Summary: ASTR 3830: Problem Set 4
(due in class Friday March 12th)
1. Explain briefly what is meant by the Tully-Fisher relation and the Faber-Jackson
relation. How can these relations be used as extragalactic distance indicators? Why
is the scatter in the Tully-Fisher relation increased if the luminosity is measured at
shorter wavelengths (in the blue rather than the infra-red)?
2. The mass density in the form of stars near the Galactic Center follows a power-law
in radius r:
r = r0r-7 4
where r0 is a constant.
(a) If the total mass of stars within 1.8 pc of the center is 3 x 106
calculate the constant r0 [this requires integrating the above density over spherical
shells between r = 0 and r = 1.8 pc. For the latter parts of the question, it will help
to work this out in c.g.s. units.]
(b) Close enough to the central black hole, the velocity of stars will be dominated
by the gravity of the hole. If the hole has mass MBH, write down an expression for
the Keplerian orbital velocity as a function of radius.
(c) Consider a massive star of mass M* orbiting at radius r from the black hole.