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 Ðrst application of this software is to the models presented in this series of papers for 17 [Fe/H] (speciÐcally, 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 and color scales of our models. In particular, the T eff 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 deÐned by local subdwarfs and subgiants on the and the morphologies of globular cluster (GC) color-magnitude diagrams are well (M V , log T eff )-plane matched by the present models, despite the neglect of di †usion, which suggests that some other process(es) must be at play to limit the expected e †ects of gravitational settling on predicted temperatures. The three Ðeld halo subgiants in our sample all appear to have ages Gyr, which is Z15 favored for the GalaxyÏs 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 e †ect should persist even if some process, such as turbulence at the base of the convective envelope, counteracts di †usion in the surface layers.) Furthermore, our isochrones accurately reproduce the Da Costa & Armandro † red giant branch Ðducials for M15, NGC 6752, NGC 1851, and 47 Tuc on the [M I , However, our models fail to predict the observed luminosities of the red giant bump (V [I)

C and N abundances of main sequence and subgiant branch stars in NGC 1851

“…For all our stars, we assumed a typical mass of 0.8 M (Bergbusch & VandenBerg 2001) and a distance modulus of (m − M) V = 15.47 (Harris 1996(Harris , 2010. Finally, we obtained the microturbulent velocities (v t ) from the relation log g and v t , i.e., v t = 1.5−0.03 log g as in Carretta et al (2004).…”

The age of the Milky Way halo stars from the Sloan Digital Sky Survey

“…Moreover, color transformations for the isochrones can also affect the absolute ages based on the turn-off color. An example can be found in the uvby − β series, where Schuster et al (2006) found an age of 13 Gyr for the halo stars using newer isochrones of Bergbusch & VandenBerg (2001), which ignore diffusion but use empirical color transformations that require in some cases ad hoc adjustments to lower the ages based on a good match between the isochrones and the GC turn-off colors. Salaris & Weiss (2001) have obtained field star ages lower by up to 4 Gyr when using stellar model tracks that included diffusion.…”

The subgiant branch ofω Centauri seen through high-resolution spectroscopy

“…A typical mass of 0.8 M was assumed for the programme stars (Bergbusch & VandenBerg 2001), and we used (m − M) V = 14.04 ± 0.11 mag (Bellazzini et al 2004). An independent estimate of T eff , which is the most influential parameter when determining abundances, was also derived from the profile fitting of the H α line wings.…”