### 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

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

Where:

$$\rho is the ambient density v is the object's velocity \( v_o$$ or the sound speed $$c_{s}$$ in the surrounding medium if $$v_{o}<c_{s}}$$
R is the Bondi radius, defined as $$2GM/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. 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) 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

Edgar, Richard (21 Jun 2004). "A Review of Bondi-Hoyle-Lyttleton Accretion". A Knowledgebase for Extragalactic Astronomy and Cosmology. New Astronomy Reviews. doi:10.1016/j.newar.2004.06.001. Retrieved 19 February 2018.

vte

Neutron star
Types

Single pulsars

Binary pulsars

Properties

Related

Discovery

LGM-1 Centaurus X-3 Timeline of white dwarfs, neutron stars, and supernovae

Satellite
investigation

Rossi X-ray Timing Explorer Fermi Gamma-ray Space Telescope Compton Gamma Ray Observatory Chandra X-ray Observatory

Other

X-ray pulsar-based navigation Tempo software program Astropulse The Magnificent Seven

Physics Encyclopedia

World

Index