# On gravitational waves of dark matter collisions

It is known that dark matter interacts gravitationally (and weakly in other ways as predicted by the WIMP model), and dark matter is present in the same space-time fabric as that of matter. When two dark matter ‘objects’ collide then wouldn’t the event produce gravitational waves? And since we know that dark matter is in greater abundance than matter, shouldn’t LIGO and other detectors be detecting,much more frequently, gravitational waves off dark matter collisions than collisions of just observable matter?

• But at least there is not merging.... – Alchimista Jan 12 '18 at 15:55
• The power radiated in gravitational waves is proportional to $\omega^6$. That means that in order to get strong gravitational radiation, you need systems that undergo extremely rapid and violent acceleration. Large, diffuse objects don't do that. – Ben Crowell Jan 15 '18 at 16:13
• This question seems to be interesting! You mean dark matter produced from the the motion of the galactic halo as a whole? Can you be clearer? @NaveenBalaji – SRS Apr 4 at 16:23
• @SRS I meant the dark matter as a whole and it's interaction in the way predicted by the WIMP model. – Naveen Balaji Apr 20 at 12:46

Strong gravitational waves come from dense massive objects like neutron stars. Normal matter collapses into dense objects, because its kinetic energy is converted to heat and radiated away. Dark matter does not interact electromagnetically. Therefore it never loses its kinetic energy and does not normally collapse to dense objects, but forms halos around galaxies.

• Thanks for your answer! Yup, DM indeed does not interact electromagnetically but we can’t think of a DM object’s gravitational collapse in the perspective of normal matter collapse since its mechanism of collapse is presently unknown. – Naveen Balaji Jan 12 '18 at 17:27
• DM does collapse; not to the same high densities as ordinary matter, but the 'halo' around a galaxy has a density several hundred times the cosmic average. – Kyle Oman Jan 15 '18 at 13:41
• @KyleOman Could you please elaborate on the reasons and mechanisms of the DM collapse into halos? – safesphere Jan 16 '18 at 1:28
• Sure, see my answer here physics.stackexchange.com/q/174977/11053 – Kyle Oman Jan 16 '18 at 6:04
• Your answer there repeats exactly what I stated above, DM "never loses its kinetic energy and does not normally collapse to dense objects, but forms halos around galaxies". I don't understand your objection, as I've never said that DM does not collapse at all. What I said was that DM does not collapse to dense objects, but does collapse to halos. Please explain. – safesphere Jan 16 '18 at 17:03

The previous answers correctly explain why dense massive objects are not expected to result from traditional weakly interacting massive particle (WIMP) models of dark matter. I want to add, however, that there are other dark matter models for which various sorts of gravitational waves (GWs) are expected, and in some of these cases existing GW studies can already help to constrain these models.

For example, if some fraction of dark matter consists of primordial black holes (PBHs), we could expect binary-inspiral GW signals potentially much like those seen by LIGO (depending on the mass range of the PBHs). arXiv:1707.01480 is a place to start learning about that. (In addition to reading this paper itself, you can check out the previous works it cites and use the INSPIRE database to find more recent works that cite it---and then do the same for any of those that interest you.)

Another possibility is that the dark matter could be part of a larger "dark sector" featuring strong (but non-dissipative) self-interactions. arXiv:1610.06931 discusses binary-inspiral GW signatures of "dark stars" that might be formed in this case.

Finally, dark sector models often feature first-order phase transitions in the early universe (for example, a dark confinement transition), which can produce stochastic GW backgrounds as opposed to binary-inspiral signals. A long review that discusses this possibility (among several others) just appeared today as arXiv:1801.04268, though it was arXiv:1504.07263 that first brought this possibility to my attention. Note, however, that such stochastic GW backgrounds tend to be too weak for LIGO to observe; future GW observatories such as eLISA are likely needed in order to test these possibilities.

Gravitational waves are a feature of general relativity but not of Newtonian gravity. For systems which are well-approximated by Newtonian gravity any gravitational waves are absurdly weak (the Earth-Sun system, for instance radiates about 200W). So to get detectible gravitational radiation requires systems which are not well-approximated by Newtonian gravity: systems where the gravitational field is very strong.

In order for the field to be strong, you require very dense concentrations of matter. If you start from a distribution of matter which is not dense, then you can get to a dense distribution only by shedding a lot of energy, and the way you do that is, loosely, by friction: you turn potential energy into kinetic energy and then kinetic energy into heat. To do that you need to be able to have inelastic collisions between particles of whatever stuff it is you want to condense (you need, for instance, an atom of your stuff to be able to collide with another atom of it and knock electrons off each other, or knock electrons into excited states, from where they radiate as they fall back into their ground states). And to get any reasonable rate of inelastic collisions requires that your stuff interact electromagnetically.

But dark matter, by assumption, does not interact electromagnetically. So if you have a big, sparse cloud of dark matter it has no real mechanism of losing enough energy to become a small, dense cloud. This means that it has no mechanism to get into a configuration where its gravitational field is strong, and thus no mechanism for producing gravitational radiation in quantities which are detectible.