  Motivated by recent measurements which suggest that roughly half the mass of
the galactic halo may be in the form of white dwarfs, we study the implications
of such a halo. We first use current limits on the infrared background light
and the galactic metallicity to constrain the allowed initial mass function
(IMF) of the stellar population that produced the white dwarfs. The IMF must be
sharply peaked about a characteristic mass scale $M_C \approx 2.3 M_\odot$.
Since only a fraction of the initial mass of a star is incorporated into the
remnant white dwarf, we argue that the mass fraction of white dwarfs in the
halo is likely to be 25\% or less, and that 50\% is an extreme upper limit. We
use the IMF results to place corresponding constraints on the primordial
initial conditions for star formation. The initial conditions must be much more
homogeneous and skewed toward higher temperatures ($T_{\rm gas} \sim$ 200 K)
than the conditions which lead to the present day IMF. Next we determine the
luminosity function of white dwarfs. By comparing this result with the observed
luminosity function, we find that the age of the halo population must be
greater than $\sim 16$ Gyr. Finally, we calculate the radiative signature of a
white dwarf halo. This infrared background is very faint, but is potentially
detectable with future observations.
