Models for Old, Metal‐poor Stars with Enhanced α‐Element Abundances. III. Isochrones and Isochrone Population Functions

Abstract

An isochrone population function (IPF) gives the relative distribution of stars along an isochrone. IPFs contain the information needed to calculate both luminosity functions and color functions, and they provide a straightforward way of generating synthetic stellar populations. An improved algorithm for interpolating isochrones and IPFs, based on the scheme introduced by Bergbusch & VandenBerg, is described. Software has been developed to permit such interpolations for any age encompassed by an input grid of stellar evolutionary tracks. Our first application of this software is to the models presented in this series of papers for 17 [Fe/H] values between -2.31 and -0.3, with three choices of [α/Fe] at each iron abundance (specifically, 0.0, 0.3, and 0.6). (These models do not treat gravitational settling or radiative acceleration processes, but otherwise they are based on up-to-date physics. Additional grids will be added to this database as they are completed.) The computer programs (written in FORTRAN 77) and the grids of evolutionary tracks that are presently available for processing by these codes into isochrones and IPFs are freely available to interested users. In addition, we add to the evidence presented in previous papers in this series in support of the Teff and color scales of our models. In particular, the temperatures derived by Gratton et al. for local Population II subdwarfs with accurate (Hipparcos) parallaxes are shown to be in excellent agreement with those predicted for them, when the Gratton et al. [Fe/H] scale is also assumed. Interestingly, the locus defined by local subdwarfs and subgiants on the (MV, log Teff)-plane and the morphologies of globular cluster (GC) color-magnitude diagrams are well matched by the present models, despite the neglect of diffusion, which suggests that some other process(es) must be at play to limit the expected effects of gravitational settling on predicted temperatures. The three field halo subgiants in our sample all appear to have ages 15 Gyr, which is favored for the Galaxy's most metal-poor GCs as well. (The settling of helium and heavy elements in the central regions of stars is expected to cause about a 10% reduction in these age estimates: this effect should persist even if some process, such as turbulence at the base of the convective envelope, counteracts diffusion in the surface layers.) Furthermore, our isochrones accurately reproduce the Da Costa & Armandroff red giant branch fiducials for M15, NGC 6752, NGC 1851, and 47 Tuc on the [MI, (V-I)0]-diagram. However, our models fail to predict the observed luminosities of the red giant bump by ≈0.25 mag: this could be an indication that there is some amount of inward overshooting of convective envelopes in red giants. For consistency reasons, the Zinn & West metallicities for intermediate metal-poor GCs (-1.8 [Fe/H] -1.1) seem to be preferred over recent spectroscopic results (based on the brightest cluster giants), suggesting that there is an inconsistency between current subdwarf and GC [Fe/H] scales.