**Problem
Set #4**

**ASTR 3830**

- The broad line region features emission lines from the accretion disk around the black hole at the center of the AGN. Velocities as high as 30,000km/s in Ha have been seen. The disk is thought to be stable down to three Schwarzschild radii, where the plunging region begins. Calculate the velocity at the edge of the plunging region using Newtonian approximations. How do you reconcile your result with the 30,000km/s limit? How might you check your explanation?

- The radio lobe of a galaxy is 30kpc in
diameter. It is emitting 10
^{44}erg/s of synchrotron radiation at 10^{9}Hz. Assuming a B field of 10^{-4}Gauss, derive the a) the value of g for the electrons, b) the total number of electrons required and c) the total energy in electrons required and d) the total energy of magnetic field required. Then, redo the calculations for 10^{-3}Gauss and for 10^{-5}Gauss. Which value of B is the most reasonable?

- You observe a blob of emission being emitted from a quasar nucleus. The qso is known to be at z=0.5. One year later you return and observe that the blob is now 0.003 arcseconds from the nucleus. How fast does it appear to be moving? At what angle is it moving relative to our line of sight if g is assumed to be 1000?