Download Introduction General Relativity and Astrophysical Applications 2016

Introduction General Relativity and Astrophysical
Applications 2016
Problem set 8
Problem 1 due: November 14, 2016, 9am, by email to [email protected]
Note: In these problems, do not use geometrized units, but use c and G explicitly.
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Problem 1: Brightness of an evaporating black hole (hand
in this problem)
In class we discussed the evaporation of black holes by Hawking radiation. Suppose a primordial
black hole (i.e., a black hole formed in the first fraction of a second following the Big Bang)
evaporates now. Suppose also that there is an astronomer surveying the sky for such events by
covering every position for exactly 1 sec before moving on to the next position. Suppose finally
that this astronomer catches the final second of this black hole, which appears in his data as
a transient source as bright as the Sun placed at a distance of 10 pc (i.e., the brightness of a
typical star). Give an order-of magnitude estimate of the distance of the evaporating black hole.
Make any reasonable approximation that you like as long as it is order-of-magnitude correct.
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Problem 2: Accretion rate for an X-ray source (not for
handing in)
An astronomical X-ray source is observed to have a luminosity L ∼ 1000 L⊙ . The source
is powered by accretion onto a black hole of mass 6 M⊙ . Make an estimate of the required
mass accretion rate Ṁ in M⊙ yr−1 , assuming all radiation is emitted from the innermost stable
circular orbit. Once again, make any reasonable approximation you like, as long as it is order of
magnitude correct.
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