Summary: ASTR 3830: Problem Set 5
(due in class Friday April 16th)
1. Recent observations (e.g. Haering & Rix, ApJ, 604, L89) show that there is a
relationship between the mass of the supermassive black hole MBH and the mass of the
bulge of the galaxy Mbulge that the black hole is in. The relationship is:
Suppose that when the black hole formed, the efficiency with which rest mass spiraling
into the hole generated radiation was e = 0.1. The fusion of hydrogen to helium in stars
liberates a fraction e = 7 x 10-3
of the rest mass involved.
(i) Calculate the factor by which the energy radiated by stars in the bulge (integrated over
the stellar lifetimes) exceeds that radiated by the accreting black hole during the time
over which it is forming.
(ii) Why then, does light from the nucleus of a quasar enormously outshine the light from
the stars in its host galaxy?
2. A cluster of galaxies contains 1000 galaxies within a spherical volume of radius R = 2
Mpc. The galaxies have random velocities of 1000 km s-1
, and radii of rgal = 10 kpc.