Quasar variability timescale and black hole Schwarzschild radius

[CaptainEvil]

Homework Statement

If a quasar varies on a time scale of four months, how does the maximum size of the emitting region compare with the Schwarzschild radius for a 10⁹ MSun black hole?

Homework Equations

The Attempt at a Solution

Calculating the S radius of the black hole is trivial, but I think I missed the lecture on varying quasars. I don't know of any equations for 'emitting regions' let alone how to use its rotation period to do so. Can anyone start me off on the right track?

fwiw I calculated the S radius by the eqn 3km(M/Msun) = 3 x10¹² m

 

[mgb_phys]

if the source varies on a time scale of 4months what's the maximum size it can have?

hint - you are probably supposed to picture it's extent in a line of sight to you and assume the actual brightness change is instantaneous an comes from the full extent of the source.

 

[CaptainEvil]

if the source varies on a time scale of 4months what's the maximum size it can have?

hint - you are probably supposed to picture it's extent in a line of sight to you and assume the actual brightness change is instantaneous an comes from the full extent of the source.

I see, so are we assuming that it can only extend to a maximum size of 4 light months?
4 light months corresponds to roughly 3.1 e15 meters, which is about 1000 times the size of the S radius of the black hole.

Does this sound right?

 

[mgb_phys]

That's how I read it.
In reality the emission is going to come from a large acreation disk around the hole so it's easy to imagine that as 1000x the Rs