astrophysics - Can the Sun capture dark matter gravitationally?

I think my title sums it up. Given that we think the dark matter is pseudo-spherically distributed and orbits in the Galactic potential with everything else, then I assume that its speed with respect to the Sun will have a distribution with an rms of a few 100 km/s.

But the escape velocity at the solar surface is 600 km/s. So does that mean that, even though sparse, the Sun will trap dark matter particles as it moves around the Galaxy? Will it accumulate a cloud of dark matter particles by simple Bondi-Hoyle accretion and, in the absence of any inelastic interactions, have a swarm of dark matter particles orbiting in and around it with a much higher concentration than the usual interstellar density? If so, what density would that be?

EDIT: My initial premise appears to be ill-founded since a dark matter particle falling into the Sun's gravity well will gain enough KE to escape again. However, will there still be a gravitational focusing effect such that the DM density will be higher in the Sun?

Answer

Well, like anything else that comes in from distant parts it's going out again without a either a three-body momentum transfer or some kind of a non-gravitational interaction.

If you assume a weakly interacting form of dark matter, then I think the answer has to be yes, but the rate is presumably throttled by the weak interaction cross-section of your WIMPs.