# Black hole Accretion Luminosity

1. Oct 21, 2013

### bowlbase

1. The problem statement, all variables and given/known data
Suppose that a black hole of mass M accretes mass at a rate $\dot{M}$. Further suppose that accretion of mass Δm leads to the radiation of energy $\Delta E= \eta Δmc^2$, for some effeciency of energy conversion, $\eta$. What is the luminosity of emitted radiation in terms of $\dot{M}$ and $\eta$?

2. Relevant equations
Luminosity equation, sort of?

3. The attempt at a solution
The only equation I've ever seen for luminosity has been in terms of temperature and radius. So I'm at a loss here where to go with this. I understand that luminosity is the amount of energy an object gives off over time but I'm sure I can't just put that ΔE over a Δt and call it good. This is suppose to be a simple question but I'm just not making the connections I need to solve it.

Last edited: Oct 22, 2013
2. Oct 22, 2013

### bowlbase

Edited for clarification. Currently my answer is just the ΔE over 4pi. Anyone have a suggestion for this?

3. Oct 22, 2013

### Dick

Ok. I'm not an expert but I really don't see any other way to go with this. Luminosity is dE/dt as far as I know. So dE/dt=η*dM/dt*c^2=η*$\dot M$*c^2. You don't quite divide them both by Δt, but it's really almost the same thing. You said this is an easy question, right? Maybe it is that easy. At least I don't see what else to do. I don't see what sense ΔE over 4pi makes, it has the units of energy, not energy/second.

Last edited: Oct 22, 2013
4. Oct 22, 2013

### bowlbase

Maybe I'm just thinking too hard about this. What you have must be correct I would assume, but it makes me question why he'd even make that part of the problem set. Unless just to check if we recall what luminosity is. Anyway, thanks for the assistance.

5. Oct 22, 2013

### Dick

Yes, it does seem too easy. Let me know if I've missed something important.