# Bondi accretion

Bondi accretion is spherical accretion onto an object. It is generally used in the context of neutron star and black hole accretion for a compact object traveling through the interstellar medium. It is named after Hermann Bondi.

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

$\dot{M} = \frac{4 \pi \rho G^2 M^2 }{c_s^3}$.

This derivation is only approximate, using scaling relations rather than rigorous definitions. A more complete solution can be found in Bondi's original work and two other papers.

## Bibliography

• Bondi (1952) MNRAS 112, 195, link
• Mestel (1954) MNRAS 114, 437
• Hoyle and Lyttleton (1941) MNRAS 101, 227