2 research outputs found
Critical collapse and the primordial black hole initial mass function
It has normally been assumed that primordial black holes (PBHs) always form
with mass approximately equal to the mass contained within the horizon at that
time. Recent work studying the application of critical phenomena in
gravitational collapse to PBH formation has shown that in fact, at a fixed
time, PBHs with a range of masses are formed. When calculating the PBH initial
mass function it is usually assumed that all PBHs form at the same horizon
mass. It is not clear, however, that it is consistent to consider the spread in
the mass of PBHs formed at a single horizon mass, whilst neglecting the range
of horizon masses at which PBHs can form. We use the excursion set formalism to
compute the PBH initial mass function, allowing for PBH formation at a range of
horizon masses, for two forms of the density perturbation spectrum. First we
examine power-law spectra with , where PBHs form on small scales. We find
that, in the limit where the number of PBHs formed is small enough to satisfy
the observational constraints on their initial abundance, the mass function
approaches that found by Niemeyer and Jedamzik under the assumption that all
PBHs form at a single horizon mass. Second, we consider a flat perturbation
spectrum with a spike at a scale corresponding to horizon mass , and compare the resulting PBH mass function with that of the MACHOs
(MAssive Compact Halo Objects) detected by microlensing observations. The
predicted mass spectrum appears significantly wider than the steeply-falling
spectrum found observationally.Comment: 8 pages RevTeX file with ten figures incorporated (uses RevTeX and
epsf). Minor changes to dicussion onl