Calculating the Feeding Rate of Supermassive Black Holes to Power Quasars

[amt2124]

Homework Statement

Quasars arise when supermassive black holes swallow nearby gas, or even
entire stars. Their masses are typically 10&7 solar masses, and their luminosities are
typically around 10&39 W. Hide the children! Roughly how many stars must one of
these monsters eat per year, in order to power that luminosity?

Homework Equations

L = GM/R * deltaM/deltaR

The Attempt at a Solution

So far I can find deltaM/deltaR like the professor said we should. I am having trouble understanding where we go from there.

 

[gneill]

So far I can find deltaM/deltaR like the professor said we should. I am having trouble understanding where we go from there.

Perhaps you can expound a bit upon what deltaM and deltaR are, and how you have found them?

 

[amt2124]

Perhaps you can expound a bit upon what deltaM and deltaR are, and how you have found them?

I assumed that I am able to plug in the schwarzschild radius for the radius, G is a constant, and I am given the luminosity and mass. When I plug those in I can solve for deltaM and deltaR (which is the rate of accretion).

 

[gneill]

Can you show the algebra that you did, plugging the Schwarzschild radius into your luminosity equation?

 

[amt2124]

Can you show the algebra that you did, plugging the Schwarzschild radius into your luminosity equation?

 

[gneill]

Okay. Now what are the units on your ΔM/ΔR value?