Based on the circular orbits of stars at the edge of the

Question

Astronomy Assignment-

1. Accretion Power

An astronomer is monitoring the activity in a pair of QSOs. Based on their respective redshifts, the astronomer determines that QSO B is at a distance from Earth four times greater than QSO A (i.e. d_B = 4 × d_A). Both QSOs have the same apparent brightness, i.e. flux.

(a) The astronomer also determines that QSO A is accreting mass onto its central black hole at a rate of ?m/?t = 0.5M_?/year. What is the luminosity of QSO A in Joules/sec?

(b) What are the accretion rate (in M_?/year) and luminosity (in Joules/sec) of QSO B?

2. Weighing the Milky Way

(a) Based on the circular orbits of stars at the edge of the luminous component of the Milky Way disk, we can calculate how much mass is contained within their orbits. These stars orbit the Milky Way at a distance of r = 15 kpc from the Galactic center, and at a speed of v = 220 km/s. How much mass is contained within the radius of their orbits?

(b) If the entire mass of the Milky Way was contained within a radius of 15 kpc (i.e. your answer from part (a)), what orbital speed would you expect for a star at a radius of 50 kpc from the center of the Galaxy?

(c) It turns out that astronomers can measure the orbital speeds of gas clouds far out from the center of the Milky Way (even though the majority of the luminous matter is contained within a radius of 15 kpc from the center). When they do so, they find that the orbital speeds of stars and gas clouds remain constant at a value of v = 220 km/s, even out to a distance of r = 50 kpc. How much mass must be contained within a radius of 50 kpc? What does this result imply about the nature of mass in our Galaxy?