Bondi accretion
Bondi Accretion
Accretion (astrophysics)
In astrophysics, the term accretion is used for at least two distinct processes.The first and most common is the growth of a massive object by gravitationally attracting more matter, typically gaseous matter in an accretion disc. Accretion discs are common around smaller stars or stellar remnants...

is spherical accretion onto an object. It is generally used in the context of neutron star
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

 and black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

 accretion for compact objects traveling through the interstellar medium
Interstellar medium
In astronomy, the interstellar medium is the matter that exists in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, dust, and cosmic rays. It fills interstellar space and blends smoothly into the surrounding intergalactic space...

. It is named after Hermann Bondi
Hermann Bondi
Sir Hermann Bondi, KCB, FRS was an Anglo-Austrian mathematician and cosmologist. He is best known for developing the steady-state theory of the universe with Fred Hoyle and Thomas Gold as an alternative to the Big Bang theory, but his most lasting legacy will probably be his important...


To achieve an approximate form of the Bondi accretion rate, accretion is assumed to occur at a rate where is the ambient density, is either the velocity of the object or the sound speed  in the surrounding medium if the object's velocity is lower than the sound speed, and the radius provides an effective area. The effective radius is acquired by equating the object's escape velocity
Escape velocity
In physics, escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero gravitational potential energy is negative since gravity is an attractive force and the potential is defined to be zero at infinity...

and the relevant speed, i.e.
or . The accretion rate therefore becomes .

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.
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