3) (10 points). Observations of KV stars near the Sun show that the velocity dispersion (a)
increases from 13.5 km/s near the Galactic midplane to ~ 35 km/s at Z = 1 kpc (above which
there are no disk KV stars) and can be roughly approximated by o(z) = ae+bizl: where a =
13.5 km/s, b = 0.001 pc-1, and Z is the height above/below the midplane (in pc). In addition,
the vertical density of KV stars near the Sun has been shown to follow the distribution n(z) =
noe-lzl/hz : where no is the density in the midplane and hz = 350 pc.
a) (8 pts) From these observations calculate the surface mass (in units of Mo pc-2) of the
Galaxy near the Sun (at Z = 0) assuming the Galaxy has a vertical extent of Z = +1
kpc. Be careful of your units!
b) (2 pts) From the result in a) estimate the total mass of the Galaxy (in Mo) Be sure to
explain any assumptions you make.
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