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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 $\dot{M} = π R^{2} ρ v$ where $ρ$ 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 $\dot{M} = \frac{4 π ρ G^{2} M^{2}}{c_{s}^{3}}$ .

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

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+'''Bondi [[Accretion (astrophysics)|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 <math> \dot{M} = \pi R^2 \rho v </math> where <math> \rho </math> is the ambient density, <math>v</math> is either the velocity of the object or the [[sound speed]] <math>c_s</math> in the surrounding medium if the object's velocity is lower than the sound speed, and the radius <math>R</math> provides an effective area.  The effective radius is acquired by equating the object's [[escape velocity]] and the relevant speed, i.e.
+<math> \sqrt{\frac{2 G M}{R}} = c_s </math> or <math> R=\frac{2 G M}{c_s^2} </math>.  The accretion rate therefore becomes <math> \dot{M} = \frac{4 \pi \rho G^2 M^2 }{c_s^3} </math>.
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+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) [[Monthly Notices of the Royal Astronomical Society|MNRAS]] 112, 195, [http://adsabs.harvard.edu/abs/1952MNRAS.112..195B link]
+*Mestel (1954) MNRAS 114, 437
+*Hoyle and Lyttleton (1941) MNRAS 101, 227
+[[Category:Interstellar media]]
+{{physics-stub}}

Change-making problem: Difference between revisions

Revision as of 23:55, 18 December 2013

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