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Astron. Astrophys. 350, 587-597 (1999)

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2. Present status of helium content and mixing-length parameter determinations

Since observations do not provide direct determinations of helium, assumptions have to be made for the initial helium content of models of low-mass stars. Very often it is supposed that the metallicity Z and helium Y are related through a constant [FORMULA]-value.

[FORMULA] = (Y - [FORMULA])/Z is often determined from the results of the solar calibration and for any other star of known metallicity, the helium abundance is scaled on the solar one. In addition of the behaviour of Y with Z, another problem is the universality of the [FORMULA] ratio of the mixing length over the pressure scale-height in the mixing-length treatment of the convection. We now briefly review the various determinations of these parameters, in the closest stars and various astrophysical sites.

2.1. Nearby stars

Perrin et al. (1977) were the first to examine the HR diagram of a selected sample of the nearest low-mass stars. Because in 1977 the error bars in the HR diagram were quite large, Perrin et al. (1977) suggested that all the non-evolved stars were sitting on the same ZAMS, whatever their metallicity was. They showed that this behaviour was reproduced by theoretical stellar models if helium and metallicity were related through a value of [FORMULA] constant and equal to 5. Recently Fernandes et al. (1996) claimed that stars do not all lie on the same ZAMS and measured the observational lower main sequence width in the solar neighbourhood. They showed that if the width is entirely due to chemical composition dispersion in the solar neighbourhood, then [FORMULA] is greater than 2 in the corresponding stars.

More recently Hog et al. (1997) and Pagel & Portinari (1998) have found [FORMULA]= 3 [FORMULA] 2 from a sample of nearby stars with Hipparcos parallaxes.

We recall further constraints on these points.

2.1.1. The Sun

The Sun is a milestone in internal structure theory, because its age and fundamental parameters are known with great accuracy, and helioseismology (Pérez Hernández & Christensen-Dalsgaard 1994) has brought additional constraints. All observations have to be reproduced by the theoretical solar model, with underlying input physics and free parameters. The initial helium abundance is a free parameter of the solar model and is estimated with the luminosity constraint (Christensen-Dalsgaard 1982). The difference between the present helium value derived from seismology(Y[FORMULA] 0.25) and the initial value obtained from calibration (Y [FORMULA] 0.275) provides a constraint on the input physics of the model: it can be explained by invoking the microscopic diffusion of helium and heavy elements which has taken place during the evolution of the Sun (see e.g. Cox et al. 1989, Richard et al. 1996, Brun et al. 1998). Furthermore the mixing-length parameter, which enters the mixing-length phenomenology of convection is fixed by the radius constraint at a value [FORMULA] 1.7-1.8.

2.1.2. Binary stars and clusters

The study of a few visual binary systems of known mass, effective temperature, luminosity and metallicity provides further information on low mass stars. The two components of a binary system, which are assumed to have the same age and initial chemical composition, can be modelled simultaneously providing the age of the system, its initial helium content and the mixing-length ratio (Noels et al. 1991). The method was first applied to the [FORMULA] Centauri system by Noels et al. (1991). Recently, Fernandes et al. (1998) studied four Population I low mass binary systems with high quality data and determined the initial helium abundance by mass for three of them with a precision of 0.02. A global conclusion of these papers is that the mixing-length parameter [FORMULA] seems independent of metallicity, and that a [FORMULA] ratio of 2.3 [FORMULA] is appropriate (their Fig. 5).

Using the high quality observations of Hipparcos together with ground-based spectroscopic data, Perryman et al. (1998) and Lebreton et al. (1997) determined the helium abundance by mass, Y, of the Hyades with a precision of 0.02. This abundance does not follow the overabundance of the metallicity (+.15 dex). This suggests that a scatter does exist on the [FORMULA] ratio. This paper also confirms the universality of the [FORMULA] parameter.

2.2. Extragalactic observations

The studies mentioned above have provided the initial helium content of a few stars of known metallicity which allows to calculate their helium to metal enrichment ratio [FORMULA] = (Y - [FORMULA])/Z. The primordial helium abundance [FORMULA] has been determined by several groups: for instance, Balbes et al. (1993) gave [FORMULA]=0.227[FORMULA]0.006 while, more recently, Izotov et al. (1997) found a higher value [FORMULA]=0.243[FORMULA]0.003. However, Hogan et al. (1997) consider this value as an upper limit. This gives two secure points of the Y(Z) relationship: [FORMULA] at [FORMULA], and [FORMULA] at [FORMULA]. The observations of blue compact galaxies and other systems have allowed to determine a [FORMULA] ratio: a recent discussion is given by Thuan & Izotov (1998). The value is 2.3 [FORMULA] 1.0, considerably below former determinations [FORMULA].

2.3. Nucleosynthesis

On the other hand nucleosynthetic predictions integrated over the whole stellar mass range lead to [FORMULA]-values ranging from about 1 to about 2 depending on the inclusion of stellar winds; [FORMULA] can even reach values of about 5 if black holes are considered (Maeder 1992). Although helium is expected to increase with metallicity, it must be noted that metals are only produced by SNe, whereas helium is also produced by mass-loss of medium-mass stars, in their post-AGB phase.

This body of results indicates that a significant dispersion of the helium abundance around the solar-scaled value cannot be excluded.

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© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999