How Do You Estimate the Mass Accretion Rate for a Quasar?

[leonne]

Homework Statement

A typical quasar luminosity is about 1012 L, where L = 3:83 1033 erg s1 is
the luminosity of the Sun. If the energy is released by mass falling into a SMBH,
estimate the mass accretion rate. (Convenient units are solar masses per year.)

B)If the mass accretion rate is roughly constant, how long would it take to build
a mass of 108M ? Is that long or short compared with the age of the Universe
(about 14 Gyr)? Comment on whether the idea that quasars are powered by
accretion onto SMBH makes sense or not.
2

Homework Equations

L~de/dt~1/2 M c^2

The Attempt at a Solution

Would this be the formula I use to solve it? Seems a little to easy lol were M is the accretion rate The original formula is Du~-(GM/2GM/c^2)m dt m is the accretion rate then after few steps they have the formula i listed on top So just solve for M?

for the second part thinking of using de~dk~ (GM/Rs) m dt thinking of taking the integral of both sides then just move T to the other side then plug in but seems like GM/rs would cancel out so not sure. Is this right or need to do something else?

 

[NateD]

For the last part, the age of universe is significantly longer than the time it would take to build the mass of 108M, so yes it makes sense.