# I Spherical Accretion Mass inflow Rate

1. Jul 17, 2016

### PhotonKing

Hello everyone I am a new user around here. I have been attempting to understand spherical accretion and create a simple model of that process but I am running into a problem. This is getting at the heart of the issue. So far I have come up with two concentric spheres, the outer sphere is the shell of gas the inner sphere is a black hole. I have assumed that the shell sphere will shrink in radius at a rate determined by gravity and it's distance from the center of the black hole. So the accretion shell is not self gravitating. My trouble is figuring how much mass is actually accreted onto the black hole, ie the accretion rate. Any help or hints would be extremely helpful. I have given a link to my work so far in a google document. Let me know what you all think. I am doing this to better understand Bondi accretion. The radius of the black hole depends only on mass, so if I know the mass flow rate I should be able to solve these equations for, Volume of the shell as a function of time, Density of the shell as a function of time, Recession velocity of the shell's collapse as a function of time, perhaps even pressure and temperature. Any help would be hot. Here's a link to my google doc, this isn't a homework question it's a question about research i'm involved in. I could simply take the result from the Bondi paper but i'd like a better understanding of how they got to that result. I have been stumped at finding a solution to this for a while now.

The result of the accretion rate given in the paper is:

dM/dt=4πr2

My work:

Thanks

2. Jul 22, 2016