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Astron. Astrophys. 355, 299-307 (2000)

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1. Introduction

Atomic diffusion is a basic physical element transport mechanism usually neglected in standard stellar models. It is driven by pressure gradients (or gravity), temperature gradients and composition gradients. Gravity and temperature gradients tend to concentrate the heavier elements toward the center of the star, while concentration gradients oppose the above processes. Overall diffusion acts very slowly in stars, with time scales of the order of [FORMULA] years, so that the only evolutionary phases where diffusion is efficient are Main Sequence (but see also Michaud et al. 1983 for a discussion about the effect of diffusion in hot Horizontal Branch stars) and the White Dwarf cooling.

The occurrence of diffusion in the Sun has been recently demonstrated by helioseismic studies (see, e.g, Christensen-Dalsgaard et al. 1993; Guenther et al. 1996). Solar models including this process can reproduce much better than standard models the solar pulsation spectrum and the helioseismic values of helium surface abundance and depth of the convective envelope. Moreover, it seems that neither turbulence nor other hydrodynamical mixing processes substantially reduce the full efficiency of element diffusion in the Sun, otherwise the helioseismic constraints could not be satisfied (Richard et al. 1996). Since the Sun is a typical Main Sequence (MS) star whose structure closely resembles the one of metal poor MS objects, it appears likely that diffusion should also occur in MS globular cluster (GC) and field Halo stars and be as efficient as in the Sun. Very recently, Lebreton et al. (1999) have shown that diffusion is necessary for reproducing the effective temperatures of Hipparcos subdwarfs in the metallicity range [FORMULA][Fe/H][FORMULA]0.3, belonging mainly to the thick disk of the Galaxy. On the other hand the occurrence of a full efficiency of this process in Halo stars is still a matter of debate, since it appears to be unable to explain the near constancy of the [FORMULA] abundances in metal-poor stars with [FORMULA] larger than [FORMULA]6000 K (see, e.g., Vauclair & Charbonnel 1998). As reviewed by Vandenberg et al. (1996), turbulent mixing below the convective zone, rotation, mass loss, have been proposed as additional processes able to partially inhibit atomic diffusion; mass loss in particular (mass loss rates at the level of [FORMULA]-[FORMULA] would be necessary to reproduce the observations) is an interesting candidate (Swenson 1995; Vauclair & Charbonnel 1995), but there are no strong observational constraints at present.

Investigations dealing with the effect of diffusion on Population II stars - and the present work goes along the same line - have generally considered a full efficiency of this process (but see also Proffitt & Michaud 1991), and their results can be regarded as an estimate of the upper limit of the effect of atomic diffusion on the Halo stars evolution (another non-conventional transport mechanism, radiative acceleration, does not appear to appreciably affect the evolutionary properties of low mass stars, at least in the range 1.1 [FORMULA] 1.3, as investigated by Turcotte et al. 1998).

Due to diffusion (see, e.g., Castellani et al. 1997; Weiss & Schlattl 1999) the stellar surface metallicity and helium content progressively decrease during the MS phase - due to their sinking below the boundary of the convective envelope -, reaching a minimum around the Turn-Off (TO) stage; then, since envelope convection deepens, a large part of the metals and helium diffused toward the center are again engulfed in the convective envelope, thus restoring the surface Z (with Z we indicate, as usual, the mass fraction of the metals) to almost the initial value and Y (helium mass fraction), after the first dredge up, to a value almost as high as for evolution without diffusion. Along the Red Giant Branch (RGB) phase diffusion is basically inefficient because of the much shorter evolutionary time scales. The net effect on the evolutionary tracks is to have the MS (for a given stellar mass and initial chemical composition) colder for fixed value of the luminosity, and a less luminous and colder TO (which is reached earlier), with respect to standard models. The reason for this behaviour is that the inward settling of helium raises the core molecular weight and the molecular weight gradient between surface and center of the star. This increases the stellar radius and the rate of energy generation in the center. The metal diffusion only partially counterbalances this effect by decreasing the opacity in the envelope and increasing the central CNO abundance.

With respect to a standard isochrone of given initial metallicity and reference TO luminosity, isochrones computed accounting for the diffusion of helium and metals give an age lower by [FORMULA]1 Gyr, if the same initial metallicity is used. As far as the RGB evolution is concerned, the location of the RGB in the Hertzsprung-Russell (HR) diagram is basically unchanged with respect to standard models, and the level of the Horizontal Branch is also almost negligibly affected (Castellani et al. 1997).

Several papers have been published about the influence of atomic diffusion in old stars (see, e.g., Proffitt & Vandenberg 1991; Chaboyer et al. 1992; D'Antona et al. 1997; Castellani et al. 1997; Cassisi et al. 1998; Castellani & Degl'Innocenti 1999), with the main goal of studying the influence on GC ages. The approach usually followed is to compute models with diffusion for a certain set of initial metallicities, and then to compare with the observational Colour-Magnitude-Diagram (CMD) of a given GC the isochrones whose initial metal content matches the spectroscopical GC one. Since the chemical composition of a GC is determined by means of observations of its RGB stars (see, e.g., Carretta & Gratton 1997), the spectroscopical GC metallicity truly reflects the initial one.

A very different situation holds for field MS subdwarfs, a point recently raised by Morel & Baglin (1999 - hereinafter MB99). The spectroscopical subdwarfs metallicity is not the original one, because diffusion along the MS decreases the envelope metallicity (and helium content). When comparing theoretical diffusive isochrones with subdwarfs, one must compute models with suitable initial chemical abundances which produce, at the subdwarf age, its observed surface metallicity. This means that subdwarfs models must be computed using a larger initial Z with respect to the observed one, the exact value depending on the star age. This occurrence has potentially very important implications for example for MS-fitting distances and subdwarfs GC ages, since it implies that the MS (and TO) of subdwarfs and GC sharing the same observational value of the metallicity are not coincident.

In this paper we present models for the MS phase of low mass metal-poor stars, accounting for atomic diffusion (Sect. 2); we have considered the full efficiency of this process, as in the Sun. We will then analyze for the first time in a consistent way the effect of diffusion on three important quantities for cosmological and Galactic evolution models, namely GC distances derived by means of the MS-fitting technique (Sect. 3), age of field subdwarfs (Sect. 4), and the helium enrichment ratio [FORMULA] estimated from the width of the local subdwarfs MS (Sect. 5). A summary follows in the final section. In view of the previously discussed possibility that the efficiency of diffusion could be somewhat reduced in Population II stars, our results may be viewed as upper limits.

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Online publication: March 17, 2000