From: "Roland H."
Date: 18 Sep 2008
Q If the dark matter behaves like a gas cloud of particles centered on the galactic center, it should be steadily consumed by the black hole at the galactic center. Is there any estimation of the consumption rate and is it comparable to the consumption of ordinary matter by the black hole?
A That's right - dark matter should be absorbed alongside ordinary matter by the supermassive black hole in the galactic center. It should not be absorbed as quickly as ordinary matter, however.
To understand this, we need to consider how ordinary matter falls into black holes. Gas falling into the black hole forms an accretion disk: a rotating, disk-shaped cloud of hot gas. The disk is heated enormously by friction within this cloud, as all the gas tries to cram into a very tiny volume. The hot gas releases vast amounts of energy in the form of X-rays and other radiation. causing it to lose orbital energy and spiral inward to lower orbits around the hole. The hot gas eventually falls in entirely.
The difference comes from the very property that makes dark matter "dark": it's lack of interaction with ordinary matter (or, in fact, with other dark matter). This means that dark matter particles cannot easily lose energy - they don't experience significant friction or emit radiation. This means that dark matter does not join the accretion disk, instead remaining in relatively large orbits around the galactic center. Since it cannot lose energy as quickly, dark matter is expected to accrete into the black hole much more slowly than ordinary matter.
For further details on this subject, you may find the following links interesting:
Thanks for the question!
Particle Cosmology Group
University of California - Berkeley