# Bondi accretion

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Not to be confused with [Bondi-Hoyle-Lyttleton accretion](/source/Bondi-Hoyle-Lyttleton_accretion).

In [astrophysics](/source/Astrophysics), the **Bondi accretion**, named after [Hermann Bondi](/source/Hermann_Bondi), is spherical [accretion](/source/Accretion_(astrophysics)) onto a [compact object](/source/Compact_object) traveling through the [interstellar medium](/source/Interstellar_medium). It is generally used in the context of [neutron star](/source/Neutron_star) and [black hole](/source/Black_hole) accretion. To achieve an approximate form of the Bondi accretion rate, accretion is assumed to occur at a rate

- \dot{M} \simeq \pi R^2 \rho v.

where:

- \rho is the ambient density
- v is the object's velocity v_o or the [sound speed](/source/Sound_speed) c_s in the surrounding medium if v_o < c_s
- R is the Bondi radius, defined as 2 G M / 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:

\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](/source/Kelvin%E2%80%93Helmholtz_mechanism)) for the planet to be able to accrete more of an atmosphere.

## Bibliography

- Bondi (1952) *[MNRAS](/source/Monthly_Notices_of_the_Royal_Astronomical_Society)* 112, 195, [link](http://adsabs.harvard.edu/abs/1952MNRAS.112..195B)
- [Mestel](/source/Leon_Mestel) (1954) *MNRAS* 114, 437, [link](http://adsabs.harvard.edu/abs/1954MNRAS.114..437M)
- [Hoyle](/source/Fred_Hoyle) and [Lyttleton](/source/Raymond_Lyttleton) (1941) *MNRAS* 101, 227

## References

1. Edgar, Richard (21 Jun 2004). ["A Review of Bondi-Hoyle-Lyttleton Accretion"](https://ned.ipac.caltech.edu/level5/March09/Edgar/Edgar2.html). *New Astronomy Reviews*. **48** (10): 843–859. [arXiv:astro-ph/0406166](https://arxiv.org/abs/astro-ph/0406166). [Bibcode:2004NewAR..48..843E](https://ui.adsabs.harvard.edu/abs/2004NewAR..48..843E). [doi:10.1016/j.newar.2004.06.001](https://doi.org/10.1016/j.newar.2004.06.001). [S2CID 17638601](https://api.semanticscholar.org/CorpusID:17638601). Retrieved 19 February 2018.

## See also

- [Bondi-Hoyle-Lyttleton accretion](/source/Bondi-Hoyle-Lyttleton_accretion)

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Adapted from the Wikipedia article [Bondi accretion](https://en.wikipedia.org/wiki/Bondi_accretion) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Bondi_accretion?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.