Black hole Accretion Luminosity

  • Thread starter bowlbase
  • Start date
  • #1
bowlbase
146
2

Homework Statement


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##?


Homework Equations


Luminosity equation, sort of?


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:

Answers and Replies

  • #2
bowlbase
146
2
Edited for clarification. Currently my answer is just the ΔE over 4pi. Anyone have a suggestion for this?
 
  • #3
Dick
Science Advisor
Homework Helper
26,263
619
Edited for clarification. Currently my answer is just the ΔE over 4pi. Anyone have a suggestion for this?

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:
  • #4
bowlbase
146
2
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
Dick
Science Advisor
Homework Helper
26,263
619
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.

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

Suggested for: Black hole Accretion Luminosity

Replies
0
Views
442
Replies
1
Views
314
  • Last Post
Replies
4
Views
815
  • Last Post
Replies
1
Views
533
  • Last Post
Replies
0
Views
699
Replies
7
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
618
Replies
8
Views
781
Replies
3
Views
556
Top