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? 
 A: 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.
A: (edited version. My thanks to Rob for clearing up my misunderstandings)
As dmckee writes, weak interactions between DM particles and baryons are necessary to capture dark matter, otherwise particles that enter the solar system would simply move through it and eventually leave it again.
More specifically, the local rms velocity of DM particles is commonly estimated by approximating the DM halo with an isothermal sphere profile with a Maxwellian velocity distribution. If $\sigma$ is the velocity dispersion, then one can show that the rms (DM) velocity is $v_\text{DM}=\sqrt{3}\sigma$ and the circular (solar) velocity is $v_\odot\approx \sqrt{2}\sigma$, so that $v_\text{DM} \approx\sqrt{3/2}v_\odot \approx 270\;\text{km/s}$. If particles move through the solar system and enter the Sun, their speed will have increased beyond the solar escape velocity. However, if sufficient scattering occurs between these particles and nuclei within the Sun, these interactions could lower their velocity, so that they could be captured and stay trapped within the Sun.
This is in fact an active field of research, because captured DM particles could have detectable effects, depending on their properties. In particular, models suggest that particles with low mass (4 - 10 GeV), small annihilation cross sections and large spin-dependent elastic scattering cross sections could significantly alter the core temperature, energy transport and neutrino flux of the Sun. In addition, they could have an observable effect on the stellar evolution of other stars. So, comparisons between stellar models and observations can put constraints on DM properties.
In most models, the DM capture process is considered to be a combination of gravity, and spin-dependent and spin-independent elastic scattering in the Sun. But inelastic scattering models are also being studied.
The literature is extensive (and not my area of expertise), but I'll give a few references for more info:
The pioneering paper is
Weakly interacting massive particle distribution in and evaporation from the sun (Gould, 1987)
Other interesting articles: 
Light WIMPs in the Sun: Constraints from Helioseismology
Effect of low mass dark matter particles on the Sun
First asteroseismic limits on the nature of dark matter
Asymmetric dark matter and the Sun
Review of asymmetric dark matter
and references therein.
A: Your number of 100km/s might be true for the "average speed", but probably way off for the "root mean square" speed. Dark matter can be - on average - orbiting the galactic potential with everything else, however individual WIMPS will be of much higher velocity, thus making the $v_{rms}$ very high. (this high speed follows from the standard assumptions on dark matter interactions)
Once we agree they have such high velocities individually, then it's clear why their high angular momentum prevents them from accreting around the sun.
