White dwarfs and the ages of stellar populations
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Our group has developed a Bayesian modeling technique to determine the ages of stellar populations (in particular, open and globular clusters) using white dwarf (WD) cooling physics. As the theory of WD cooling is both simpler than, and essentially independent of, main sequence evolutionary theory, white dwarfs provide an independent measure of the ages of Galactic populations. We have developed a Bayesian technique that objectively incorporates our prior knowledge of stellar evolution, star cluster properties, and data quality estimates to derive posterior probability distributions for a cluster's age, metallicity, distance, and line-of-sight absorption, as well as the individual stellar parameters of mass, mass ratio (for unresolved binaries) and cluster membership probability. The key advantage of our Bayesian method is that we can calculate probability distributions for cluster and stellar parameters with reference only to known, quantifiable, objective, and repeatable quantities. In doing so, we also have more sensitivity to subtle changes in cluster isochrones than traditional ``chi-by-eye'' cluster fitting methods. As a critical test of our Bayesian modeling technique, we apply it to Hyades UBV photometry, with membership priors based on proper motions and radial velocities, where available. We use secular parallaxes derived from Hipparcos proper motions via the moving cluster method to put all members of the Hyades at a common distance. Under the assumption of a particular set of WD cooling and atmosphere models, we estimate the age of the Hyades based on cooling white dwarfs to be 610 +- 110 Myr, consistent with the best prior analysis of the cluster main-sequence turn-off age (Perryman, et al. 1998). Since the faintest white dwarfs have most likely evaporated from the Hyades, prior work provided only a lower limit to the cluster's white dwarf age. Our result demonstrates the power of the bright white dwarf technique for deriving ages (Jeffery, et al. 2007) and further demonstrates complete age consistency between white dwarf cooling and main-sequence turn-off ages for seven out of seven clusters analyzed to date, ranging from 150 Myr to 4 Gyr. We then turn our attention to the white dwarf luminosity function. We use Sloan Digital Sky Survey (SDSS) data to create a white dwarf luminosity function with nearly an order of magnitude (3,358) more spectroscopically confirmed white dwarfs than any previous work. We determine the completeness of the SDSS spectroscopic white dwarf sample by comparing a proper-motion selected sample of WDs from SDSS imaging data with a large catalog of spectroscopically determined WDs. We derive a selection probability as a function of a single color (g-i) and apparent magnitude (g) that covers the range -1.0 < g-i < 0.2 and 15 < g < 19.5. We address the observed upturn in log g for white dwarfs with Teff < ~12,000K and offer arguments that the problem is limited to the line profiles and is not present in the continuum. We offer an empirical method of removing the upturn, recovering a reasonable mass function for white dwarfs with Teff < 12,000K. Finally, we outline several other current and future applications of our method and our code to determine not only ages of Galactic stellar populations, but helium abundances of clusters, ages of individual field WDs, and the initial (main sequence) to final (WD) mass relation.