sign in sign up
<<
Home , Main sequence

379

THE H-R DIAGRAM FOR LATE-TYPE NEARBY

AS A FUNCTION OF CONTENT AND

1 2 3 2 1 1

Y. Lebreton , M.-N. Perrin ,J.Fernandes ,R.Cayrel ,G.Cayrel de Strob el , A. Baglin

1

Observatoire de Paris, Place J. Janssen - 92195 Meudon Cedex, France

2

Observatoire de Paris, 61 Avenue de l'Observatoire - 75014 Paris, France

3

Observat orio Astron omico da Universidade de Coimbra, 3040 Coimbra, Portugal

Key words: : solar neighb ourho o d; stars: ABSTRACT

abundances; stars: low-; stars: HR diagram;

Galaxy: abundances.

Recent theoretical stellar mo dels are used to discuss

the helium abundance of a numberoflow-mass stars

for which the p osition in the Hertzsprung-Russell di-

1. INTRODUCTION

agram and the metallicity are known with high accu-

racy.

The knowledge of the initial helium abundance of

Hipparcos has provided very high quality

stars b orn in di erent sites with di erent

of a sample of a hundred disk stars, of typeFtoK,lo-

is of great imp ortance for many astrophysical stud-

cated in the solar neighb ourho o d. Among these stars

ies. The lifetime of a and its internal structure

we have carefully selected those for which detailed

very much dep end on its initial helium content and

sp ectroscopic analysis has provided e ective temp er-

this has imp ortant consequences not only for stellar

ature and [Fe/H] ratio with a high accuracy.

astrophysics but also in cosmology or in studies of

the chemical evolution of .

Wehave calculated evolved stellar mo dels and their

Direct measurement of the helium abundance in the

asso ciated iso chrones in a large range of mass, for

of a low mass star cannot b e made since

several values of the metallicity and of the helium

there are no helium lines in the sp ectra. In a few

abundance and we to ok into account an -element

ob jects the helium abundance can be determined

enrichment in the metal-de cient stars. The input

by means of theoretical stellar mo dels. In the

physics is recent and appropriate to the considered

the initial helium abundance can b e drawn from the

range.

careful calibration of the solar mo del, which with

given input physics, has to yield at solar age the ob-

We discuss the p osition in the H-R diagram of those

served and radius which enforces its ini-

stars which can b e considered as non-evolved. Once

tial helium abundance Christensen-Dalsgaard 1982.

the physics of the mo dels has b een xed, this p osition

Moreover the present helium abundance in the con-

only dep ends on metallicity and helium abundance.

vection zone of the Sun can b e determined from he-

lioseismological measurements P erez Hern andez &

We nd that the thickness of the observational main

Christensen-Dalsgaard 1994. This value is di erent

sequence is of ab out 0.25 , for stars span-

from the one obtained by calibration which can be

ning a metallicity range from [Fe/H] = 1to+0:2,

explained byinvoking transp ort pro cesses at work in

while theoretical stellar mo dels predict a width of

the solar zone Cox et al. 1989.

ab out 0.45 magnitude.

Stellar mo dels can also b e used to determine the ini-

The p osition in the H-R diagram of stars of solar

tial helium abundance of stars of known

metallicity or close to it is well accounted for by

mass and metallicity. The metho d is similar to that

theoretical stellar mo dels. Problems arise with the

used for the Sun; mo dels have to satisfy the con-

mo derately metal de cient stars which lie quite close

straints on luminosity and e ective temp erature for

to the stars of solar metallicity and very far from

the two stars of the system which are assumed to

the theoretical iso chrones corresp onding to their ex-

have same age, metallicity and initial helium content

p ected chemical comp osition. To reconcile theory

No els et al. 1991.

and observations very lowvalues of the helium abun-

dance, well b elow the primordial helium abundance,

In single low-mass stars, neither the mass, nor the

would b e needed. We brie y discuss the p ossible rea-

age are known. For a few stars the [Fe/H] ratio

sons of this discrepancy: improvements to bring to

is measured. To mo del these stars an assumption

the physics of the mo dels, inaccuracies of observa-

has to be made on the value of the initial helium

tions.

content. Very often it is supp osed that the metal-

licity Z and helium Y in mass fraction are related

380

by the so-called helium to metal enrichment ratio 2. OBSERVATIONAL MATERIAL

Y=Z =Y Y =Z, where Y is the primordial

p p

helium abundance and Y=Z is constant from star

to star.

We study an homogeneous sample of late-typ e nearby

stars which has b een carefully selected by M.-N. Per-

rin. These stars are closer than ab out 25 parsecs

However the assumption that Y=Z is a `univer-

which ensures an excellent accuracy of their

sal' constant can be questioned. Many attempts

determination by Hipparcos. Moreover these stars

have b een made to estimate Y=Z. Investigations

are among those which were b est studied from the

in di erent sites of observations as well as theoreti-

ground: they all have b een submitted to photometric

cal nucleosynthesis predictions have b een made and

measurements and to detailed sp ectroscopic analysis.

were reviewed byFernandes et al. 1996. Values of

Y=Z from 2. to 6. were found. A simultaneous

Among the 114 stars selected there are 38 stars which

increase of helium and metallicity is always found but

are very well known and which are not susp ected

with large variations of Y=Z.

to be unresolved binaries. Their parallax has b een

determined by Hipparcos with an accuracy b etter

Y=Z can also be calculated from the metallici-

than 5 p er cent. Their b olometric ux has b een de-

ties and helium contents found in the Sun and in

rived by Alonso et al. 1995 with an accuracy of

the few binary stars which can be calibrated. The

ab out 3 p er centbyintegrating UBVRIJHK photom-

recent work by Fernandes et al. 1997 shows that

etry. This provides the b olometric magnitude with no

Y=Z is of ab out 3:0, slightly dep ending on the

need of b olometric corrections M < 0:03 magni-

bol

input physics of the theoretical stellar mo dels. Le-

tude. The e ective temp erature has b een obtained

breton et al. 1997 used similar theoretical stellar

by Alonso et al. 1996 from the b olometric ux and

mo dels to calibrate simultaneously the Sun and the

using a grid of theoretical mo del line-blanketed ux

lower main sequence of the Hyades and found that

distributions Kurucz 1991. The resulting accuracy

Y=Z is higher in the Sun than in the Hyades

on e ective temp erature is of ab out 1.5 p er cent. The

although the metal content [Fe/H] is higher in the

metal content[Fe/H] has b een obtained through de-

Hyades.

tailed sp ectroscopic analysis Cayrel de Strob el et al.

1997, the mean error on [Fe/H] b eing of the order of

The solar neighb ourho o d is a very interesting site

0.1 dex.

to study the relationship b etween helium and metal-

licity: it is constituted of the nearest stars which

have b een thoroughly observed. Perrin et al. 1977

rst studied the HR diagram of a selected sample of

3. THEORETICAL MODELS

the nearest low-mass stars and found that Y=Z

is constant and equal to 5.0 in the solar neighb our-

hood. Recently Fernandes et al. 1996 measured the

The calculations have b een com-

observational lower main sequence width in the solar

puted with the CESAM co de Morel 1997 in which

neighb ourho o d. They estimated the asso ciated value

wehave included appropriate input physics. In the

of Y=Z using theoretical stellar mo dels. They

range of mass considered the CEFF equation of state

found that if the observed width is entirely due to

Eggleton et al. 1973, Christensen-Dalsgaard 1991,

achemical comp osition disp ersion in the solar neigh-

which includes Coulomb corrections to the pressure

b ourho o d then anyvalue of Y=Z greater than 2.0

is appropriate. We use the Caughlan & Fowler 1988

could account for this width.

nuclear reaction rates. To determine the initial com-

p osition we used either the Grevesse & No els 1993

Our purp ose here is to go further in that study us-

solar mixture GN93 mixture or a GN93 mixture

ing the recent results of the Hipparcos mission. It

where the -elements O, Mg, Si, S, K, Ca, Ti are

is now p ossible to work on a very well de ned sam-

enriched relative to the Sun [ /Fe] = +0.4 dex. An

ple constituted of stars of the solar neighb ourho o d.

enrichment of -elements is observed in metal de -

This sample was selected by M.-N. Perrin and then

cient stars with metallicities [Fe/H] lower than 0:5

by A. Baglin et al. Hipparcos Prop osals 132, 1982

Wheeler et al. 1989.

and INCA011, 1992. The sample is comp osed of

ab out 100 late-typ e nearby dwarfs of sp ectral typ e

We used the most recent OPAL opacities Iglesias

from F to late K. The lo cation of those stars in the

& Rogers 1996 complemented at low temp eratures

HR diagram is known with high accuracy: the Hip-

T  10000 K by atomic and molecular opacities

parcos satellite has provided their parallaxes and high

from Alexander & Fergusson 1994 for the GN93

resolution sp ectroscopy has given their e ective tem-

mixture or from Kurucz 1991 for the -enriched

p eratures and metallicities.

mixture. We use the Eddington's T   law to de-

scrib e the atmosphere after a comparaison with the

In this very preliminary work, we compare observa-

ATLAS9 mo dels Kurucz 1991 and the mixing-

tions to stellar mo dels calculated with appropriate

length theory of Bohm-Vitense 1958 to describ e

up dated input physics to draw information on the

convection. With the input physics describ ed ab ove

helium content and on the eventual relationship b e-

the calibration in luminosity and radius of a solar

tween helium and metallicity in those stars.

mo del having Z/X = 0.0244 where X is the

abundance by mass Grevesse & No els 1993 requires

a mixing-length ` =1:64 H , an initial helium abun-

In Section 1 we describ e the observational sample and

p

dance Y = 0.266 and a metallicityZ = 0.0175. We

fo cus on the high accuracy of the observational data.

adopt the solar mixing-length value in all our calcu-

In Section 2, mo dels relevant for the interpretation

lations in accordance with results of Fernandes et al.

of the observations are describ ed. The results are

1997.

presented and discussed in Section 3.

381

Figure1. The Hipparcos Hertzsprung-Russel l diagram of nearby stars.

on the left of the H-R diagram has b een calculated We calculated several grids of evolutionary mo dels

with the lowest metallicityvalue [Fe/H] = 1.0 and and asso ciated iso chrones. The mass range covers

an helium abundance close to the primordial value from 0:5to5:0 M . We considered di erent

and it corresp onds to an -elements enriched mix- metallicities corresp onding to the observational range

ture. The iso chrone lo cated on the right has b een [Fe/H] in the interval -1.0 to 0.5. The metallicityZ

obtained with mo dels of solar metallicity and solar in mass fraction is related to [Fe/H] by the relation

helium abundance. We also plotted on Figure 1 a [Fe=H] = logZ=X logZ=X . In these mo dels the

metal enriched zero age main sequence Z = 0.03 cor-

helium abundance is derived from the metallicity Z

resp onding to [Fe/H] = +0.25.

using the Y=Z relationship and the solar value

of Y=Z. Two distinct grids of mo dels were cal-

If we rst consider the whole sample fo cusing at the

culated in the metal de cient cases [Fe=H] = 0:5

non-evolved stars i.e. those whichhave an e ective

and 1:0: a grid with normal solar mixture and a

temp erature lower than ab out 3.74 it is clear that

grid with an -elements enrichment of 0.4 dex. In

the available space b etween the two extreme theoret-

order to obtain the sensitivity of zero-age main se-

ical iso chrones corresp onding to the observed metal-

quence lo cation with chemical comp osition we also

licityinterval is not lled. On the contrary the stars

calculated non-evolved mo dels of masses from 0:5to

have a tendancy to gather close to the solar iso chrone

1:4 M for 8 values of Z ranging from 0.004 to 0.06

even when their metallicity is quite low. The thick-

and6values of Y ranging from 0.18 to 0.43, therefore

ness of the observational main sequence, measured

corresp onding to di erentvalues of Y=Z.

on the non-evolved lower part, is of ab out 0.25 mag-

nitude while the theoretical thickness is of 0.45 mag-

nitude.

4. RESULTS AND DISCUSSION

It is also worth to note that the slop e of the theoret-

ical main sequence agrees very well with the obser-

We present in Figure 1 the Hertzsprung-Russell di-

vational slop e. This is in favour of the unicityofthe

agram of the 38 stars of the selected sample which

mixing-length parameter in low-mass stars.

have an observed metallicity[Fe/H] b etween -1.0 and

If we examine the stars whichhave a solar metallicity

+0.20 and a very accurate parallax  =  0.050.



or close to it 0:20 < [Fe=H] < 0:20 and the very

We have sup erimp osed on that diagram two `ex-

mo derately de cient stars 0:45 < [Fe=H] < 0:20

treme' theoretical iso chrones. The iso chrone lo cated

382

it app ears that theoretical mo dels t the observations ACKNOWLEDGMENTS

satisfactorily. Each star can b e placed on a theoret-

ical ZAMS corresp onding to its metallicity and to a

JF is supp orted by JNICT BPD/9919/96. This

Yvalue di erent from the solar one but not smaller

work was partially supp orted by the France-Portugal

than the primordial helium abundance Y ' 0:23.

co-op eration pro ject 059-B0.

On the other hand no agreement can be found for

stars with metal de ciencies in the range 1:05 <

[Fe=H] < 0:45. These stars cannot be placed on

REFERENCES

a theoretical iso chrone corresp onding to their metal-

licity unless the helium abundance is decreased to

Alexander, D.R., Fergusson J.W. 1994, ApJ, 437, 879

an unacceptable value Y ' 0:10 very much smaller

Alonso, A., Arribas, S., Mart nez-Roger, C. 1995,

than the primordial helium abundance.

A&A, 297, 197

Alonso, A., Arribas, S., Mart nez-Roger, C. 1996,

To solve the problem related to the metal de cient

A&AS, 227, 254

stars one has to question the validity of the theoreti-

cal stellar mo dels as well as the accuracy of observa-

Bohm-Vitense, E. 1958, Z. Astrophys., 54, 114

tions. The p osition of the theoretical ZAMS would

Caughlan, G.R., Fowler, W.A. 1988, Atomic Data

have to be shifted either rightwards by an amount

Nuc. Data Tables, 40, 284

of ab out 250 K or upwards by an amount of ab out

Cayrel, R., Lebreton, Y., Perrin M.-N. et al. 1997,

0.2 magnitude to b e in agreement with observations.

this symp osium

The e ect of the chemical mixture used for the cal-

culations has already b een taken into account: we

Cayrel de Strob el, G., Soubiran, C., Friel, E.D.,

found that changing the metal mixture from a solar

Ralite, N., Francois, P. 1997, A&AS, 124, 1

mixture to an -enriched mixture with [ /Fe] = +0.4

Christensen-Dalsgaard, J. 1982, MNRAS, 199, 735

dex shifts the ZAMS in the rightwayby an amount

Christensen-Dalsgaard, J. 1991,in `Challenges to the-

of ab out 120 K for [Fe/H] = 0.5 and only 50 K for

ories of the structure of mo derate-mass stars',

[Fe/H] = 1.0. Nothing more can b e exp ected since

Gough D.O. & To omre J. eds., Springer-Verlag,

[ /Fe] = +0.4 dex app ears to b e an upp er observa-

11

tional limit Wheeler et al. 1989 and the e ects of

the -elements enrichment on the mo dels decreases

Cox, A.N., Guzik, J.A., Kidman, R.B. 1989, ApJ,

as [Fe/H] decreases. We examined the e ects of a

342, 1187

change of the mixing-length parameter and found

Eggleton P.P., Faulkner J., Flannery B.P. 1973,

that decreasing from the solar value 1.64 to 1.2

A&A, 23, 325

pro duces a change of 70 K only. We also lo oked at

Fernandes, J., Lebreton, Y., Baglin, A. 1996, A&A,

the e ects of a change in the atmosphere mo del us-

311, 127

ing the sophisticated ATLAS 9 mo dels Kurucz 1991

instead of the usual grey atmosphere but we did not

Fernandes, J., Lebreton, Y., Baglin, A., Morel, P.J.

nd a di erence of more than ab out 30 K.

1997, A&A to b e submitted

Grevesse, N., No els, A. 1993, in `Origin and Evolu-

Among the pro cesses that are neglected in standard

tion of the Elements', Prantzos N., Vangioni-Flam

stellar evolution theory, microscopic di usion of he-

E., Cass e M. eds., CUP

lium and heavy elements in the stars during their

Iglesias, C.A., Rogers, F.J. 1996, ApJ, 464, 943

evolution could play a role: gravitational settling is

Kurucz, R.L. 1991, in `Stellar atmospheres: Beyond

more active in metal p o or stars than in stars of solar

Classical Mo dels', NATO ASI Series C, Vol. 341,

metallicity b ecause the density at the b ottom of the

eds. L. Crivarelli, I. Hub eny, D.G. Hummer

convective zone is smaller and the mass of the convec-

tive zone is also smaller so that it is easier to mo dify

Lebreton, Y., G omez, A.E., Mermillio d, J.C. et al.

the surface abundances. These stars are exp ected to

1997, this Symp osium

have ages of ab out 9 Gyr exp ected age of the galac-

Lebreton, Y., Charb onnel, C., Cayrel, R., Vauclair,

tic disk so that di usion could have b een ecient

S., Fernandes, J., Perrin, M.-N. 1997, A&A, in

and could have mo di ed the atmospheric abundances

preparation

which would di er from the initial abundances de-

Morel, P.J. 1997, A&A, in press

termining their structure. From the mo dels we nd

that stars with an atmospheric chemical comp osition

No els, A., Grevesse, N., Magain, P. et al. 1991, A&A,

[Fe/H] = 0.8 are lo cated on a theoretical iso chrone

247, 91

of [Fe/H] = 0.3.

P erez Hern andez, F., Christensen-Dalsgaard, J. 1994,

MNRAS, 267, 111

Work is in progress to quantify the e ects of mi-

Perrin, M.N., Hejlesen, P.M., Cayrel de Strob el, G.,

croscopic di usion in the metal de cient stars of

Cayrel, R. 1977, A&A, 54, 779

the sample. Actually there is an indication that an

Wheeler, J.C., Sneden, C., Truran, J.W. 1989,

iso chrone more metal-rich than the metallicity of -0.8

ARA&A, 27, 279

which is the atmospheric metallicity of the binary

star  Cas A not only resolves the iso chrone dis-

crepancy but also gives the right mass for  Cas A.

A detailed pap er on this sub ject is in preparation

Lebreton et al. 1997. As discussed byCayrel et al.

1997 there is also a problem for the very low metal-

licities corresp onding to sub dwarfs [Fe/H] '1:5.