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Suppose that dark matter is in the form of a Bose-Einstein Condensate, with a DeBroglie wavelength of ~10,000 LY. (There are some axion models of DM where the axions are in a BEC.) In this model, the wavelength of the dark matter particles is very large (e.g. spread out).

Would dark matter be captured by and accumulate in black holes and neutron stars in this model?

If the wavelength of the particles is very large, there is a low probability that a particle will be found to be located near a small object (the NS or BH). But (1) the immense gravitational field of the NS/BH should blueshift the wavelength of some particles to essentially bring those particles out of a BEC state, (2) if a very large number of particles are spread out over a large region, I would expect some particles would inevitably find themselves near enough the object to be captured, such that the capture rate should more or less average out and be similar to the capture rate of particle dark matter.

*I don't know much about Bose-Einstein Condensates, so if I am making some critical error in my thinking, please correct me.

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    $\begingroup$ Generally, the velocity of dark matter particles is too high to be captured by compact objects such as black holes. However, if the dark matter has some interactions with baryonic matter it can be slowed down sufficiently, by ambient baryons, to be captured by the compact object. $\endgroup$ – Virgo Dec 28 '17 at 17:54
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    $\begingroup$ Consider the mathematics of electron capture for a another case where particle with broad position distribution interacts with a spatially compact counterpart. $\endgroup$ – dmckee Dec 28 '17 at 18:07
  • $\begingroup$ Thanks @Virgo. The dark matter falling onto the surface of the black hole (and for the sake of argument let's say neutron star too.....we'll assume a neutron star with radius that is slightly larger than Schwatrzchild radius) will certainly be captured. There is work done on dark matter accumulation in the centre of the sun. $\endgroup$ – Bob Dec 28 '17 at 18:42
  • $\begingroup$ Thanks @dmckee. Is there a certain name given to these interactions, or any links you would recommend looking at? $\endgroup$ – Bob Dec 28 '17 at 18:44
  • $\begingroup$ After looking around, I want to say that this interaction (a neutron star or black hole moving through a BEC) may be similar to Rayleigh scattering (but gravitational capture, not just scattering....and more interesting due to blue shifting the wave(s?) as they approach the massive object)? $\endgroup$ – Bob Dec 28 '17 at 22:16
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The problem is as,@Virgo pointed out, DM should interact with itself or with baryonic matter to fall into the black hole. 

This is necessary since the falling process requires that DM should lose angular momentum. But since DM has no self interaction with itself and other particles it does not lose angular momentum. So in general BH do not capture DM. I am also not expert on BEC, but this the general case for DM. 

There s an article that calculated the allowed DM density if the DM could fall into the black hole. You can find it [here][1]

. But I couldn't see which DM model they considered to make this calculations.

The problem is highly self interacting DM models are not in the favor of the observational data.

[An article about it][2]

Of course, there are models with self interacting DM but i am not sure they are valid, or in BEC-DM model they are self interacting etc.   [1]: https://arxiv.org/abs/1002.0553   [2]: https://arxiv.org/abs/0806.2320

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