90 +0. 64 +6. 34 +6.07 3.69 +0. 95 +0.74 +6. 5 8 +6.22 3. 675 +1.00 +0. 84 +6.80 +6. 40 3. 66 +1. 05 +0.94 +7. 02 +6. 5 5 3. 645 +1.10 +0. 99 +7. 25 +6. 70 3. 63 +1.15 +7. 45 +6. 86 3. 62 +1.20 +7.66 +6 . 99 3. 61 +1. 30 +8.08 +7. 20 3. 60 +1. 40 +8.5 4 +7. 45 3.5 9 +1. 5 0 +9. 0: +7. 6 : 3. 5 8:

TABLE II

B- V Log T. Bolometric corrections

-0'!'12 4. 09 -0'!'9 -0. 14 4. 13 -1. 1 -0. 16 4. 18 -1. 4 -0.18 4. 23 -1.6 -0. 20 4.28 -1. 9 -0. 23 4. 33 -2. 2

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 2 3 7

However, several attempts ( 7 , 8) from rockets have yielded estimates o f the radiation below}, 3000, and these indicate an ultraviolet deficiency compared to the predicted flux from model computations. In subsequent discussions of these results there have been some overestimates of this deficiency because of incorrectly assumed temperatures or confusion between the fluxes F(II) and FeA) . Figures 1 and 2 show the rocket and ground-based results for the B8 dwarf a Leo and the two B 1 II stars {3 and e CMa, compared with model atmosphere computations that fit the energy distributions in wavelengths longer than about 3400 A. The monochromatic magnitudes for a Leo by Oke (9) and by Woolley, Gascoigne & de Vaucouleurs ( 10) for {3 and E CMa, to­gether with the visual magnitudes and the value of 3.8X 10-9 erg/cm2/sec/ A for the flux of a star of visual magnitude 0':'00 at}, 5500 ( 1 1 , 12) , were used in computing the values of F(II) between 1/>. = 1.0 and 2.5. The rocket observa­tions are in absolute units, and although there is an uncertainty of some 10 per cent in the value of the flux at >. 5500 from a star of visual magnitude O'!'OO the agreement with the ground-based results near 1/}, = 2.6 for IX Leo is precise. This unexpected agreement is also illustrated in Figure 3 where the absolute fluxes of a Car (V = -0':'70) obtained from a rocket flight are com­pared with those computed from the monochromatic magnitudes by Aller,

u w en -.. JE U -en

1.2

� 0·8 w

� x

� LEO

o OKE X STECHER & MILLIGAN ... CHUBB � BYRAM

--- MODEL; 13,500°

..... /'

/ ,/

,/ ,/

,/

lC .f. x x , I

8·0 7·2 6·4 5·6

I - ---�

Xx XXx"" XX

lC

x

X X

I 4·8 4·0 3·2 2·" '.6 I/>.

FIG. 1. The ground-based (open circles ) and rocket (crosses and plus sign) ob­servations of the flux from a Leo compared with a stellar model with T. = 13,500°.

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Page 4: Some Observational Aspects of Stellar Evolution

238 EGGEN

Faulkner & Norton ( 13), using the value of the flux at A 5500 given above for a star of V = 0':'00. The difference, in the wavelength region common to both series, hardly exceeds 1 per cent and taken at face value can only give confi­dence in the rocket observations in the region shortward of A 3000. The model atmosphere represented in Figure 3 has a value of T. = 6750° ( 14) and ap­pears to satisfy the observations over the observed wavelength range.

In the case of a Leo in Figure 1 there is a noticeable deficiency in the stel­lar radiation, compared to the model, for values of l/A larger than about 4. A small amount of line blanketing at wavelengths shorter than A 3000 ( 15) and a small reddening, E(B - V) = +0':'01 to +0':'03, would reduce this defi­ciency. The stellar model with which a Leo is compared in Figure 1 yields a bolometric correction of - 1m but the missing radiation shortward of A 3000 could reduce this by nearly 0':'5. The hotter stars in Figure 2 have less than 50 per cent of the radiation predicted by a stellar model with T. = 20,4000 (16), with that between 1/A = 5 and the Lyman limit near 1/A=10 uni­formly down by about 1':'5. The computed bolometric correction of _2m may need a drastic reduction. The consistency of the ultraviolet deficiency for stars earlier than about B8 is shown in Table I I I where the differencesD.m (A 1314- V) determined from the visual magnitudes and the rocket observa­tions of Chubb & Byram (7) are compared with those computed from model atmospheres (6). Attempts to account for the missing radiation in the hot stars include the following: Hoyle & Wickramasinghe (17) have suggested

u Q) III

"-N

E <.> "-." 0-... Q)

N 0 )(

� u..

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

I I I I I I I I I I I I I o log g = 3.8

V-O otV 1e • 20.400 •

0 = € C Ma (Stecher 0 X � f$ C Mo (Stecher � • • Woolley et 01. + = Chubb 09 Byrom (fJ)

+

Milligan) Milligan)

I I

x x

I

0

I I I I I I I I 0 I x I I I IX I I

x I X I 0 I

I I

/ 0,; ....... °_0/0

I I I 1 I I I I I I I I I I I

xx\ x

XX�� x·. )O()(fx • ..

I I I I I I 10.6 1.0 9.2 6.4 7.6 6.8 6.0 5.2 4.4 3.6 2.6 2.0

FIG. 2. Ground-based (filled circles) and rocket (crosses and plus sign) observations of {J and E CMa.

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 239

that the interstellar absorption at wavelengths shorter than A 2000 may be enough to make A (}. 1314) / A ( V) as high as 10 ; the interstellar absorption near the Sun may have been underestimated and the intrinsic ( U -B, B - V) relation given in Table I for early-type stars may need a correction of about 0'?03 in B - V; and the line blanketing of a star of type B1 may block as much as 30 per cent of the radiation shortward of A 3000 ( 15) .

If all three of these extreme possibilities are operating, they would just account for the ultraviolet deficiencies noted in Table III. However, the available data indicate that if absorption exists near the Sun it is uniform

I; 0(. CAR

7

X STEOIER 6 o ALLER

/ 6750·

U 5 � " �

� ... II) (j ct UJ

�O 3 )( u?

2

I I

I/A 4·8 2� '·6

FIG. 3. Ground-based (open circles) and rocket (crosses) observations of a Car compares with a stellar model of T.=6750o.

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240 EGGEN

TABLE III

OBSERVED ULTRAVIOLET DEFICIENCIES

.1.m(X1314-V) Star (U-Bh E(B-V) Log T. O-C

Obs. Computed 15 E

r CMa -0.68 0.00 4.20 +1.0 -0.4 +1.4 I( CMa -0.8 9 0.00 4.39 +0.4 -1.2 +1.6 {3 CMi -0.30 0.00 4.09 +2.2 +1.0 +1.2

Mean +1.4

a Leo -0.38 +0.02 4.12 +2.5 +0.7 +0.3 +1.5 • Cas -0.59 +0.02 4.23 +1.5 -0.2 +0.3 +1.4 1r' Ori -0.85 +0.05 4.36 +0.9 -1.1 +0.8 +1.2 '1 Aur -0.70 +0.02 4.28 +0.9 -0.5 +0.3 +1.1 (3 Tau -0.5 0 +0.02 4.18 +2.2 +0.3 +0.3 +1.6

+1.4

over a distance of about 100 parsecs ( 18 ). Also, a correction to the values of B - V of as much as 0'!'03 for the hot stars would require materially hotter stellar atmosphere models to fit the observations in the visual and photo­graphic regions which would, in turn, increase the observed deficiency in the ultraviolet. The agreement of the mean deficiencies for the reddened and un­reddened stars in Table III indicates that a value of A(>' 1314)/A(V) much greater than that predicted by the 1/>. law is probably not correct. Although some of the observed deficiency is undoubtedly caused by line blanketing, the present data indicate that bolo metric corrections computed from stellar models for early-type stars may be too large by 0'!'5 to 1'!'0.

(c) The following temperature determinations (Table IV), and Johnson's (5) values of the infrared indices, (R - I) and (J - K), were used to obtain the (B - V, log Te) relation for stars redder than B - V = 0.0 in Table I:

TABLE IV

Star (B-V) T.(OK) Ref.

aCMa +0'!'02 94 00±400 Brown et al. (19) aLyr +0.00 9200 ±300 Brown et al. (19) (f' BooB +0.41 68 00 Code (20)

Suna +0.67 578 0 Allen (21) a Boo +1.23 4100 Kuiper (22)

YYGem +1.49 365 0 Kron (23)

a The value of B-V has been corrected for the line-blanketing effects (24) indicated by the ultraviolet excess (3).

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 241

For stars bluer than B - V = if. 0 this relation depends entirely on model atmospheres and is consequently very provisional.

The (Mv, B -V) and (Mhol, B - V) relations of Table I are drawn in Fig­ure 4, which also shows the position of main sequence models with hydrogen and helium compositions (X, y) = (0.68, 0.30) computed by Henyey et al. (25) and DeMarque & Larson (26) and listed in Table V; DeMarque & Lar­son's models used here have a mixing length 1 and pressure-scale height h, related by 1 = 1.6 h.

MASS-LUMINOSITY RELATION The mass-luminosity relation for the models in Table V is shown in Figure

5 together with the individual masses for binaries in the Hyades and Pleiades groups (27) listed in Table VI. Table VI also contains the vectors of the space motion (U, V, W) (28), In most cases the magnitude of the components of these binaries are nearly equal and median luminosities and masses are listed. The position of the group members in the (Mho!, B - V) plane is shown in Figure 6. The Hyades is older than the Pleiades; and the stars in both the cluster and the group, with B- V bluer than about 0':'3, are evolved (18). A

comparison of Figures 4 and 5 shows that although the models well represent the observed colour-luminosity array, they deviate considerably from the

M -.04

-2 0 t£NYEY X DEMAR QUE

0 ,/ Mv

+2

'+4

+6

+8 I I I I I

B-V 0 .0·2 +0-4 +0'6 to·8 tl<> -/-1'2 +1'4

FIG. 4. (Mbol,B-V) and (Mv,B. V) relations from stellar models compared with the zero-age main sequence.

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242

MeoL. -4

-2

0

+2

EGGEN

X

X X

• MODEL.S X HYADES AND PLEIADES GPS. � & (U-B) <+0.01

Xx Xx x

X X � X

Xx '

FIG. 5. Masses of components of visual binaries in the Pleiades and Hyades groups and field binaries showing no ultraviolet excess compared with the mass­luminosity relation for some stellar models.

TABLE V

MAIN SEQUENCE MODELS WITH (X, Y)=(0.68 , 0.30)

M(0) Mhol Log T. R(0) Ref.

11.0 -5.17 4.438 (24 ) 6.0 -3.06 4.305 3.00 (24 ) 3.5 -0.99 4. 169 2.20 (24) 2.0 +1.47 3.98 1 1. 70 (24 ) 1.5 +2.63 3.919 1.30 (24 ) 1.3 +3.76 3.831 1. 15 (25)& 1.2 +4.16 3. 808 1.06 (25 ) 1. 1 +4.62 3.38 0 1. 02 (25 ) 1.0 +5 .14 3.747 0.90 (25 ) 0. 9 +5.73 3.704 0.84 (25) 0. 8 +6.39 3. 65 3 0.78 (25 )

a l== 1.6 h.

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 243

M

+2

1"4

+6

I I I I I I I I I

• PLEIADES GP. o HYADES GP.

_I I B-V 0.0

I I 0·2 I I I I I

0-4 0'6

FIG. 6. The (Mbol,B- V) rela tion for the group sta rs in Figure 5.

TABLE VI

MASSES OF HYADES AND PLEIADES GROUP MEMBERS

ADS (B- V)O Mbol m(0) U V

102 AB +0.21 +1.9 1.3 +40 -17 862 AB +0.25 +1.9 2.0 +39 -16

3210 AB" +0.68 +5.1 0.6 +40 -17 3483 Aa +0.47 +3.7 0 78\

+40 -17 3483 Ba +0.72 +5.2 0.56

10 UMa A +0.37 +3.2 0.90 +41 -17

10 UMa B +0.65 +4. 9 0.48 10140 AB +0.43 +3.2 1.0 +40 -17 16057 AB +0.32 +2.6 1.4 +38 -19 16497 AB +0.31 +2.1 2.5 +40 -16 16708 AB +0.06 +1.4 4.2 +42 -16

1630 AB 0.00 +1.5 1.4 + 5 -27 2799 AB +0. 24 +1. 8 2.1 + 5 -27 4265 AB -0.19 -2.4 11. 7 +15 -27 7555 AB +0.04 +0.9 4.3 +12 -26

HD 114529 AB -0.14 -1.5 20.2 +10 -27 8939 AB +0.20 +2.4 1. 0 +11 -28 8954 AB -0.02 +1.4 2.5 + 5 -27 9301 AB +0.21 +2.6 1.4 + 9 -26 9744 AB +0.04 +1.2 3.3 + 8 -27

10360 AB +0.31 +2.0 2.7 +10 -28 14761 AB +0.24 +2.6 1.3 +15 -29

HD 206644 AB +0.06 +1.3 3.2 +12 -25

• Hyades cluster.

W

-18 - 5 - 2

- 2

- 6

+11 + 1 - 4 +11

- 9 +25 -15 -24 + 1 - 9 +15 + 4 - 6 -12 - 2 - 7

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244 EGGEN

observed mass-luminosity relation. That this deviation is not confined to group members is shown by the masses of the following systems (Table VII) , (27) , which have a third, distant main sequence companion that permits accurate photometric parallaxes to be obtained, and which fall on the (U-B, B- V) relation for the Hyades stars (i.e. have o(U-B) '::;+0�01) :

TABLE VII

ADS (B-V) Mbol m(0) U V W

3711 AB +0�33 +2':'5 1.7 + 5 -14 - 7 6650 AB +0.54 +4. 4 0. 7 +10 -10 - 2 9247 Be +0. 43 +3.7 0.9 +24 -14 -10 9909 AB +0. 45 +3.1 1.2 +27 - 7 -12

The Sirius group also contains several binaries for which accurate mass determinations are available (27) . The results for some of these systems are listed in Table VII I. The Sirius group members are older than the Hyades and Pleiades stars, and objects more luminous than about om are highly evolved. Also the stars in the Sirius group show an ultraviolet excess of about �( U -B) = + 0':'03 with respect to the Hyades stars; and the val ues of B - V, corrected for the line-blanketing effect, d(B - V) (24), are listed in Table VI I I; C=(B- V)+d(B- V). Several binaries with either a large trigono­metric parallax (>0':1) or a third, distant main sequence component from which an accurate photometric parallax can be obtained (27) , are listed in Table IX; all of these stars show an ultraviolet excess with respect to the Hyades of o( U -B) � +0'!'02. The masses and luminosities of the stars in Tables VIII and IX are shown in Figure 7, where the mass-luminosity rela­tion for the models in Table V is also shown. Unlike the situation in Figure V for the Hyades and Pleiades stars, and field binaries with no ultraviolet ex­cess, the agreement between the observed and predicted relations is excellent.

A few highly evolved stars with well established luminosities and masses (27) are listed in Table X and plotted in Figure 8. The continuous and broken mass-luminosity relations in Figure 8 represent the run of the observed rela­tions in Figures 7 and 5, respectively. Two systems are similar to the Hyades group members (ADS 3841 =a Aur is a group member and ADS 2220 shows no ultraviolet excess with respect to Hyades stars); members of both of these systems are shown in the (Mbolr B - V) and mass-luminosity planes of Figure 8 by open circles. The other pairs have o( U -B) � +0':'02 and are shown as filled circles; ADS 10157 = .\Her has a large trigonometric parallax and ADS 6993 AB has a distant, main sequence component from which an accurate photometric parallax is obtained. The evolutionary tracks for stars of 3, 2, 1.5, and 1.1 solar masses (25, 26, 27) are also shown in Figure 8b. Running the binary components in Figure 8b back to the zero-age main sequence along the appropriate evolutionary tracks moves each star in Figure 8a to the point indicated by the tip of an arrow.

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 245

TABLE VIII

MASSES OF SIRIUS GROUP MEMBERS

ADS C Mbal m (0) U V W

1598 A +0.14 +1.8 1.8l -12 +3 -10 1598 B +0.425 +3.6 1.5f

1709 AB +0.425 +3.6 1.3 -14 -2 -12 3182 AB +0.07 +0.3 2.5 - 8 +3 - 8 5423 A +0.02 +1.3 2.2 -14 0 -12 8 739 A +0.38 +3.1 1. 7} -14 +2 - 9 8 739 B +0.75 : +5 .4 0.7 8891 AB 0.00 +1.1 2.4 -15 +3 - 9 9094 AB +0.5 2 +3.8 1.4 -12 +3 - 9 9747 AB +0.20 +2.3 1.6 -12 +2 - 9

17178 AB +0.8 5 +5.9 0.7 -12 0 -11

TABLE IX

MASSES OF SYSTEMS WITH Il( U-B) � +0':'02

ADS C o( U-B) Mbo! m(0) U V W

6811 BC +0.5 95 +0.09 +4.7 1.0 +16 -24 - 6 6828 AB +0.33 +0.03 +3.0 1.8 -10 + 5 - 9

a CenA ( +0.04) +4.3 11) +29 + 2 +13

a Cen B ( +0.04) +5.5 0.9 9413 A +0.75 +0.05 +5 .4 0.77 - 6 + 1 + 1 9413 B +1.0 +7.4 0.68 9689 BC +0.35 +0.04 +3.1 1.4

10660 A +0.58 +0.03 +4.4 1.0 } -37 - 1 -21 10660 B +1.1 +6.7 0.65 12145 BC +0.905 +0.08 +6.1 0.85 -33 +7 +33 15419 BC +0.8 0 +0.04 +5 .5 0.85 +37 +48 + 8

TABLE X

EVOLVED STARS

ADS C Mbol m (0) U V W

2220 AB +0.42 +2.2 1.2 +14 -19 -14 3841 A +0.90 -0.3 3.0 } +38 -17 -10 3841 B +0.65 +0.1 2.9 6993 AB +0.70 +0.6 2.5 +42 -25 -18

J015 7 A +0.64 +2.7 1.0 } +54 -47 -26 1015 7 B +0.75 +5 .4 0.75

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-2

o

+2

+4 • MODELS X SIRIUS ® iCU-B)?+C>-02

LOG m (}) +0·6 I

+0·2 -+0·0 FIG. 7. Same as Fig. 5 but for systems in the Sirius group or field binaries with

6( U-B) � +()m.02.

MBol

0

+2

+4

T-I I 1 I I --

fA "'--..... ,,-...... -..J B

I I -,- I I

A=ADS3841 "'-- 0 .-AOS6993

~ C = ADS 10157 "

D. ADS 2220 ", (0) J I I I I I I I I eCb

log m (0) 0.8 0.6 0.4 0.2 0.0

I I I I I I 30 Ab Aa

20 �.I!---

1.10

(b) .Cb I I I I I I I I

B-V +0.2 +0.4 +0.6 +0.8 •

FIG. 8 . The mass-luminosity and colour-luminosity arrays for evolved stars: A =ADS 348 1, B=ADS 2220AB, C=ADS 1015 7 , and D=ADS 6993 AB. The tips of the arrows in (a) indicate the main sequence luminosities.

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Page 13: Some Observational Aspects of Stellar Evolution

OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 247

Mass and luminosity determinations for stars more luminous than about om are rare and, in general, unreliable. Several of these stars appear in eclips­ing binary systems. However, not only are the masses subject to some uncertainty because of the difficulty in accurate measurement and correct interpretation of the radial velocity variations, but also the luminosities are generally not available. Two such systems (Table XI), which also contain a distant common proper motion, main sequence companion (30) are the following:

TABLE XI

Star Mbol (B- V)u m (0) U V W Ref.

U Cep Aa -0':'2 -0':'15 4.7 +20 - 8 +4 Hardie (31) U Cep Ab +2.4 +0.8 1.9 U Oph Aab -1.6 -0.20 5.0 +3 -14 -7 Petrie (32)

Both the mean component of U Oph and the brighter component of U Cep follow the general run of the observed mass-luminosity relation in Figure 5. For stars brighter than about -1m some of the discrepancy between the ob­served slope and that indicated by the mass-luminosity relation of the models in Table V may be caused by an underestimate of the bolometric corrections, but for fainter stars this explanation is not likely to be correct. Unfortunately the luminosity of the eclipsing system Y Cyg, which has the largest well de­termined mass, is not known accurately. The mean of the equal components, which are of spectral type 09.5 V (B -V = - 0':'30), has a mass of 17.3 solar masses. McNamara (33) finds an Hj3 index of 2.59 for the system which cor­responds to Mv near -3':'7 from a (Hj3, Mv) calibration discussed below. Several model atmospheres indicate a bolometric correction of 3m and if we arbitrarily reduce this by one magnitude, on the basis of the rocket observa­tions in the ultraviolet, the resulting value of Mbol- 5':'7 is in accord with with the values of -5m and -7m obtained from models ( 25) of 1 1 and 2 0 solar masses, respectively.

In summary, there appears to be little doubt that for stars fainter than Mbol = - 2m there are two discrete mass-luminosity relations: one holds for the Hyades-Pleiades stars, and for stars falling on the Hyades-Pleiades (U-B, B-V) relation; the other holds for members of the Sirius group, the Sun, and field binaries showing an untraviolet excess with respect to the Hyades-Pleiades stars. Although stars brighter than about Mbol = + 2m and showing this ultraviolet excess are evolved, they may have satisfied the Hyades-Pleiades mass-luminosity relation when on the main sequence (Fig. 8).

Iben (34) has shown that the mass-luminosity and colour-luminosity re­lations for different chemical compositions are essentially parallel and the effect of changing the composition can be approximated as follows:

Mbol(X2, Z2) = Mbal(X1, Zl) - 2.15 tJ( -31.25 t,Z (at a given temperature) log m(X2, Z2) = log m(XI, ZI) + 0.625 t.X + 2.91 t,Z (at a given Mbal)

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Page 14: Some Observational Aspects of Stellar Evolution

248 EGGEN

The most obvious explanation of the two mass-luminosity relations for stars fainter than about Mbol = + 2m is that they represent stars of different com­positions. In theory we should be able to estimate the approximate differences in (X, Y, Z) between the stars in Figures 5 and 7 if we also know the displace­ments of the main sequences. Fortunately, the Ursa Major cluster, which with Sirius defines the motion of the Sirius group, is even closer (25 parsecs) than the Hyades cluster (40 parsecs). However, the main sequence of the Ursa Major cluster is not well defined, partly because of the small number of stars but especially because of special difficulties connected with determining the convergent point. The best available estimate indicates that the main se­quence is at least 0':'2 brighter (35) than the Hyades main sequence at a given value of C, the observed B - V corrected for line-blanketing effects of +0':'03. If the composition of the Sun is taken as (X, Y, Z) = (0.72,0.26,0.02) (36,37), values of, say, (0.49, 0.49, 0.02) for the Hyades would approximate the ob­served displacements in the mass-luminosity and colour luminosity relations and the resulting value of (Z/ X)Hy= 1.5 (Z/ X)0 is within the uncertainties of the direct determinations (38).

VERY YOUNG STARS One of the richest regions of young stars is that occupied by the clusters h

and X Per (NGC 869 and 884) and the neighbouring stars in the Perseus arm of the Galaxy. An intensive photometric study of the absorption in this region has been carried out by Wildey (39). The region of the (Mv, B - V) plane oc­cupied by the majority of the early-type stars in the nuclei of these clusters is shown by the enclosed region in Figure 9. The individual supergiants sur­rounding the cluster are indicated in the figure by opeN circles ; a few stars in the cluster nuclei falling outside the enclosed region and brighter than Mv = - 2m are indicated by crosses. The modulus (39) of m - M = 11':'9 has been used. Because of the difficulties already mentioned, the bolometric cor­rections and temperatures of the bluest main sequence stars are very uncer­tain. Among the late-type stars, the bolometric corrections for supergiants derived by Johnson ( 5) from his infrared observations and the diameters of a Ori, a Sco, {3 Peg, and 0 Cet have been adopted. The resulting evolutionary tracks in the (Mv, B - V) plane of stars with 7 (40) and 15.6 (41) solar masses are shown in the figure. The end of the track for stars of 15.6 solar masses is particularly uncertain because, as Smak (42) has discussed, corrections of about 2m for the TiO absorption are necessary in addition to the bolometric corrections before theory and observation can be carefully compared for the M-type stars.

There is undoubtedly some spread in the ages of the stars involved in the region around the clusters ; j udging from the evolutionary times involved in the tracks shown, this range exceeds 107 years, with the younger stars almost exclusively in the association rather than in the dusters. Bidelman (43) has suggested that the Cepheids within the region covered by the stars shown in Figure 9 may belong to the association. The photometry of these stars (44) gives the following (Table XI I):

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Page 15: Some Observational Aspects of Stellar Evolution

Mv -a

-6 .

-..

-2 .

r ------.-------r----T--.-------' -----.--------,----------1" ---------r---- --, I. I SR .. o 0 ASSOCIATION � 15.60 • CLUSTER

o COO 0 + CEPHEIDS 000<8 cPct'o 000 • 0 0 0 0 0

;0 .:<0: \.0 �@ c( � ' 0. ':. oK

x cS GO 0 "A � .... 0 �� .; < ,2 ,- r � t:r •

7 �

+.L 7/ �· o '- 0 0 0 0 0 0 0 \"JJ \ <--r-- " � CEPHEIDS

-0,4 Ie _\/1 0 +0-4 +0-8 +1-2 +1-6 +20

0-

FIG. 9. Colour-luminosity array for stars in the nuclei of h and X Persei clusters (enclosed area plus crosses) and the surrounding association (open circles). Some classical Cepheids (plus signs) and semiregular variables (filled circles) in the region are also shown. The evolutionary tracks are for stars of 7 and 15.6 solar masses. The Cepheid region of instability and the positions of the long-period

(LP) Mira stars are indicated.

o to Cfl t:rj :::0 � >-3 o Z ;J> t'"' B; '"1:l t:rj (j Ul o 'Tj Cfl � t'"' � :;:0 t:rj a t'"' c::: >-3 o Z

� >I=>-1.0

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Page 16: Some Observational Aspects of Stellar Evolution

250 EGGEN

TABLE XII

Variable LogP E(B- V) Vo(med) (B- V)omed Mv p(km/sec)

VX Per 1.04 +0�5 8 7�6 +0�66 -4�3 -33.0 5Z Cas 1.03 +0.88 7 .2 +0.64 -4.7 -41.0 VY Per 0.74 +1.06 8.1 +0.58 -3.8 -39.5 UY Per 0.73 +0.98 8.4 +0.62 -3.5 -59.0 DWPer 0.5 6 +0.53 9.6 +0.5 3 -2.3

The reddening values are similar to those derived from early-type stars in the region, and the radial velocities are near the mean value of p= -42 km/sec for the clusters. The median luminosities and colours are indicated by plus signs in Figure 9, and the region of the colour-luminosity array populated by the nearest Cepheids (45) is outlined. The model with a mass of 70 passes through the Cepheid region five times in its evolution, each time be­coming unstable with respect to radial pulsations; the first time and the last time (which is beyond the point marked A and omitted to avoid confusion in the diagram) spending only about 103 years in the process compared to 106 years on the other occasions. During the slowest passage (the second) through this region, when the star is in its first helium-burning stage, the most unstable model has log P = 1.06, Mv = -4':'5, and B - V = +or:'8, which agree as well as might be expected with the observed values for VX Per and SZ Cas.

Seven semiregular variables of the "SRc" type occur in the region of the clusters (Table XIII):

TABLE XIII

Variable P± Mv (B- V)o

S Per 900d -4':'5 +2':'05 T Per 320 -4.7 +1.89

R5 Per 150 -5.2 +1.84 SU Per 47 0 -5.2 +1.84 YZ Per 380 -6.7 +1.64 AD Per 320 -5 .4 +1.82 BU Per 365 -4.9 +1.85

These stars are indicated by filled circles in Figure 9. With two exceptions (S and YZ Per) the variables have values of (B - V)O between + 1 .8 and + 1 .9 and all but two stars in Figure 9 in this range of colour are variable ; the value of B - V is nearly constant throughout the cycle in semiregular vari­ables (42). The position of the "LP," Mira stars in Figure 9 (42) is also indi-

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Page 17: Some Observational Aspects of Stellar Evolution

v o

OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 251

-20 o

u o 0

�GC.

+ 20 o 00 0 0 ff 0 0

8'0 &�0S6��8��

o

o 0 ox COco JJ 0 0 0 " 0 o o 0 0 0 00 0 o " X +200 +100 o -100 -200 PS.

FIG. 10. The correlation of the ( U, V) velocities of B-type stars within 300 par­secs of the Sun and distance X toward ( -) or away ( + ) from the galactic centre.

cated. Apparently the region of instability in the colour-luminosity array for the cool variables is similar in shape to that for the Cepheids.

Nearer the Sun the young population is represented by the brightest B­type stars. Accurate photometry is available for all those brighter than visual magnitude 5 and earlier than spectral type B8, but radial velocities for many of even the brightest are not accurately known. The 120 stars within 300 parsecs for which relatively accurate radial velocities, as well as spectral and luminosity classifications, are available have been used to construct Figures 10 and 11. The distances were obtained from the following calibration of the spectroscopic classifications (Table XIV) :

TABLE XIV

Spectral V type

IV III

BO -4�4 -5 �0 -5 �4 B 1 -3.6 -4.1 -4.4 B2 -3.0 -3. 5 -3.7 B3 -2.0 -2.5 -2.7 B5 -1.6 -2.0 -2.2 B 7 -1.0 -1.3 -1.5

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252

Z +100

0

-100

• ••

• •

X +200

EGGEN

N.G.P'

••

, 1. • -. .

fII" •

+100 o

• • . ..

I�� • •

1

.-

• •• •

-100 -�oo PS. FIG. 11. The (X,Z) distribution of the stars in Fig. 10.

G.C .

Irrespective of errors in classification, which are not negligible, the spread in each of the values listed above may easily exceed one magnitude: such cali­brations are nearly useless for accurate luminosity determination of an indi­vidual star. Figure 10 shows the distribution of the space motion components ( U, V) , as a function of distance X from the Sun and toward ( - ) or away ( + ) from the galactic centre. Both o f these components o f the space motion show a range of about 30 km/sec; and although the values of V are apparently not correlated with X, those of U are, with a systematic increase of about 40 km/sec/kiloparsec in the distance away from the galactic centre (46). The range in the W velocities is about 20 km/sec and the values are not cor­related with X. The distribution of these stars in the (X, Z) plane, where Z is positive toward the north galactic pole, is shown in Figure 11 where their concentration to a plane, and the tilt of that plane with respect to the galactic equator, is obvious.

There have been attempts to divide this "local association" into sub­groups such as the Scorpio-Centaurus association (47) , the Cassiopeia-Tau­rus association (48) , and the II Persei association (49) ; and Blaauw (50) has suggested even further subdivision of some of these, for various reasons. However, from Figures 10 and 11 it would seem simpler to regard all of these objects as members of a local association with, perhaps, some variation in the epochs of formation. There is an extensive literature on the expansion of some of these subassociations as well as others in distant arms of the Galaxy (5 1) ; various "expansion ages" have been derived from the available observed mo­tions. Many of these discussions implicitly adopt the hypothesis that the ex­pansion is a physical phenomenon, perhaps caused by some violent event at the formation of the stars, and treat the observed motions as showing a linear

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Page 19: Some Observational Aspects of Stellar Evolution

OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 253

expansion from a point source. Blaauw (51) has shown that such an expan­sion does not destroy the concept of a "convergent" point of the proper mo­tions. However, the concept of a linear expansion, the presence of which is difficult to establish from the available proper motions, may be oversimpli­fied. What seems clear is that there will be a dynamical expansion of any batch of stars after formation, if only because the dispersion in velocities of the newly formed stars (perhaps resulting from the random motions in the parent medium) will eventually establish a "dispersion ring" (52) that will include the final orbits of all the individual stars. Because there is no reason to believe that the initial values of the U velocities, the dispersion of which will establish the radius of the ring, are related to the individual values of the initial V velocity, this "expansion" would not be expected to be linear.

Most of these stars, though very young, have reached the main sequence and are burning hydrogen in their cores. Intrinsically fainter stars of the same age, however, may still be gravitationally contracting (53). In approximately 3 X 107 years a B-type star of 10 solar masses will have depleted its core hy­drogen and evolved into a red giant while a star of solar mass is just finishing its pre-main sequence contraction. Therefore a young cluster, such as the Pleiades, which is about 3 X 107 years old as judged from its brightest stars, should have no main sequence stars fainter than about Mv = +5m• An exten­sive photoelectric study of Pleiades stars by Johnson & Mitchell (54) yields the colour-luminosity array in Figure 12. Only photoelectric observations of stars for which proper motions indicate certain membership are used. A modulus of m- M = 5':'55, derived from fitting to the Hyades main sequence, was applied, and the individual stars were corrected for the reddening, which ranges from E(B - V) = +0':'04 to +0':'15 across the field; a small region near Merope (23 Tau) has reddening values approaching 0':'25. A few stars fainter than Mv = + 7, which in general were observed only once and for which red­dening corrections are interpolated from neighbouring stars of earlier type, are indicated by crosses. Two faint cluster members found by van Maanen (55, Nos, 46 and 50), for which the observations have not previously been published, are indicated by plus signs. It is obvious that, contrary to predic­tion, there are main sequence stars not only at Mv = +5m but all along the sequence to at least + 10m; the run of the Hyades main sequence from Mv = + 7m is shown as a continuous line. In examining this problem, Herbig (56) has searched for T Tauri variables-present in large numbers in several other young clusters and believed to be in the pre-main sequence stage of evo­lution (57)-with completely negative results. He did find bright Ca II cores in one star, indicated by an arrow in Figure 12. Johnson & Mitchell dis­covered a flare of nearly 0':'5 in the visual magnitude of this same star and suspected other objects fainter than Mv = +6':'5 also to be slightly variable. Haro & Chavira (58) have found 26 flare stars, mostly fainter than V = 14m, during 118 hours of exposure in the Pleiades region; several flared two or three times during this interval. There is undoubtedly some surface activity on the cluster stars fainter than Mv near +8ffi but it seems just as certain

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254 EGGEN

My 01

'1 -2 r ,....PLEIONE PLEIADES

0 {;J0

0 'c'O +2 ��

... 4

... 6

+8

+10 I I , , , I I I I Lf (B-V)oO.O +0·4 +0.8 + '·2

FIG. 12. The (Mv-B- V) diagram for the Pleiades cluster from photoelectric ob­

servations. The crOSses indicate fainter stars for which generally only one observation is available, and two very faint stars for which photometry has not been previously published are shown as plus signs.

that M -type main sequence stars are present. Hayashi (59) has revised the earlier contraction times for main sequence stars by introducing a wholly con­vective, early contracting phase, but some 108 years are still required to pro­duce an M-type dwarf.

Herbig (56) has suggested that the stars of small and intermediate mass form first, and points to the Taurus-Auriga and Scorpio-Ophiucus dark clouds with their dense population of T Tauri variables as examples of future clusters or associations now being formed in this w ay. This gradual increase in the stellar content of the dark cloud will continue until interrupted by the formation of very hot, massive stars whose radiant flux will dissipate the gaseous mass that is producing the stars and terminate star formation. I n the case of the Pleiades, the M -type dwarfs were at least 108 years old before the brightest stars, which average near 3 X 107 years, were formed. Because the conditions of formation of the massive stars, which terminate all star produc­tion, may not be directly related to those for the formation of the fainter ob­jects, the occurrence of the massive stars may be random; and the time at which they occur will dictate the resulting luminosity function of the fainter cluster stars. Such a situation would explain the scarcity, and even absence, of low-mass stars in some clusters. The position of Pleione (28 Tau) in the colour-luminosity array of Figure 12 is perhaps a consequence of the pro­longed stage of star production in the Pleiades. Although there are a half

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Page 21: Some Observational Aspects of Stellar Evolution

OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 255 dozen brighter stars in the cluster, Pleione alone has shown evidence of vio­lent evolution in recent years (60). If Pleione represents the top of the main sequence of the "older" Pleiades, the hydrogen-burning age would be nearly consistent with the presence of M-type dwarfs.

KINEMATICS OF'YOUNG STARS The well determined space motion of the Pleiades cluster is (U, V, W)

= (+9, -27, -13) km/sec relative to the Sun ; the U, V, and W velocities are, respectively, directed away from the galactic centre, in the direction of galactic rotation and toward the north galactic pole. Three other clusters, all very similar to the Pleiades in stellar content, are also moving with nearly the same space motion (Table XV),

TABLE XV

Cluster p(km/sec) m-M U V W

ex Persei -2.0 6.25 +13 -27 -5 NGC 2516 +20±1 7 .80 +11: -25: -4:

IC 2602 +26±2 5.95 + 2 -28 -8

The radial velocities for the first and third clusters are derived from the mean value for sharp-lined members observed at the Lick Observatory (61); that for NGC 2516 is based on the values for 13 early-type stars observed at the Cape (62). The photometry is taken from several sources (62-65). The colour-luminosity arrays are shown in Figure 13. All three clusters show breaks in the distribution of stars : at Mv near (}Ill and at B - V = +0':'25 and +0':'35. A comparison with the Pleiades cluster in Figure 12 shows that it also has these breaks near Mv=O'" and at B- V near +0':'35. The published ob­servations (66) for NGC 1039 (M34), which has a very poorly determined motion of (U, V, W)=(+3:, -27:, -20), shows a distribution along the main sequence nearly identical with that in Figure 13. Of special interest in NGC 2516 are the three stars redder than B - V = + 1':'0: the brightest, HR 2125, is MO II (62) and the other two are K-type giants. The two reddest ob­jects are very near the centre of the cluster and have radial velocities and proper motions almost identical to the mean cluster values.

Several of the high luminosity stars near the Sun share the motion of the Pleiades cluster. Some of these objects are listed in Table XVI together with the luminosity resulting from group membership and, when available, the results of "H{3" photometry by Crawford (67); a value of H{3 given in paren­thesis has been transformed to Crawford's system from the observations by Bappu et al. (68) of H-y. The three reddest stars, plus a Per which is a mem­ber of the a Persei cluster, are shown in Figure 13. The cepheid a UMi, which lies close to the edge of the �ariable star region shown in Figure 9, has a very small light and velocity amplitude and a period of four days. The supergiant a Per, which falls j ust outside the Cepheid region in the colour-luminosity

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Page 22: Some Observational Aspects of Stellar Evolution

Mv -4-

-2 -

0-

+2 -_

+4-

x

o +.

0-

i: + +

-?�\'C. ++ // +I!. + t o - J - t *' )<.i �+ + �

OlPE�-- •

Ol UMI ----- A

o

+ NGC2516

o Ieft++ ���+ X +0. '9 �+i � l( IC 2602

• I(.PE� o [C 2391 A PLEIADES Gp'

(B-V)o -0'2

-

o +0'2

'\,* 0. d'

+0'4

,,<;,' )( . • • "0J(

• .. 0

+0·6

'¥ AND

A / +

+[,2

A + \tHER

+[.�

FIG. 13. Colour-magnitude diagrams for some stars and clusters in the Pleiades group.

MO:!! -..+_

+[-6

N CJl Q'\

� 8 � z

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 257 TABLE XVI

NEAR-BY HIGH LUMINOSITY MEMBERS OF THE PLEIADES GROUP

Star E(B - V) Vo (B - V) o Spectral

type HiJ Mv U j1 W

E Per +0.09 2 . 64 -0 . 28 BO 5 V 2 . 595 -3 . 7 +13 -27 - 7 iJ Cru +0 . 03 1 . 15 -0.27 BO 5 V -4. 1 + 4 -27 - 8

", Vir 0 . 00 0 . 98 -2 . 26 Bl V (2 . 595) -3 . 9 +10 -27 - 8 I' Seo +0 . 03 2 . 98 -0 . 26 Bl 5 V 2 . 615 -3.3 + 4 -27 - 8

iJ Lup +0.01 2 . 64 -0.24 B2 V (2 . 610) - 3 . 2 +15 -27 -10 HR 5190 0 . 00 3 . 40 -0 . 24 B'2 V (2 . 625) - 2 . 9 +10 -27 - 7 o Cas +0 .07 4 . 38 -0 . 15 B2 V 2 . 672 - 2 . 6 + 8 -27 - 5

a Pay 0 .00 1 . 93 -0 . 2 1 B 3 V - 2 . 3 +10 -27 - 4 ", Tel +0 .01 3 . 47 -0 . 19 B3 V - 2 . 2 + 8 -27 - 7 X Cen +0.03 4 . 26 -0 . 22 B3 V (2 . 655) - 2 . 2 + 7 -27 - 5

HR 5378 +0.02 4 . 35 -0 . 2 1 B3 V -2 . 0 + 7 -27 - 6

� Aur +0 . 03 3 . 07 -0.20 B3 V 2 . 690 - 1 . 6 +14 -27 - 8 69 0ri +0 . 01 4 . 92 -0 . 1 8 B5 V 2 . 695 - 1 . 9 +19 -27 - 2

a Eri 0 . 00 0 . 50 -0 . 18 B5 V - 1 . 8 + 8 -27 - 6

Ot. Gru +0 . 01 1 . 70 -0.14 B5 V -0.9 + 9 - 27 - 6 3 Cen +0 . 06 4 . 13 -0 . 18 B5 IV - 1 . 0 + 3 -27 - 8

a Col +0.04 2 . S1 -0. 16 B 7 V -0.5 +12 -28 - 1 8

'" Cas +0.08 4 . 7 1 - 0 . 16 B7 V 2 . 755 - 0 . 5 + 4 -27 - 4 HR 6997 +0 . 02 5 . 42 - 0 . 13 B8 V 2 . 739 -0.2 + 9 -29 - 6

a Lup +0.05 2 . 14 -0 . 25 Bl III - 4 . 9 +10 -27 - 6

6 Per +0 . 03 2 . 94 -0 . 18 B5 III (2 . 640) -2 . 5 + 5 -27 - 4 o Lup +0 . 03 4 . 23 -0 . 18 B6 III -2 . 1 + 8 -27 - 5 iJ Tau +0 . 03 1 . 55 -0 . 16 B7 III 2 . 720 - 1 . 3 + 8 -28 -15

a Per +0.05 1 . 64 + 0 . 44 F5 Ib -4 . 6 +14 -27 - 5 a UMi +0 . 03 1 . 70 +0 . 52 F8 Ib -4 . 2 + 5 -27 - 4 'Y And +0 . 04 2 . 00 + 1 . 1 2 K2 II - 2 . 4 + 4 -27 - 8 .. Her +0.05 3 . 00 +1 .37 K3 I I - 2 . 4 +14 -27 - 2

array, has semiregular, small-amplitude light and velocity variations with a period also near four days (69) . The two red stars of luminosity class I I fall near the members of NGC 2516 in Figure 13. These red stars may represent objects of seven solar masses in the carbon-burning stage, beyond the point marked A on the evolutionary track in Figure 9.

The (H!3, Mv) relation for the stars in the first part of Table XVI is shown in Figure 14 by open circles. The individual stars are well represented by the relation Mv = - 3':'5 + 20 (H!3 - 2.60). The stars (67) in the Pleiades (crosses) and ex Persei (filled circles) clusters apparently follow the same relation and show the homogeneity of the stars in the Pleiades group ; the average devia-tion from the mean relation is ± 0�25, which is only slightly greater than ex-pected from the uncertainty in the observed values of H!3. That the Pleiades group stars are part of the "local association" is seen in Figure 10 where the values of (U, V) , indicated by crosses, fall in with the run of all the early-type stars. How soon the group will separate from the rest of the association de-pends on how much of the apparent velocity spread in Figure 10 is inherent

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Page 24: Some Observational Aspects of Stellar Evolution

258 EGGEN

in the stars. Accurate values of Hj3 for all of these objects would help to answer the question.

Another feature of interest in the clusters of the Pleiades group is the presence of peculiar A-type stars (Ap) at Mv near - 0':'5 ; these are indicated by arrows in Figure 13. Such stars are unknown in the Pleiades itself, but Figure 12 shows that the peculiar shell star Pleione occurs at the same lumi­nosity. The Ap stars are probably all of the Si (X 4200) type (62, 70). Another cluster, whose motion is similar to, but not identical with, that of the Pleiades is Ie 239 1 ; ( U, v, W) = ( + 22, - 17, - 6) based on a radial velocity of + 17 km/sec from 45 plates of 9 stars (61, 7 1). The distribution of the members of this cluster in Figure 13 is very similar to that of the Pleiades group stars, including the presence of two Si (X 4200) stars with Mv near -O'!'S. The member of the a Persei cluster that falls in the region of the Ap stars in Figure 13 is HR 1029, which has been classified as B6 V (72) and shows fairly sharp lines (73); it should be examined for peculiarities. Another member of the a Persei cluster, HR 10S l , with (Mv, B - V) = ( - 0':'7, -0':'14) shows a shell spectrum (73) and is similar in luminosity and colour to Pleione ( - 0':'6, -0':' 10).

All of the well defined Ap stars brighter than visual magnitude 5'!'5 and with reliable motions are listed in Table XVII together with the predominant peculiar element (74). The colours and the type of peculiarity show a break

o· -, - r - ,

- 3'0 o

2.6

X PLEiADES • 0( PE R C L. o TABLE XV[

I . , I 2·7 H(3

FIG. 14. The correlation between H{3 and Mv for Pleiades group stars.

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 2 5 9

TABLE XVII

Ap STARS BRIGHTER THAN VISUAL MAGNITUDE 5 .5

HR ECB-V) CB -V)o Vo Pee. Mv U V W

HR 1732 1732 0 . 00 - 0 . 1 7 5 . 35 " 4200 -0.90 +30 -14 - 6

108 Aqr 9031 0 . 00 -0 . 1 7 5 . 17 " 4200 -0.90 +12 - 1 7 - 1 7

HR 4817 4817 +0.06 -0 . 16 4 . 46 Mn -0.80 + 8 -28 - <) HR 612 612 0 . 00 -0 . 16 4 . 68 " 4200 -0 . 80 +15 - 4 - 15

41 Tau 1268 +0.03 -0 . 16 5 . 10 " 4200 -0.80 + 6 -27 -12

p Lep 1702 +0.03 -0. 14 3 . 29 Mn -0 . 70 +15 -26 - 7

• Cne 3623 +0. 02 -0 . 14 5 . 1 7 Mn -0 . 70 +24 -20 - 2

36 Ed 1240 0 . 00 -0 . 13 4 . 63 " 4200 -0.65 +19 -14 -11

56 Tau 1341 0 . 00 -0. 1.3 5 . 38 >. 4200 -0.65 +14 -37 - 8

49 0ri 937 +0 .03 -0 . 13 4 . 2 7 Mn -0.65 +42 -10 - 16

a And 15 0 . 00 -0 . 13 2 . 1 7 Mn -0.65 + 6 -27 -15

a Dor 1465 +0.02 -0. 1 2 3 . 20 >. 4200 - 0 . 55 + 6 -28 - 6

, Cr B 5971 +0 . 05 -0 . 10 4 . 85 Mn -0.40 + 1 1 -27 - 2 ", Her 6023 +0 . 04 -0 . 10 4 . 12 Mn -0.40 +20 - 1 1 - 5

1 1 Or! 1638 +0 .01 - 0 . 08 4 . 62 51 -0 . 25 +14 -18 - 7 B Aur 2095 0 . 00 -0.08 2 . 70 Sl -0 . 25 +30 - 9 + 4 Cd Her 61 1 7 +0 . 04 -0.03 4 . 44 Cr-Eu +0 . 10 -10 - 5 -20

. UMa 4905 0 . 00 - 0 . 02 1 . 76 Cr-Eu +0 . 20 -12 + 2 - 8

B Mic 8151 +0 . 03 -0.01 4 . 72 Cr-Eu +0 .30 +18 0 -21 o Aur 1971 0 . 00 +0.03 5 .47 Cr-Eu +0.60 - 6 0 - 5 . Psc 8911 0 . 00 +0 . 03 4 . 9 1 Cr-Eu +0 . 60 +12 -36 -23

78 Vir 5105 0 . 0 +0 . 04 4 . 94 Cr-Eu +0 . 65 - 13 + 4 -13

X Ser 5843 0 . 0 +0 . 04 5 . 33 Cr-Eu-Sr +0.65 - 1 2 + 8 - 1 0

21 Com 4766 0 . 0 +0.05 5 . 46 Cr-Eu-Sr +0 . 70 + 4 - 6 - 1 73 Dra 7879 0 . 0 +0.07 5 . 20 Cr-Eu-Sr +0.90 0 + 1 1 + 1

52 Her 6254 0 . 0 +0.08 4 . 81 Sr + 1 . 00 +17 -28 - 6

, Phe 8949 0 . 0 +0 . 08 4 . 70 Sr + 1 . 00 + 4 - 7 -22 HR 8216 8216 0 . 0 +0 . 09 5 . 28 Cr-Eu + 1 . 05 +19 -13 - 6 w Oph 6153 0 . 0 +0 . 12 4 . 46 Sr (+1 . 20) - 2 + 8 + 2

'Y Equ 0 . 0 +0 . 26 4 . 68 Fp (+1 . 2) - 2 -35 -22

Ii Cr B 0 . 0 +0 . 27 3 . 69 Fp + 1 . 0 +34 -18 + 3

near (B - V)o = - 0':'05 with the bluer stars being all of the Si, Si (X 4200) or Mn types. The luminosities are obtained from the very well defined (Mv, B - V) relation for the objects in galactic clusters and wide visual binaries (75). The distribution of these stars in the ( U, V) plane is shown in Figure 15 where those bluer than B - V = 0':'05 are represented by open circles and the redder stars by dots. With very few exceptions the diagonal lines from ( U, V) = (+ 20, 0) to (0, - 20) separates the red and blue objects. The bluest, which are presumably the youngest, have a ( U, V) distribution similar to the B-type stars in Figure 10. The Hyades and Pleiades group stars, which give a unique mass-luminosity relation (Figure 5) , fall in with these blue, Ap stars in Figure 15, whereas the stars populating the mass-luminosity relation of Fig-ure 7 are either distributed like the redder Ap stars or fall outside the bound-aries of Figure 15 . From three-colour observations of several hundred F - and G-type dwarfs (76) it was found that those objects showing no ultraviolet excess with respect to the Hyades, and therefore supposed to have the same ratio of metals to hydrogen, also populate the ( U, V) plane above the diago-

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260 EGGEN

nal line drawn in Figure 15 . One interpretation of these results is that all of the young population in the solar neighbourhood (> 1 to 5 X 108 years) are closely related both chemically and kinematically (27, 77) , whereas the older stars are a much more heterogeneous mixture with wide variations in time and place of origin.

Two clusters in the Sirius group, with ( U, V) = ( - 15, + 1) and therefore in the ( U, V) plane below the diagonal line in Figure 15 , are the Ursa Major cluster and NGC 7092 (M39) ; the motion of the latter is discussed by Evans & Meadows (78) . The colour-luminosity arrays for these clusters are shown in Figure 16 where the Ap stars, which are of the Cr-Eu-Sr types, are indi­cated by arrows. The three brightest stars in M39, which are similar in colour and luminosity to E UMa, an Ap star in the Ursa Majoris cluster at (Mv, B - V) = (0':'2, - 0':'02) , may be incipient Ap stars (79) . The Coma Berenices cluster, whose motion of ( U, V) = (+5 , - 6) places it below the diagonal line in Figure 15, shows a very similar colour-luminosity array and contains Ap stars of the Eu-Cr, Sr types. Like the other clusters in this region of the ( U, V) plane, the F - and G-type dwarfs of all three clusters show a small (r-...; +0':'03) ultraviolet excess with respect to the Hyades stars.

The evolutionary history of Ap stars presents a difficult problem. The fol­l owing suggestions have been made :

(a) Bide1man (80) has suggested that these objects have returned to the

u I II I �

o

o o 0

+20 ri o

0 G.R . • • . �.

I I , I

V -20 + G.C.

FIG. 1 5. The Ap s tars in the solar neighbourhood with E- V bluer (open circles) and redder (filled circles) than - O�05.

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 2 6 1

J

• U Ma

o 0.,. cP

I +0.4

• 0

• +0-6

FIG. 16. Colour-luminosity array for clusters in the Sirius group.

vicinity of the main sequence after passing through the hydrogen-, helium-, and carbon-burning stages of their evolution. They are, then, the counter­parts in the disc population of the horizontal branch stars in globular clus­

ters. A star of 4 solar masses would take approximately 106 years (81) to ac­complish this, but after the helium flash (82) and during the helium burning in the interior and in the surrounding shell, the star again approaches the main sequence only some 5 X 107 years after the initial departure (81) . If mixing between the hydrogen-rich shell and helium-rich interior occurs at the helium flash, the star may returni mmediately to the region of the main se­quence (82) .

(b) The Ap stars populate a unique region of the (Mbol, log T.) plane, and all stars that pass through this region during the course of their evolution are affected by the causes of the spectral peculiarities.

(c) Deutsch (83) has suggested that the presence or absence of the spec­tral peculiarities may depend on the stars' rotation. Large magnetic fields may be favoured by slow rotation with the abundance anomalies caused by conditions of abnormal excitation or electromagnetic separation of elements.

The positions of Ap stars with accurately determined luminosities are indicated in the colour-luminosity array of Figure 17 where the blue stars, (B - V) < - if.'1, and the redder objects are shown as open and filled circles,

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respectively. The Pleiades main sequence and the position of the shell star Pleione, as well as the region occupied by the luminosity class I I I stars of types A and F ( 18) , are represented. The ultrasharp line star 3 Cen A, a mem­ber of the Pleiades group (Table XVI) , is identified in Figure 17 . Bidelman (80) has identified lines of phosphorus, krypton, and gallium in this object, and He3 has been found (84) ; many of the spectral anomalies closely resemble those in some of the M n-type Ap stars, which show a strong magnetic field ; but Babcock, quoted by Sargent (74) , foun d no magn etic effects in 3 Cen.

The so-called metallic-line sta rs (Am) p r esent an evolutio n a ry p r oblem similar to the Ap stars; the position in Figure 1 7 of those with accurately de­termined luminosities, mainly from cluster membership, is indicated by plus signs. In view of the fact that most, if not all, Am stars are spectroscopic bi­naries (85) , their dispersion in luminosity for a given colour is unexpectedly small. However, the degree of metallicity that becomes obvious, spectro­scopically, may place an artificial boundary on a much more extensive region region (77) . The Am and Ap stars occupy contiguous regions in the colour­luminosity array, separated sharply at Mv = + lln.

From the position in Figure 13 of the Ap stars in the clusters shown there it appears that, if suggestion (a) above is correct : a large spread (from about 3 X 101 to 108 years) exists within a duster; the rate of evolution is controlled by some facto r othe r than luminosity-perhaps the rotation mentioned in

Mv , -

-I X� -PL£IONE

0 0

• • •

t I PLEIADES 6-10' VR-

• • •

+2 I I

-0-2 (B-V) 0

, . • . - •

VAR. � ��& DEL

- " J/J j & iCU :t: I •

• -5)( 10 VR

L

+02 -t()41

FIG. 17. Dist r ibution of Ap stars (filled and open ci rc les) and metallic· line sta rs (plus signs) in the (Mv,B. V) diag ra m. The bounda r y of the instability re gion, which includes the 0 Scuti va r iables, is shown togethe r with main sequences at 6 X 107 (Pleiades) and 5 X 108 ( Hyades) years. The position of the luminosity class III sta rs of types A-F is also indicated.

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 2 63

suggestion (c) ; or the Ap stars do not necessarily represent a definite evolu­tionary phase for all stars of a particular mass range, as stated in (b) . There are other reasons, already mentioned, for believing that just such a range in evolutionary ages exists for these stars. One consequence of suggestion (a) is that in its helium-burning stage a star of 4 solar masses would approach the hydrogen main sequence at nearly 2m brighter than when it originally left it (81) and the mass-luminosity relation would be considerably altered for these stars. Only one reliable mass determination for an Ap star is available-LUb, a Si-type star, which is ADS 9532 Aa with a mean mass of 5 0 for the equal components (30) . The system is a member of the Pleiades group with ( U, V, W) = + 14, - 24, - 12) determined with a photometric parallax ob­tained from the common proper motion companion ADS 9532B (30) . The quantities (Mv, B - V) are equal to (+0�2, -0�12) , placing the mean com­ponent among the blue, Ap stars in Figure 17 . The lines are rotationally broadened ; Babcock (86) found no magnetic effects in the spectrum. The mass and luminosity agree well with the run of other stars in Figure 5, but decreasing the luminosity by as much as 2m would make the star uniquely dis­crepant in that figure. A similar argument holds for the Am component of the eclipsing binary RR Lyn, in the Sirius group (87) . Popper (88) finds the mass and radius of the Am star to be almost identical to those of its F-type com­panion (Am : m = 1 .7 0, r = 2.5 0; F : m = 1.5 0, r = 2.0 0) . With the luminosity of + 2':'6 obtained from the group membership, the Am star falls on the mass- . luminosity relation in Figure 7.

Advanced evolution as an explanation of the Am stars is probably ruled out by the tightness of the sequence that at least most of the obvious exam­ples form in the colour-luminosity array and by the fact that they are found in clusters whose evolved main sequences pass through this region. The theoretical hydrogen-burning, evolved main sequence after 5 X 108 years is sketched in Figure 17 . It has occasionally been stated that Am stars depart from the main sequence but this is generally true only in the sense that the main sequences of the clusters they occur in have evolved from the zero-age main sequence.

It would be of interest to know how much the position in the colour­luminosity array of Ap and Am stars is affected by line-blanketing differences between them and main sequence stars of the same temperature. Six-colour observations (89)2 of selected peculiar and normal main sequence stars of the same temperature (i.e. the same [G - I]) are listed in Table XVII I together with the results of ( U, B, V) photometry. The star a Scl, which is one of the bluest Ap stars (90) , shows no excessive blanketing in [ V] compared with main sequence stars of the Pleiades group in Table XVII I that have similar values of [G - I]. Also, a And, an Ap star in the Pleiades group, shows little or no blanketing with respect to 19 Tau in the Pleiades cluster.

A peculiar discrepancy occurs for a CMa, a main sequence star that de-

I I am indebted to Dr. Kron for furnishing some six-colour results before publica­tion.

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TABLE XVI I I N SIX-COLOUR OBSERVATIONS

0\ >l>-

Spectral Star [U] ' [ VI {B] [G] [R) [I) [G-I) B- V U-B E(B- V)

type

B5 V a Eri - 1 . 72 - 1 . 10 - 0 . 46 -0 . 01 +0 . 54 + 1 . 1 1 - 1 . 24 - 0 . 18 - 0 . 59 0 . 00 Bp a Scl - 1 . 59 - 1 . 06 - 0 . 49 -0 . 05 +0 . 54 + 1 . 1 6 - 1 . 2 1 -0 . 1 7 - 0 . 55 0 . 00 B5 V a Gru - 1 . 47 - 1 . 03 - 0 . 48 -0 . 05 +0 . 54 + 1 . 1 3 - 1 . 18 - 0 . 13 - 0 . 44 +0 . 0 1 Ap a And - 1 . 44 - 1 . 00 - 0 . 48 - 0 . 05 +0 . 53 + 1 . 1 1 - 1 . 16 - 0 . 13 - 0 . 38 0 . 00 B6 V 19 Tau - 1 . 43 - 1 . 0 1 - 0 . 48 -0 . 05 +0 . 52 + 1 . 1 1 - 1 . 16 -0 . 1 1 - 0 . 46 +0 . 05 AO V a CMa -0 . 86 - 0 . 87 - 0 . 43 -0 . 05 +0 . 48 + 1 . 02 - 1 .07 0 . 00 - 0 .04 0 . 00 Ap (J Aur - 1 . 0 1 -0 . 93 - 0 . 44 -0 .06 +0 . 50 + 1 . 00 - 1 . 06 - 0 . 08 - 0 . 14 0 . 00 B9 V 22 Tau - 1 . 04 -0 . 94 - 0 . 45 -0 . 06 +0 . 50 + 1 . 00 - 1 . 06 - 0 . 02 - 0 . 15 +0 . 0 7 B9 V a Peg -0 . 85 -0 . 93 -0 . 44 - 0 . 05 +0 . 49 +1 . 00 - 1 . 05 - 0 . 04 - 0 .06 0 . 00 t'l

C'l Shell Pleione - 0 . 89 - 0 . 93 - 0 . 44 - 0 .05 +0 . 49 +0 . 96 - 1 . 0 1 - 0 . 05 +0 .04 : C'l AO V (3 UMa -0 . 81 - 0 . 86 - 0 . 43 -0 . 05 +0 . 48 +0 . 97 - 1 .02 - 0 . 02 +0 . 02 0 . 0 t'l

Z Ap E UMa - 0 . 77 -0 . 90 - 0 . 43 - 0 . 05 + 0 . 48 +0 . 94 - 0 . 99 - 0 . 02 +0 . 03 0.0 AO V 'Y UMa - 0 . 76 - 0 . 88 - 0 . 42 -0 .05 +0 .47 +0 . 94 -0 .99 0 .00 +0 .01 0 . 0 A3 (3 Leo -0 . 64 -0 . 76 - 0 . 37 -0 . 05 +0 .42 +0 . 84 -0 . 89 +0 . 09 + 0 . 0 7 0 . 0 Am r Lyr A -0 . 46 -0 . 64 - 0 . 32 -0 . 02 +0 . 34 +0 . 69 -0 . 7 1 +0 . 18 +0 . 17 0 .0 A7 V a Aql -0 . 54 -0 . 62 - 0 . 30 -0 . 0 1 +0 . 3 1 +0 . 68 - 0 . 69 +0 . 22 +0 . 07 0 . 0 A7 IV a Cep - 0 . 49 -0 . 6 1 - 0 . 29 -0 .04 +0 . 33 +0 . 62 -0 . 66 +0 . 23 +0 . 10 0 .0 Fp 'Y Equ -0 . 42 -0 . 51 - 0 . 26 -0 . 03 +0 . 30 +0 . 62 -0 . 65 +0 . 26 +0 . 10 0 . 0 FO V r Lyr B -0 . 48 -0 . 52 - 0 . 23 -0 . 02 +0 . 25 +0 . 56 -0 . 58 +0 . 28 +0 . 10 0 .0 (8 Seu) /) Del -0 . 36 - 0 . 50 - 0 . 22 -0 . 02 +0 .24 +0 . 53 - 0 . 55 +0 . 28 +0 . 1 1 0 . 0 F 2 IV (3 Tr A -0 . 46 - 0 , 47 - 0 . 20 0 . 00 +0 . 2 1 +0 . 52 - 0 . 52 +0 . 30 +0 . 02 0 . 0

FO V 'Y Vir -0 . 51 - 0 , 42 - 0 . 1 8 -0 . 02 +0 . 2 1 +0 . 46 -0 . 48 +0 . 36 - 0 . 05 0 . 0 F8 V (3 Vir - 0 . 2 1 - 0 . 19 - 0 . 06 - 0 . 03 + 0 .09 +0 . 21 - 0 . 24 +0 . 56 +0 . 09 0 . 0 Gp HD 101065 +0 . 08 +0 . 06 - 0 . 04 -0 . 02 +0 . 07 +0 . 20 -0 . 22 +0 . 78 +0 . 27 ? F8 V o Aql - 0 . 25 -0 . 19 - 0 .07 - 0 . 02 +0 . 09 +0 . 20 -0 . 22 +0 . 54 +0 . 08 0 . 0

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 2 6 5

fines the group motion of the Sirius group; its position is indicated i n Figure 17 . The (B - V) colour is similar to that of {3 and "Y UMa, which are members of the Ursa Major cluster in the Sirius group, and the run of the six colours from [ Vj through [Rj also are in agreement. The excess in [ U] of a CMa over {3 and "Y UMa, which is also reflected in the ( U -B) colours, and the defi­ciency in the [I ] , and therefore in [G - 1], is difficult to understand. It is con­firmed by Johnson's (5) infrared indices, which are as follows (Table XIX) :

a CMa (3 UMa

B- V

0':'00 0.00

TABLE XIX

V-R

0':'00 0.00

V-I

-0':'03 -0.04

V-J

-0':'12 +0. 04

V-K

- 0':'14 + 0. 06

These results indicate that the divergence between the energy distributions begins near the wavelength of the J filter, near 12, 00 0 A. If the higher tem­

perature of a: CMa, relative to {3 and 'Y UMa indicated by the [G - Ij index, were accepted, -0'!'06 to -0'!'08 would have to be applied to the observed B - V colour, placing the star to the left of the Pleiades main sequence in Figure 17. The shell star Pleione shows the blanketing in the ultraviolet by the shell, but the observed values of (B - V) for the Ap star E UMa and the Am star r Lyr A show little or no differential blanketing with respect to main sequence stars of the same temperature.

Even the Fp star "y Equ, which with {3 Cr B lies near the border of the in­stability region occupied by the 0 Scu variables in Figure 17 , is affected by less than 0'!'05 of differential line blanketing. However, the extremely peculiar "holmium star" HD 101065 (9 1) definitely shows the effect of line blanketing in the (B - V) colours. The six-colour results in Table XVI I I suggest that the corrected colour C is +0'!'54 (92) . The radial velocity of this star is + 2 km /sec (9 1 ) , and the extremely uncertain proper motion leads to ( U, V, W)

= ( +38, - 17, + 12) km/sec for a distance of 150 parsecs. The Hyades group motion is ( U, V, W) = ( +40, - 17 , - 2) : an accurate proper motion of HD 101065 i s needed to test the possibility that the star i s a group member. As a member its luminosity is near Mv = + 2m, indicating that the spectral pecu­liarities may extend almost to the Hyades red giants at (Mv, B - V) = ( +0'!'7 +0'!'9). However, the spectra of 0 Scu, a variable in the Hyades group at ( + 1'!'0, +0':'35) , and 35 Cnc, a GO giant member of the Praesepe cluster in the Hyades group with ( + 1'!'0, + 0':'67) , have not been reported as having this type of peculiarity.

VERY OLD STARS The available data for some of the oldest stars in the Galaxy are shown in

Figures 18 and 19. Figure 18 contains the colour-luminosity arrays for two globular clusters, M 5 (93) and M 13 (94) , whose main sequences have been

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266 EGGEN

Mv -2

0

r +2

.. 4 . 1104 13 o 1104 5

+6

0'2 C 0 0 ... 0·8 102 106

FIG. 1 8. (Mv,C) diagram for two globular clusters.

extensively observed photoelectrically. The form of the arrays has been de­termined from all observed stars but only representative photoelectric re­sults are shown ; the photoelectric observations for stars fainter than Mv = +4In have been smoothed with photographic plates. The moduli used (95, 96) are m - M = 14'!'3 and 14'!'7 for MS and M 13, respectively ; and the values of B - V corrected for the blanketing effect, determined from the observed values of o( U-B), are used : C= (B- V) +d(B - V) . Figure 19 shows the (Mv, B - V) relation for members of three groups of high velocity stars (75) near the Sun : the Groombridge 1830 group, which contains RR Lyr ; Kap-

.. 2

...

+.6

+ a

.. 10

I . 0 ___

SU orl. � LYR

/ 1104 5 /. HYAQES • KAPTEYN'S * G P. o GROOM 1830GP.

)( QJ,VKI60,-32Ct Gp.

o lB-v) +0-4

o

+e>e I

+1·2

FIG. 19. (Mv,B- V) diagram for some high velocity groups.

I • .

+1·6

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION " 2 6 7

teyn's star group, which contains S U Dra; and a group with ( U, V) "'( - 160, - 320) . The mean values of 5( U -B) for the F- and G-type subdwarfs in these groups are +Cf.'21, +0':'20, and +Cf.'23 for Kapteyn's star, Groombridge 1830, and the anonymous group, respectively ; and the value of AS (97) , which measures the spectral type difference between the hydrogen and Ca I I (K) lines near minimum phase, is 6 for both of the variables.

The moduli of globular clusters are obtained from the assumption that the corrections to the observed values of B - V, based on the observed values of 5( U -B) , place the colours on the same temperature scale as that represented by the observed colours of Hyades main sequence stars (Table I ) . However, as already discussed, the luminosity corresponding to the corrected colours of main sequence stars depends on the chemical composition. There are two reasons for believing that the main sequence in the (Mbol, log T.) plane of globular clusters and of the Hyades cluster are nearly the same : (a) the sub­dwarfs, which are believed to be the same as the main sequence stars in globular clusters, lie, in the mean, within 0':' 1 or 0':'2 of the Hyades main se­quence when the observed values of B - V of those with trigonometric paral­laxes are corrected for the blanketing effects (98) ; and (b) field RR Lyr vari­ables, with periods similar to those in globular clusters, indicate a mean value of Mv = +Cf.'5 (98) , whereas the mean value of 4 globular clusters is +0':'4 (96) and from two high velocity groups it is +0�6. The amount of variation in the mean luminosity of the variables from cluster to cluster may be cor­related with the variation in metal abundance and therefore with the ultra­violet excess, 5( U -B) . However, available stellar models do not match the observed colour-luminosity arrays in many particulars, and a range of models with variations in the chemical composition is necessary before the observa­tions can be interpreted in detail. Also, the theory by which the observed values of 5( U-B) are converted to corrections in (B - V) is for main se­quence stars, where the observational difficulties in globular clusters are very great. A similar theory for giant and subgiant stars, which can be observed with some accuracy for a large variety of globular clusters, would be ex­tremely useful but difficult to formulate because the luminosity (i.e. the sur­face gravity) would have to be included as an additional parameter. How­ever, a solution to the problem may lie in the fact that the available data (100) indicate that the influence of the surface gravity is cancelled out near a colour of +0':'9.

The stars in Figure 18 and 19 are associated with the galactic halo. The colour-luminosity arrays of some clusters and groups in the galactic disk indicate that the difference in age between them and the globular clusters is not large. Figure 20 gives the array for stars in the region of M67 (100) whose proper motion (101) indicates cluster membership. Two groups, the 61 Cygni group and the 1] Cephei group (102), show almost identical arrays. The values of /l( U -B)� +0':'06 for these clusters and groups are considerably smaller than those for globular cluster stars ; the shapes of the subgiant, giant, and horizontal branches are also different. This is shown in Figure 2 1 where

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268 EGGEN

MV 0 •

•• •

• • +2 ,.

•• . .. .

t4

+6 M 67 • •

• •

f8 I . I

C 0 +0 4 +0 8 +1 2

FIG. 20. Colour-luminosity array for M67.

the schematic array for NGC 188 (103) , a cluster similar to M67, is com­

pared with the arrays for 47 Tue (104) and M 13. Also in Figure 21 are the individual members of the ()" Puppis group (76) , which consists of stars within

about 300 parsecs of the Sun. The shape of the subgiant branch is intermedi­

ate between those of 47 Tue and NGC 188, but the breakaway point from the main sequence occurs at a fainter level, near My = +4'!'6. The short-period group variable DY Peg (P =0�07) lies at My = + 1'?5 : the long-period red

variable R Hor (P = 400d) , at My = 0"' •

o

+2 o

+6

+8

c

. ,

o x

OVt P£G

a PUP GROUP

o I ..

+0'4

o

+0'8

• , I � _

'!\� ,. - -

, R HOR

1 _ " '.

FIG. 21. The colour-luminosity array for the u Puppis group, and schematic arrays for some old clusters.

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OBSERVATIONAL ASPECTS OF STELLAR EVOLUTION 2 69

The run of the magnitude differences !1 V between the giant branch, read at (B - V)o = + 1�4 and the horizontal branch ( 105), and the values of ( U- B)o, read at (B - V) o = +0'!'9 on the subgiant branches, is as follows (Table XX) .

TABLE XX

Il V ( U-B )o

M 1 3 2':'6 +0':'41 M 5 2 .6 47 Tue 1 .8 +0.46 (T Pup 1.5 +0.5 2 M67 1 .6 +0. 6 0 Hyades +0.64

There are evolved stars near the Sun still fainter than the subgiants in the (]' Puppis group (76) . Two well documented examples are 0 Pav and H D 169822 ; the latter star forms a widely separated pair with HD 169889. The trigonometric determinations of the parallax of 0 Pav, for which V = 3�55 and c = +0�74, are 0 � 1 7 1 Y and 0� 167 C, giving My = +4�7 and placing it 0�7 above the Hyades main sequence and redder than the break-away point of the main sequence in the (]' Puppis group. HD 169882 and 169889, both of which indicate a value of O (U-B)�+0':'06, have V = 7':'85 and 8':'3 1 and c = +0':'77 and +0�82, respectively. Fitting the fainter component to the Hyades main sequence gives My = +4':'7 for HD 169882, and places the primary 1'!'1 above the Hyades main sequence.

Until stellar models with a wide range of chemical composition become available, the ages of the clusters and groups shown in Figure 18-2 1 cannot be estimated with high accuracy. Sandage (95) and DeMarque & Larson (26) find an age of NGC 188 near 10 X 109 years if (X, Z) = (0.67, 0.03) or 1 2 X 109 years if (X, Z) = (0.76, 0.01) . The globular clusters, such as M3, give 17 or 10 X 109 years, depending on whether (X, Z) = (0.99, 0.01) or (0.75, 0,01) . A determination of hydrogen abundances in the disk and halo clusters is obvi­ously of the greatest importance. Observation of the planetary nebula in the globular cluster MIS gives X/ Y = 0.72 ; O'Dell et al. ( 106) argue that the helium may have been fairly abundant when stars as old as the globular clus­ters were formed. Information concerning the masses of subdwarfs could con­tribute to this question but, unfortunately, the number of close binaries among subdwarfs is low and those that are known have been insufficiently observed. The best documented example is ADS 16644 AB (87) which con­sists of two subdwarfs, o( U - B) = +0'!'21 , of nearly equal magnitude. The available observations indicate a period of 100 years with an apparent semi­axis major of 0�4S. The photometric parallax, obtained from the observed colour, corrected for line-blanketing effects, is 0'�016 giving My = +4'!'9 and a mass of 1 0 , making the mean component nearly identical with the Sun. The

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2 70 EGGEN

equations of stellar interiors give L ",Z-lX-4m5 for the dependence of the mass-luminosity relation on the chemical composition ; and, since (X!Z) * �1!30 (X!Z) 0 for ADS 16644 (107), X0 ",0.6X., or X. ",1 .

The brightest stars observed photoelectrically in the clusters M 13 ( 108), M5 (93) , and M3 (109), for which accurate moduli are available (93, 96) , are shown in Figure 22 together with the median luminosities and colours of the Cepheids with periods greater than one day; the photometry of the variables (1 10) has been corrected to the (B, V) system. Also, the bright stars in w Cen, whose luminosities have been obtained from the modulus m - M = 13':'8 and E(B - V) = +O'!' l l ( 111) , are shown in the figure ; only stars for which radial velocity and proper motion data indicate membership, and variables away from the crowded cluster centre, are included. I n addition to the horizontal branch, which includes the RR Lyr "gap," there are two blue, nonvariable stars in w Cen which proper motion and radial velocity prove to be cluster members with (Mv, B - V) = ( -3,!,0, +0':'28) and ( - 1':'1, 1':'10) ; similar stars, which are members of M3 and M 13 (112), respectively, occur at ( - 0'!'4, -0'!'27) and ( - 1'!'4, -0'!'10) . All of the stars in Figure 22 with (B - V) > + 1':'4 ate probably variable with a range near 0':'5 in the visual magnitude.

An outstanding problem concerning the evolution of the stars in Figure 22-all of which probably have masses near 1 0 less whatever mass loss may have taken place prior to their arrival in this portion of the colour-luminosity array-is whether it is from right-to-left or left-to-right in the figure. Modern theories mainly agree that the main sequence stars of near solar mass have evolved, with growing helium cores, up through the subgiant sequence to the region of the reddest stars, (B - V)O > + 1 ':'3, in Figure 22. Does the star then move back to the left side of the figure along the horizontal branch, which asymptotically approaches the red giant region, and through the vari­able star gap to the region of the blue, horizontal branch stars; or does it im­mediately jump back, after the helium flash, to the blue side of the variable star gap and then work its way back to the red side, again approaching the

-2

o

+ 2

)(

"'----_ 1 I o

I I + 0· ..

I I + 0· 8

ween

+ 1'2

o • X + A

FIG. 22. The colour-luminosity array for the brightest stars in globular clusters.

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red giant region? When accurate models are available it may be possible to choose between these alternatives on the basis of the relative populations at various intervals of colour in Figure 22 ; now, partly because of the difficulty in several clusters of eliminating foreground F- and G-type dwarfs, it can only be said that most globular clusters have a heavy concentration of stars on the blue side of the variable star gap and show a large variation in the density on the red side. with this variation being only loosely, if at all, cor­related with the number of type of RR Lyr variables present. The few cases like 47 Tuc, that apparently do not have a high density of stars on the blue side of the variable star gap, contain relatively low luminosity red giants and few, if any, short-period variables. Accurate photometry and membership criteria of many more stars brighter than Mv ='+ 1m in globular clusters are also necessary before such density distributions in the colour-luminosity array can be used as a test of evolutionary theories. This is particularly true of the few blue stars brighter than about Mv = om, which may be progenitors (or descendants) of the variables with periods longer than one day. If the hori­zontal branch stars, and short-period variables, represent evolutionary tracks of helium-burning stars, it is possible that the few, brighter blue stars and the longer-period Cepheids represent subsequent tracks, each at a greater luminosity than the previous one, for a few stars that for some reason needed more than one helium-burning stage to reach the carbon-burning phase of their evolution. The CH features are absent from the available spectra of the longer-period Cepheids in globular clusters ( 1 13) although at least one field variable of the W Vir type, RU Cam (P = 22d) , is an R-type star at minimum light. Harding (1 14) has found that the reddest member of w Cen shown in Figure 22 is a CH star. The luminosity and colours, com­pared to those of von Zeipel No. 1397 in M3 (1 12) , are as follows (Table XXI) :

TABLE XXI

(B- V)o ( U-B)o M. Spectral type

w Cen +1':'57 + 1':'08 -2':'65 CH M 3 +1.56 + 1.63 -2.7 5 KO Ib

Taken at face value, the colour indicates a large blanketing by the CH bands, and the B - V colour may need a large correction.

In connection with the variable stars in Figure 22 it should be noted that although the RR Lyr variables in the general field with periods in the same range as those in globular clusters have space motions very similar to those of the clusters and of field subdwarfs, the field W Vir stars, which are usually identified with the longer-period variables in Figure 22, are not extremely high velocity stars and have space motions considerably smaller than the field RR Lvr variables and subdwarfs.

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4. Johnson, H. L., and lriarte, B., Lowell Obs. Bull. No. 91 (1958)

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6. Stromgren, B., Rev. Mod. Phys., 36, 532 (1964)

7. Chubb, T. A., and Byram, E. T., Astrophys. J., 138, 6 1 7 (1963)

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2 1 . Allen, C. W. , Observatory, 70, 154 (1950)

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27. Eggen, O. J., Astron. J., 70 (Jan. 1965, in press)

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(1955) 32. Petrie, R. M . , Astron. J., 65, 55 (1960) 33. McNamara, D. H., Narrow Band

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34. Iben, 1., Astrophys. J., 138, 452 (1963) 35. Eggen, O. J., Observatory (In press) 36. Gaustad , J. E., Astrophys. J., 139, 407

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(1964) 38. Wallerstein, G., Astrophys. J. Suppl.,

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