# How hot is dark matter?

1. Aug 20, 2014

### !Jon Snow!

Dark matter can't radiate heat (i.e. no electromagnetic energy).

1. Might it retain the original temperature at the moment of its creation?

2. If temperature is directly related to pressure and both are inversely related to volume, then would cosmic expansion mean that dark matter is as cool as the cosmic microwave background radiation?

3. Can the temperature of a given region of dark matter be inferred based its inferred volume and mass?

4. Does the inability of dark matter to radiate heat imply that there can be no dark matter "black holes"?

2. Aug 20, 2014

### phinds

No, the inability of dark matter to interact other than gravitationally means it cannot "clump" and therefore cannot form planets or black holes. You might find it interesting to Google "the bullet cluster".

3. Aug 20, 2014

### marcus

those strike me as all good questions. There's a question of what is meant by temperature. For a cloud of particles, average kinetic energy, either relativistic or 1/2 mv2 would work.

DM doesn't have some other features we associate with temperature so one has to think about what it means.

As you may have been suggesting, expansion itself drains momentum and kinetic energy from particles. Because in whatever direction its going, the distance to what's out there is increasing. So when it gets there its motion relative to the surrounding space is "redshifted" It's kinetic energy is redshifted.

So people assume that DM has been cooled a lot just by expansion of distances without factoring in any idea of "pressure" which would be problematical regarding DM. People talk about "cold" DM (meaning non relativistic speed) and that enters into the standard cosmic model's name: LambdaCDM.
It doesn't have a temperature in the usual sense so "cold" is, I think, just a jargon term for "slow-moving"

I think you are right to assume that DM particles (whatever they turn out to be) were probably "hot" (moving at relativistic speed) when they came into existence in very early U.

I don't know about DM black holes… Could some have formed in the extremely dense conditions of the early universe?
Wouldn't some DM be falling into existing BH now as we speak? Since there is so much of the stuff around. I can't imagine how you could have PURE DM black holes, however. What could prevent a diversity of stuff from falling in, including ordinary but also traces of dark?

Hopefully other people will respond. I think these are interesting questions but I don't know final answers to them.

4. Aug 20, 2014

### WannabeNewton

No. The temperature of any thermalized non-relativistic fluid (which is what cold dark matter is plus the fact that it does not interact electromagnetically) in an expanding universe has to decrease by a specific power of the scale factor.

No. Radiation cools off at a different rate than non-relativistic fluids.

Well you need to know the energy density which is the distribution of the mass over the volume. From this you can get the temperature using kinetic theory.

No.

5. Aug 20, 2014

### Chronos

Just an aside on DM and black holes. The primary feeding mechanism of a black hole is via its accretion disk. The accretion disk consists of gravitationally captured matter orbiting the black hole and awaiting its turn to be consumed. An important element in this process is the ability to shed kinetic energy. Because DM is collisionless, and unable to shed kinetic energy by any known means, it is not expected to be found in accretion disks. Hence, DM contributions to black hole masses are thought to be negligible. See http://www.nature.com/nature/journal/v469/n7330/full/nature09695.html; where a lack of correlation is observed between SMBH mass and dark matter content of the mother galaxy.

Last edited by a moderator: May 6, 2017
6. Aug 20, 2014

### Staff: Mentor

Marcus, would dark matter be cooled by expansion by approximately the same factor as the CMB was?

7. Aug 20, 2014

### George Jones

Staff Emeritus
In the early universe, dark matter matter was coupled to everything else, i.e, in thermodynamic equilibrium with the other stuff. Dark matter probably decoupled while non-relativistic and well-modeled by a Maxwell-Boltzmann. Once decoupled, expansion of the universe only changes the temperature of the distribution function, not the type, so this distribution function can used to describe the evolution of temperature for dark matter from decoupling until now.

For non-relativistic matter, temperature scales as the inverse of the square of the scale factor. a quick hand-waving way to see this is to consider the adiabatic expansion of an ideal gas that only has three translation degrees of freedom,

$$\mathrm{constant}= TV^{\gamma - 1} = TV^{\frac{2}{3}} = T \left(a^3\right)^{\frac{2}{3}}$$
No. The temperature of radiation (including CMB) scales as the reciprocal of the scale factor, which is different the from what I "derived" above. See also WannabeNewton's previous comment,

Last edited: Aug 20, 2014
8. Aug 21, 2014

### Chalnoth

Not quite. It still cools, through two effects:
1. Dark matter that is not yet orbiting a gravitational potential, but is moving between galaxies, is effectively slowed due to the expansion. Basically, if it's moving at a velocity v to the right according to us, then after a while it will catch up to parts of the universe that are, to us, moving away at a velocity of v/2. So now this bit of dark matter's velocity compared to the local matter is only v/2.
2. Dark matter in gravitational potentials slowly cools as the particles of dark matter still experience gravity, and through gravity transfer momentum to one another. Every once in a while, they randomly impart enough momentum to one WIMP that that WIMP is able to escape the galaxy. This process is quite slow, however.

No. This is only true for an ideal gas, which has some rather peculiar properties related to matter. Dark matter effectively exerts zero pressure (because it doesn't interact with much of anything). The ideal gas law doesn't apply.

No. You can get at it from the depth of the gravitational well it inhabits, and how spread out it is. The temperature, in this case, is directly related to the orbits of the individual WIMPs within the gravitational potential well.

Almost certainly not yet. Maybe in the far, far future. But all of the dark matter might decay before a single black hole is formed solely from dark matter.

Dark matter does, however, fall into existing black holes, albeit rather slowly (black holes are small and rather hard to hit).