ASTR 3830: Problem Set 4 (due in class Friday March 12th) 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 Solar masses, 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. Collections: Physics