# An accretion of steady flow for Gamma > 5/3?

1. Nov 20, 2014

### Vrbic

Hello,
I would like to know, what happen with accretion (cloud) when drop toward a black hole. In Bondi case and terminology. If I understand:
1) We describe the cloud falling to star (black hole) by EoS $P(\rho)=K\rho^\Gamma$.
2) This accretion is steady it means $\dot{M}=4\pi r^2u\rho=const.$.
3) Accretion to black hole is possible just for supersonic speed => solution of Bondi equation has to come through critical sound speed point.
4) For $\Gamma>\frac{5}{3}$ doesnt exist critical point and accretion is not supersonic => no steady accretion on black hole for cloud with $\Gamma>\frac{5}{3}$.
Are these 4 claims right?
Bondi solution is dealing just with $\Gamma<\frac{5}{3}$. It is quit hard constrain.
My question are:
a) What is the matter with cloud with $\Gamma>\frac{5}{3}$ during falling to black hole? Reaches the event horizon?
b) How do we must change in assumptions for dealing with cloud with $\Gamma>\frac{5}{3}$?
I was checking in literature for this part of problem, but I didn't find anything important. Please let me know, comments or links.
Thank you.

2. Nov 25, 2014