We examine the recent results of the MACHO collaboration towards the Large
Magellanic Cloud (Alcock et al. 1996) in terms of a halo brown dwarf or white
dwarf population. The possibility for most of the microlensing events to be due
to brown dwarfs is totally excluded by large-scale kinematic properties. The
white dwarf scenario is examined in details in the context of the most recent
white dwarf cooling theory (Segretain et al. 1994) which includes explicitely
the extra source of energy due to carbon-oxygen differentiation at
crystallization, and the subsequent Debye cooling. We show that the
observational constraints arising from the luminosity function of high-velocity
white dwarfs in the solar neighborhood and from the recent HST deep field
counts are consistent with a white dwarf contribution to the halo missing mass
as large as 50 %, provided i) an IMF strongly peaked around 1.7 Msol and ii) a
halo age older than 18 Gyr.Comment: 14 pages, 2 Postscript figures, to be published in Astrophysical
Journal Letters, minor revision in tex