# Bondi accretion

In astrophysics, the Bondi accretion, named after Hermann Bondi, is spherical accretion onto a compact object traveling through the interstellar medium. It is generally used in the context of neutron star and black hole accretion. To achieve an approximate form of the Bondi accretion rate, accretion is assumed to occur at a rate

${\displaystyle {\dot {M}}\simeq \pi R^{2}\rho v,}$

where ${\displaystyle \rho }$ is the ambient density, ${\displaystyle v}$ is either the velocity of the object or the sound speed ${\displaystyle c_{s}}$ in the surrounding medium if the object's velocity is lower than the sound speed, and the Bondi radius ${\displaystyle R}$ provides an effective area. The effective radius is acquired by equating the object's escape velocity and the relevant speed, i.e.

${\displaystyle {\sqrt {\frac {2GM}{R}}}\simeq c_{s},}$

or

${\displaystyle R\simeq {\frac {2GM}{c_{s}^{2}}}}$.

The accretion rate therefore becomes

${\displaystyle {\dot {M}}\simeq {\frac {\pi \rho G^{2}M^{2}}{c_{s}^{3}}}}$.

These are only scaling relations rather than rigorous definitions. A more complete solution can be found in Bondi's original work and two other papers.