A hierarchical model for the ages of Galactic halo white dwarfs

Abstract

In astrophysics, we often aim to estimate one or more parameters for each member object in a population and study the distribution of the fitted parameters across the population. In this paper, we develop novel methods that allow us to take advantage of existing software designed for such case-by-case analyses to simultaneously fit parameters of both the individual objects and the parameters that quantify their distribution across the population. Our methods are based on Bayesian hierarchical modelling that is known to produce parameter estimators for the individual objects that are on average closer to their true values than estimators based on case-by-case analyses. We verify this in the context of estimating ages of Galactic halo white dwarfs (WDs) via a series of simulation studies. Finally, we deploy our new techniques on optical and near-infrared photometry of 10 candidate halo WDs to obtain estimates of their ages along with an estimate of the mean age of Galactic halo WDs of 12.11+0.85−0.86 Gyr. Although this sample is small, our technique lays the ground work for large-scale studies using data from the Gaia mission.