Monte Carlo Simulations of the White Dwarf Population and Luminosity Function

Abstract

The white dwarf luminosity function has been used in recent years as an independent probe of the age and evolution of the local Galactic disk. A long-standing uncertainty of the technique is that the reality of the reported downturn in the luminosity function hinges on just a handful of stars and on statistical arguments that fainter (older) objects would have been observed were they present. Using a Monte Carlo approach, I explore the uncertainties in the derived ages and star formation rates resulting from the small-number statistics of the lowest-luminosity bin. The results suggest that (i) Schmidt’s 1/V _max technique underestimates by typically 25 to 50% the true space density of white dwarf stars in surveys with proper motion limits μ ^”_lim ≲ 1.“0 yr^-1, and (ii) there is ~ 1 Gyr statistical uncertainty in the age inferred from a sample with N ≲ 5 objects in the lowest-luminosity bin, confirming the conservative error estimates adopted by LDM and OSWH.