Microscopic diffusion is a basic phenomenon, but, in the physical conditions of stellar interiors the small diffusion velocities imply long time scales to obtain significant modifications on the global parameters of real stars. To be efficient, the medium has to be quiet enough, so that large scale motion cannot prevent the settling. Acting essentially in radiative zones, it is now being advocated to explain a variety of observed facts, as lithium abundances in young and old population (Vauclair & Charbonnel 1998), abundances anomalies in different classes of young stars (Hui Bon Hao & Alecian 1998 and references herein), globular cluster evolution and age determination (Chaboyer et al. 1992). In the Sun, the insertion of microscopic diffusion in the modeling improves significantly the agreement between the theoretical and the "seismic" model (see e.g. Christensen-Dalsgaard et al. 1996; Richard et al. 1996; Morel et al. 1997; Brun et al. 1998). In the present state of art the computed sound speed, beneath the solar convection zone, agrees within a rms discrepancy better than 0.2% (Gough et al. 1996); the predicted values of the radius at the bottom of the convection zone and the helium abundance at the solar surface agree within the error bar with their values inferred from helioseismology (see e.g. Basu 1997).
Subdwarfs represent a clue in the general framework of stellar evolution in particular to estimate the globular clusters ages. A precise knowledge of their internal structure and of the stage of evolution is then badly needed.
As in such old objects the evolutionary time scale becomes of the same order as the diffusion one, significant effects due to this physical process are expected on their global properties.
Several papers have already mentioned the influence of microscopic diffusion in old objects (see e.g. Chaboyer et al. 1992; Mazitelli et al. 1995; Castellani et al. 1997), but focussed generally on the consequences on the age of the oldest globular clusters.
Up to now, the poor quality of the observed parameters of population II objects did not allow to refine their theory. The recent distance determinations of subdwarfs by HIPPARCOS (Perryman et al. 1997) has revolutionized the field. Combining these results with large improvement of effective temperature and bolometric corrections for low metal atmospheres (Alonso et al. 1996), a reasonable set of subdwarfs have been located very precisely in the HR diagram. A detailed comparison with evolutionary models is now possible and requires the same precision in the description of the physics of their interiors.
It has been recently emphasized that difficulties arise when trying to fit observed and computed main-sequences, as models look hotter than the real objects (Baglin 1997; Lebreton et al. 1997; Cayrel et al. 1997; Lebreton et al. 1998).
Several effects can been advocated to explain this discrepancy, as for instance, the treatment of the superadiabatic outer layers or observational bias due to NLTE effects, in the effective temperature scale and in the abundance determinations (Thevenin & Idiart 1999).
We propose in this paper to document the role of microscopic diffusion in these stages of evolution, and to quantify its influence on the global parameters of these stars and on their position in the HR diagram.
It is well known that, on the main-sequence, variations of helium Y and of the metal content Z act in opposite directions: while decreasing Y reduces the effective temperature and the luminosity L, a decrease of the metal content increases both L and . Microscopic diffusion, which acts on both Y and Z, creates a stratification of chemicals in radiative zones. The global effects on the observables i.e. the modification of the HR diagram position, but also the changes of the surface metal abundance, are quite subtle; they have to be taken into account altogether to perform a precise comparison with observations.
The paper is organized as follows: the set of stellar models is listed in Sect. 2, whereas the input physics is described in Sect. 3. The effects of microscopic diffusion on the evolution of subdwarfs are presented in Sect. 4, the "calibration" procedure needed when comparing theoretical predictions and observations is developped in Sect. 5, whereas the influence on the HR diagram and on the shape of the isochrones as a function of their present observed metal content is described in Sect. 6. Future prospects and possible tests of this hypothesis are suggested in Sect. 7.
© European Southern Observatory (ESO) 1999
Online publication: April 12, 1999