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HEP/Astro Seminar -- Wednesday, 26 April 2000
The Last Eight Minutes of a Primordial Black Hole
Abstract
About eight minutes before a black hole expires it has a decreasing
mass of 1010 g, an increasing temperature of 1 TeV, and an
increasing luminosity of 7×1027 erg/s. I show that such a
black hole is surrounded by a quasi-stationary shell of matter
undergoing radial hydrodynamic expansion. The inner radius of this
shell is bounded by ten times the Schwarzschild radius of
1.6×10-5 fm and has a temperature about one-tenth that of the
black hole. The outer radius, as defined by the photosphere, is about
1000 fm, has a local temperature of 100 keV, and is moving with a
Lorentz gamma factor of 107. Most of the emitted radiation is in
photons with small amounts in gravitons and neutrinos. I calculate the
instantaneous photon spectrum and then integrate it over the last eight
minutes to obtain the energy distribution
dNγ/dE = 4 π mP2/15 E3
for E > several TeV. The flux of photons arriving at
Earth is calculated assuming the primodial black holes are distributed
in the galactic halo, and limits on the rate density of these explosions
are determined.
3:30pm, Smith Lab 4079