Bondi–Hoyle–Lyttleton 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. An initial estimate of the accretion rate for a supersonic wind was derived by Hoyle and Lyttleton in 1939 to explain variations in the climate of the Earth. The generally accepted form of BHL accretion was derived by Bondi, who combined an improved version the earlier work with his own work on spherically symmetric accretion (known as Bondi accretion).

Accretion rate

The accretion rate (the amount of mass accreted per unit of time) of the BHL formalism is given by

M

˙

=

α

2

π

(

G

M

)

2

ρ

(

v

2

+

c

2

)

3

/

2

,

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

where

ρ

{\displaystyle \rho }

is the density of the gas;

v

{\displaystyle v}

is the relative velocity between the gas and the accreting body;

M

{\displaystyle M}

is the mass of the accreting body;

c

{\displaystyle c}

is the speed of sound in the gas;

α

{\displaystyle \alpha }

is a dimensionless factor between 1 and 2, which cannot be determined analytically.

History

In a 1939 paper, Fred Hoyle and Raymond Lyttleton considered the possibility that variations in the Earth's climate might be caused by the accretion of the interstellar medium (ISM) by the Sun. They proposed that when the Solar System moves through a cloud in the ISM, the Sun would accrete material from it, and created a model to mathematically explain this accretion rate. This would release the gravitational potential energy of the accreted material as radiation, which would increase the Earth's temperature. They claimed that this variation could be large enough to explain the occurrence of ice ages and the increase in radiation needed to explain the occurrence of the carboniferous.