The Hr Diagram for Late-Type Nearby Stars
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379 THE H-R DIAGRAM FOR LATE-TYPE NEARBY STARS AS A FUNCTION OF HELIUM CONTENT AND METALLICITY 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: Galaxy: solar neighb ourho o d; stars: ABSTRACT abundances; stars: low-mass; 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 parallaxes stars b orn in di erent sites with di erent metallicities 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 star 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 galaxies. 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 photosphere 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 Sun physics is recent and appropriate to the considered the initial helium abundance can b e drawn from the stellar mass 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 luminosity 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 magnitude, 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 convection 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 visual binary 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 parallax 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 stellar evolution 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.