MACHOs, White Dwarfs, and the Age of the Universe

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Abstract
A favored interpretation of recent microlensing measurements toward the 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. However, a ground-based search by Liebert and a recent search of the Hubble Deep Field by Flynn did not detect a substantial dark halo population of white dwarfs; thus the putative halo population is either dim enough or sparse enough to have eluded detection. In this paper we compare model white dwarf luminosity functions to the data from the observational surveys in order to determine a lower bound on the age of any substantial white dwarf halo population (and hence possibly on the age of the universe). In the course of our analysis we pay special attention to the velocity bias in the Liebert and coworkers, survey; we show that (and 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 strongly on assumptions about three unknown quantities: (1) the white dwarfs' total space density, (2) their atmospheric composition, and (3) the initial mass function (IMF) of their progenitors. We compare various theoretical white dwarf luminosity functions, in which we vary these 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 parameters. When we use cooling curves that account for chemical fractionation and more likely values of the IMF and the bolometric correction, we find tighter limits; a white dwarf MACHO fraction of 10% (30%) requires 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.