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Crossing times: Tcross ~ R/V
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Relaxation
time then varies as
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Trelax ~ 0.2(N/logN) Tcross where
N is the number of stars
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in
the system
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For
galaxies, crossing times ~1/100 the age of the
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universe
(100 million years), and the relaxation times
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are
on order of 1017 years – so close interactions
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between
stars essentially never happen.
“Collisionless”
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is
a good approximation. This is
because N is large,
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and
the collision must be very close for another star’s
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potential
to overwhelm the ensemble potential.
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Note:
this argument is NOT true for Globular Clusters!
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Also
not true for galaxy clusters!
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The
upshot of this is that you can treat galaxies in
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terms
of motions in a global potential.
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