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Textbook
(Combes et al.) goes through the old
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approach
of flattened spheroids with a particular
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mass
density as a function of radius.
This is
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perhaps
useful review for qualifying exam as an
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exercise
in gravitational physics.
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Key
is to use the rotation curve.
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Solutions
are appropriately simple for flat curves:
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M(total) = V2rot R/G (spherical dark matter)
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M(total) = (2/π) V2rot R/G (disk dark
matter)
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Where
the disk is cut off at r=R, and V = constant (flat curve)
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inside
r < R.
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Mass
increases linearly with r, for V = constant
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Mass/Light
ratio increases faster
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