Change-making problem: Difference between revisions

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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]].
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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.
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<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>.  
 
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}}

Latest revision as of 11:00, 12 November 2014

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