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In astrophysics, the Bondi accretion, named after Hermann Bondi, is spherical accretion onto a compact object traveling through the interstellar medium. It is generally used in the context of neutron star and black hole accretion. To achieve an approximate form of the Bondi accretion rate, accretion is assumed to occur at a rate

M˙≃πR2ρv,{displaystyle {dot {M}}simeq pi R^{2}rho v,}.

Where:

• 
  ρ{displaystyle rho } is the ambient density


• 
  v{displaystyle v} is the object's velocity vo{displaystyle v_{o}} or the sound speed cs{displaystyle c_{s}} in the surrounding medium if vo<cs{displaystyle v_{o}<c_{s}}
  


• 
  R{displaystyle R} is the Bondi radius, defined as 2MG/cs2{displaystyle 2MG/c_{s}^{2}}.

The Bondi radius comes from setting escape velocity equal to the sound speed and solving for radius. It represents the boundary between subsonic and supersonic infall.^[1] Substituting the Bondi radius in the above equation yields:

M˙≃πρG2M2cs3{displaystyle {dot {M}}simeq {frac {pi rho G^{2}M^{2}}{c_{s}^{3}}}}.

These are only scaling relations rather than rigorous definitions. A more complete solution can be found in Bondi's original work and two other papers.

Application to accreting protoplanets

When a planet is forming in a protoplanetary disk, it needs the gas in the disk to fall into its Bondi sphere in order for the planet to be able to accrete an atmosphere. For a massive enough planet, the initial accreted gas can quickly fill up the Bondi sphere. At this point, the atmosphere must cool and contract (through the Kelvin-Helmholtz mechanism) for the planet to be able to accrete more of an atmosphere.

Bibliography

• Bondi (1952) MNRAS 112, 195, link
  


• 
  Mestel (1954) MNRAS 114, 437, link
  


• 
  Hoyle and Lyttleton (1941) MNRAS 101, 227

References

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