Bondi accretion

In astrophysics, the Bondi accretion (also called Bondi–Hoyle–Lyttleton 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 the object's velocity ${\displaystyle v_{o}}$ or the sound speed ${\displaystyle c_{s}}$ in the surrounding medium if ${\displaystyle v_{o}<c_{s}}$
• ${\displaystyle R}$ is the Bondi radius, defined as ${\displaystyle 2GM/c_{s}^{2}}$.

The Bondi radius comes from setting escape velocity equal to the sound speed and solving for radius. It represents the boundary between subsonic and supersonic infall.^[1] Substituting the Bondi radius in the above equation yields:

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

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.