Bondi–Hoyle–Lyttleton accretion

Not to be confused with Bondi accretion.

Bondi–Hoyle–Lyttleton (BHL) accretion (also known as Bondi–Hoyle accretion) is a mathematical model for the accretion of a uniform gas by a massive body. It is a general model of accretion with multiple applications, such as accretion of the interstellar medium by neutron stars and black holes, or wind mass transfer in binary star systems.

It is named after Hermann Bondi, Fred Hoyle, and Raymond Lyttleton.

The accretion rate (in terms of rate of change of mass) of the BHL formalism is given by^[1]

${\displaystyle {\dot {M}}=\alpha {\frac {2\pi (GM)^{2}\rho }{(v^{2}+c^{2})^{3/2}}},}$

where

• ${\displaystyle \rho }$ is the density of the gas;
• ${\displaystyle v}$ is the relative velocity between the gas and the accreting body;
• ${\displaystyle M}$ is the mass of the accreting body;
• ${\displaystyle c}$ is the speed of sound in the gas;
• ${\displaystyle \alpha }$ is a dimensionless factor between 1 and 2, which cannot be determined analytically.