MACHOS, WHITE-DWARFS, AND THE AGE OF THE UNIVERSE

A favored interpretation of recent microlensing measurements toward th e Large Magellanic Cloud implies that a large fraction (i.e., 10%-50%) of the mass of the Galactic dark halo is composed of white dwarfs. Ho wever, a ground-based search by Liebert and a recent search of the Hub ble Deep Field by Flynn did not detect a substantial dark halo populat ion of white dwarfs; thus the putative halo population is either dim e nough or sparse enough to have eluded detection. In this paper we comp are model white dwarf luminosity functions to the data from the observ ational surveys in order to determine a lower bound on the age of any substantial white dwarf halo population land hence possibly on the age of the universe). In the course of our analysis we pay special attent ion to the velocity bias in the Liebert and coworkers, survey; we show that land quantify by how much) the velocity bias renders the survey significantly less sensitive to a cool white dwarf population. We show that the minimum age of a white dwarf halo population depends most st rongly on assumptions about three unknown quantities: (1) the white dw arfs' total space density, (2) their atmospheric composition, and (3) the initial mass function (IMF) of their progenitors. We compare vario us theoretical white dwarf luminosity functions, in which we vary thes e three parameters, with the abovementioned survey results. From this comparison, we conclude that if white dwarfs do indeed constitute more than 10% (30%) of the local halo mass density and are candidates for explaining the microlensing events, then the universe must be at least 10 Gyr old (12 Gyr old) for our most extreme allowed values of the pa rameters. When we use cooling curves that account for chemical fractio nation and more likely values of the IMF and the bolometric correction , we find tighter limits; a white dwarf MACHO fraction of 10% (30%) re quires a minimum age of 14 Gyr (15.5 Gyr). Our analysis also provides evidence that the halo white dwarfs have helium-dominated atmospheres, although this conclusion may change after low-temperature white dwarf atmospheres have been calculated.