Transonic accretion in a steep dark-matter cusp
= Transonic accretion in a steep dark-matter cusp
{title2=Transonic accretion in an $r^{-5/2}$ density cusp}
For a background gravitating density $\rho_{\rm dm}=\Psi_0r^{-5/2}$, the potential is $\Phi=-16\pi G\Psi_0r^{-1/2}$. A steady polytropic inflow has a regular sonic point only for $1<\gamma<9/7$, and its accretion rate scales as $\dot M\propto\rho_0G^4\Psi_0^4c_0^{-7}$.