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Bondi Spherical Accretion

What you are seeing: a steady spherically symmetric accretion flow onto a point mass. Gas falls inward, passing through a sonic point at r=rB/2r = r_B/2 (isothermal). The Bondi rate $\dot M_B = \pi e^{3/2} G^2 M^2 \rho_\infty / c_s^3$ sets the asymptotic accretion.

Figure 1. Velocity and density profiles in the Bondi solution.
log10(M / M⊙)0.00
cs (km/s)10
log10(n∞ cm⁻³)3.00

WHAT TO TRY

  • Gas falls in subsonic (blue) from the Bondi radius and accelerates, crossing to supersonic (red) exactly at the sonic radius r_s = r_B/2. The bottom plot shows that single transonic solution threading the critical point.
  • Lower the sound speed (colder gas): the Bondi radius swells, the accretion rate Mdot climbs, and the whole flow is pulled from larger distances. Mdot scales as M squared over c_s cubed.
  • Raise the accretor mass: both circles grow together and the infalling stream thickens, the same spherical accretion that feeds compact objects and protostars.