# Bondi accretion

To achieve an approximate form of the Bondi accretion rate, accretion is assumed to occur at a rate $\dot{M} = \pi R^2 \rho v$ where $\rho$ is the ambient density, $v$ is either the velocity of the object or the sound speed $c_s$ in the surrounding medium if the object's velocity is lower than the sound speed, and the radius $R$ provides an effective area. The effective radius is acquired by equating the object's escape velocity and the relevant speed, i.e. $\sqrt{\frac{2 G M}{R}} = c_s$ or $R=\frac{2 G M}{c_s^2}$. The accretion rate therefore becomes $\dot{M} = \frac{4 \pi \rho G^2 M^2 }{c_s^3}$.