Does Dark Matter Have a Temperature?

[binis]

A black-body absorbs and emits radiation if heated, but it does not reflect or transmit radiation.What is the temperature of dark matter?

 

[Orodruin]

Can you be more specific? Asking what the temperature of dark matter is is like asking what the temperature of protons is.

 

[binis]

We have seen maps showing the distribution in our galaxy.If a piece of dark matter somewhere has temperature above of the absolute zero,shouldn't it radiate?

 

[Astronuc]

We have seen maps showing the distribution in our galaxy.If a piece of dark matter somewhere has temperature above of the absolute zero,shouldn't it radiate?

According to a CERN article -

Unlike normal matter, dark matter does not interact with the electromagnetic force. This means it does not absorb, reflect or emit light, making it extremely hard to spot. In fact, researchers have been able to infer the existence of dark matter only from the gravitational effect it seems to have on visible matter.

https://home.cern/science/physics/dark-matter

Astronomers know more about what dark matter is not than what it is.

Dark matter is dark: It emits no light and cannot be seen directly, so it cannot be stars or planets.

Dark matter is not clouds of normal matter: Normal matter particles are called baryons. If dark matter were composed of baryons it would be detectable through reflected light. [Gallery: Dark Matter Throughout the Universe]

Dark matter is not antimatter: Antimatter annihilates matter on contact, producing gamma rays. Astronomers do not detect them.

Dark matter is not black holes: Black holes are gravity lenses that bend light. Astronomers do not see enough lensing events to account for the amount of dark matter that must exist.

https://www.space.com/20502-dark-matter-universe-mystery-infographic.html

One could ask - is dark matter in thermal equilibrium with matter in its vicinity?

 

[Orodruin]

According to a CERN article -

https://home.cern/science/physics/dark-matterhttps://www.space.com/20502-dark-matter-universe-mystery-infographic.html

One could ask - is dark matter in thermal equilibrium with matter in its vicinity?

An even more relevant question is ”is dark matter in kinetic equilibrium with itself”. Without the answer to that question, it becomes quite irrelevant to talk about a temperature at all.

We have seen maps showing the distribution in our galaxy.If a piece of dark matter somewhere has temperature above of the absolute zero,shouldn't it radiate?

Dark matter, generally, does not radiate because there is no coupling to electromagnetism.

 

[kimbyd]

You can define the temperature of dark matter by the average kinetic energy of dark matter particles far from gravity wells. And that temperature is necessarily very, very low.

Neutrinos are an example of hot dark matter. They are still very "cold" in the sense that their current temperature is lower than that of the CMB. But because of their low masses, even that small temperature is enough that neutrinos were unable to clump into structures like galaxies early-on.

Because dark matter does clump to form structures, it must have an even lower temperature. Most simple dark matter models result in a vanishingly-small temperature. It's an open question whether dark matter might be "warm", in the sense that it has enough temperature to affect how dark matter clusters.

But regardless, no amount of temperature would allow dark matter to radiate. It simply doesn't couple to radiation.

 

[ohwilleke]

There is a virial theorem that, subject to some pretty modest conditions you must assume, relates average kinetic temperature to observable gravitational potential, even in the case of dark matter that is maximally sterile in the sense that it doesn't interact by any force other than gravity.

There is also a theorem that relates dark matter particle mass in a simple single type of particle dark matter model to thermal freezeout temperature and from there to average kinetic energy which can be converted to temperature.

You can also relate average kinetic energy, which translated to mean velocity in the case of a single type of particle dark matter model, to the scale at which we you structure in clumpings of mass, independent of the thermal or non-thermal nature of dark matter particles.

In a nutshell, the higher the mean velocity, the more homogeneously matter will be spread out and the less it will clump. The lower the mean velocity the more structure you will get in matter clumping producing, for example, more satellite galaxies and internal galaxy vicinity structure.

If you have a thermal freezeout model, you need something on the order of 2-9 keV mass particles at the low end (called warm dark matter), and maybe 100-1000 GeV mass particles at the high end (cold dark matter), to get the right level of structure. This is a six or seven order of magnitude range, but at least it provides some boundaries. If you get down to 1-10 eV or less in a thermal freezeout model you have hot dark matter which isn't consistent with what we see.

But, in a non-thermal freezeout model, like axion dark matter, the mean velocity which drives the amount of matter clumping and structure in the observable universe, and the mass of the dark matter particle in question, decouple. You can have axions that are a fraction of 1 eV in mass that still reproduce the right magnitude of large scale structure if they move slowly enough.

The bottom line, anyway, is that it is possible, at least in a model dependent way, to determine dark matter temperature from observables, but one has to understand that temperature really just corresponds to mean velocity or mean kinetic energy, and not to thermal processes that are ultimately electromagnetic in nature.

 

[kimbyd]

When people refer to the dark matter temperature, they're referring to its average kinetic energy when far from gravitational potential wells.

The velocity of dark matter within gravitational potential wells is entirely dominated by the depth of those wells. That temperature tells us about those gravity wells, not the behavior of dark matter.

The temperature of dark matter, however, does have a large impact on how those potential wells grew in the first place. If the kinetic energy is too high, then the particles won't get bound gravitationally: they'll keep moving. The particles that do get bound will still have kinetic energies determined by the size of the well, but how many and when they get bound are affected by their temperature.

So there's a lot of potential to learn about the temperature of dark matter by observing the growth of structure, especially in the early universe.

 

[Buzz Bloom]

The discussion seems to be saying with certainty that dark matter cannot have a relationship to some unknown form of radiation, that is radiation unrelated to photons. Is this correct? If this is wrong, and there does exist an unknown form of non-photon radiation, then the dynamics of dark matter may have a means to radiate away some its energy over time.

 

[PeterDonis]

The discussion seems to be saying with certainty that dark matter cannot have a relationship to some unknown form of radiation

Not quite, no.

First, the comment by @Orodruin in post #5 that dark matter does not radiate does not take into account gravitational radiation. We would expect dark matter to emit gravitational radiation since we know it interacts gravitationally. But gravitational radiation emits energy from ordinary systems (i.e., systems that are not undergoing violent events like black hole mergers) at much, much too slow a rate to affect the dynamics of dark matter on time scales we can observe.

Second, if there were some other unknown form of radiation that dark matter could emit, and it could emit energy at rates similar to that of electromagnetic radiation, then dark matter would clump gravitationally the way ordinary matter does. But dark matter does not do that. The reason we believe there is dark matter is that we see gravitational effects on galaxies and galaxy clusters (and other more esoteric effects on the dynamics of the universe as a whole) that can only be explained by a form of matter that does not clump gravitationally the way ordinary matter does, but remains largely diffuse. That alone is enough to tell us that even if there is some unknown form of radiation that dark matter can emit, it doesn't emit enough energy that way to make a difference.

 

[Buzz Bloom]

Second, if there were some other unknown form of radiation that dark matter could emit, and it could emit energy at rates similar to that of electromagnetic radiation, then dark matter would clump gravitationally the way ordinary matter does. But dark matter does not do that.

Hi @PeterDonis:

Your response seems quite convincing. I still have an odd feeling of uncertainty because whatever unkown dark matter-radiation interaction might exist, it will be something different than electromagnetic. Therefore it seems to be possible that the rate of interaction might be very much smaller than the matter-photon interaction, so astronomers may not have had enough time to notice such a small effect of such a reaction.

ADDED
It has occurred to me that if my hypothesis is correct, then the age of a galaxy might have a correlation related to the distribution of dark matter calculated from star orbits.

Regards,
Buzz

 

[PeterDonis]

whatever unkown dark matter-radiation interaction might exist, it will be something different than electromagnetic. Therefore it seems to be possible that the rate of interaction might be very much smaller than the matter-photon interaction, so astronomers may not have had enough time to notice such a small effect of such a reaction.

This is of course possible, but it can't make any difference to the dynamics of dark matter on the time scales we have observed (meaning, time scales up to the current age of the universe). We know that because of the lack of clumping of dark matter. So it's not that this possibility has been ruled out, it's that the possibility is irrelevant to the questions cosmologists are trying to figure out the answer to.

 

[PeterDonis]

my hypothesis is correct, then the age of a galaxy might have a correlation related to the distribution of dark matter calculated from star orbits.

Why do you think this? Note that whatever unknown radiation other than EM or gravitational dark matter might be capable of emitting, it cannot have affected the dynamics on the time scales we can observe.

 

[Buzz Bloom]

it cannot have affected the dynamics on the time scales we can observe.

Hi @PeterDonis:

Here is my thought, which I understand to be entirely hypothetical.

When a galaxy forms, the spatial distribution of atomic matter and dark matter might be more-or-less similar to other galaxies forming at a similar time. Suppose that during the time between formation and now, some of the dark matter looses kinetic energy to an unknown kind of radiation, but much less than the amount of kinetic energy that is loss from atomic mass to photons. Suppose the lost of kinetic energy affects the distribution of the matter and dark matter radially from the center of a galaxy's mass. If it is found that that groups of galaxies, each group based on their ages being in a distinct age range is observed to have somewhat similar radial patterns of matter and dark matter, then it may be possible to deduce the rate at which dark matter loses kinetic energy.

Regards,
Buzz

 

[PeterDonis]

Here is my thought, which I understand to be entirely hypothetical

Your proposed model assumes that when a galaxy forms, the distributions of both matter and dark matter are about the same. That is not expected to be true.

As far as we can tell, structure formation, i.e., gravitational clumping, in our universe happened top down. First the mostly uniform distribution of matter had some random fluctuations in it (which, if inflation models are correct, came from quantum fluctuations in the inflaton field). Then those fluctuations started to form "clumps" on very large scales, like galaxy superclusters; then random fluctuations within those clumps started to clump further into galaxy clusters; then the clumping got down to the level of galaxies; then it got down to the level of stars and planets.

But dark matter would not have followed this pattern, because it is unable to clump at anywhere near the same rate as ordinary matter. At the time of galaxy formation, dark matter would not even have clumped to that level at all, it would still be mostly uniform across the universe, or maybe it would have clumped some at the level of superclusters or clusters, but from the standpoint of an individual galaxy forming from a clump of ordinary matter, the dark matter distribution would be pretty much uniform. So even if dark matter were emitting some kind of unknown radiation at some slow rate, that emission wouldn't tend to bind it more closely to any particular galaxy. On average, the emission would have no effect on its distribution; it would just add a tiny uniform background density of this unknown radiation to the uniform background density of dark matter.

That said, it would of course be interesting to look at galaxy properties by age and see if there is any variation in, for example, rotation curves (which are the primary indicator we use to look for dark matter). But I would not expect the pattern you describe to show up, for the reasons I gave above.

 

[ohwilleke]

The discussion seems to be saying with certainty that dark matter cannot have a relationship to some unknown form of radiation, that is radiation unrelated to photons. Is this correct? If this is wrong, and there does exist an unknown form of non-photon radiation, then the dynamics of dark matter may have a means to radiate away some its energy over time.

To the extent that is said with certainty it is because one of the more restrictive definitions of radiation (which is a very common sense in which the word is used in both high energy physics and in cosmology) is the emission of photons.

If a particle is emitting something other than photons, in this restrictive definition of the term, whatever that particle is doing, it isn't emitting radiation. It may be emitting gravitational waves or gravitons. It may be generating a "dark photon" field. But it isn't emitting radiation.

 

[Buzz Bloom]

But it isn't emitting radiation.

Hi @ohwilleke:

I apologize that my ignorance used a technical term incorrectly. Would you accept instead the usage of the term "dark radiation"? If such a phenomenon as I discussed exists, then I would assume that the dark radiation would be a component of the Friedmann equation term Ω_r (or as it appears:

Ω_r/a⁴),​

in the same manner as the dark matter appears in

Ω_m/a³).​

Regards,
Buzz

EDITED TO FIX EXPONENT

 

[PeterDonis]

If such a phenomenon as I discussed exists, then I would assume that the dark radiation would be a component of the Friedmann equation term Ω_r (or as it appears:

Ω_r/a⁴),​

in the same manner as the dark matter appears in

Ω_m/a²).​

Dark matter, like ordinary matter, would appear as $a^{-3}$, not $a^{-2}$. In terms of the Friedmann equation, "matter" means stress-energy with negligible pressure, which implies the $a^{-3}$ dependence, and "radiation" implies something with $p = \rho / 3$ (pressure 1/3 of energy density), like a photon gas but not necessarily composed of photons (any massless particle will do), which appears as $a^{-4}$. The usual component that appears as $a^{-2}$ in the version of the Friedmann equation you refer to is spatial curvature.

 

[Buzz Bloom]

Hi @PeterDonis:

My apologies for carelessness. I usually scan over a post before posting it, but I must have scanned too fast and missed changing the "2" to a "3". I will make an edit to fix it.

Regards,
Buzz

 

[Imager]

@PeterDonis Wasn't sure, were you saying the if quantum fluctuations from Inflation did or didn't effect Dark Matter (clumping at a small level)?

 

[PeterDonis]

were you saying the if quantum fluctuations from Inflation did or didn't effect Dark Matter (clumping at a small level)?

The fluctuations would affect clumping of all types of matter to some extent, but how much would depend on how easily each particular type of matter clumps. Dark matter clumps much less easily than ordinary matter because it cannot radiate EM radiation, which is how ordinary matter radiates away large amounts of energy as it clumps (clumping requires a system to radiate away energy in order to become more tightly bound).

 

[snorkack]

Do we see temperature of dark matter, or speed of dark matter? Because temperature has the dimension of energy, not energy divided by mass.
What is the average speed of dark matter in the solar neighbourhood?
Does dark matter behave like it consisted of particles of equal mass, or does dark matter consist of particles of different masses whose ratio varies with neighbourhood and gravity potential?

 

[Orodruin]

Do we see temperature of dark matter, or speed of dark matter? Because temperature has the dimension of energy, not energy divided by mass.

We do not "see" either because we do not know many things about dark matter, including what it is.

What is the average speed of dark matter in the solar neighbourhood?

It is generally assumed that the dark matter is at overall rest relative to the galaxy, which would make the average speed relative to the Sun the same as the Sun's orbital speed in the galaxy. Around 250 km/s. However, there are some alternative ideas out there such as dark matter streams. We simply do not know.

Does dark matter behave like it consisted of particles of equal mass, or does dark matter consist of particles of different masses whose ratio varies with neighbourhood and gravity potential?

We do not know. The behavior would be similar whether dark matter consisted of a single particle type or several with different masses. It is an active field of investigation. The general simplifying assumption in many dark matter model is that the dark matter consists of a single particle (or, when there is a more extensive dark sector, that a single particle completely dominates the dark matter contribution).

Figure out the answers to those question and show it experimentally and you win a Nobel prize.

 

[ohwilleke]

A discussion of the relationship between temperature and average speed is explained here.

The dimensional issue is that you need to make an assumption about the mass of the particle to convert temperature to average speed. For any given particle mass, average speed squared is proportionate to temperature with some physical constants giving you the number of you can actually calculate.

The visible dynamics we observe and use to infer speed or temperature are basically a function of average speed, rather than kinetic temperature per se.

What is typically done in practice, is to use a canonical established relationship between particle mass and average velocity for a subtype of dark matter model called "thermal relic" dark matter that basically assumes that particles of a particular mass decouple from the rest of the stuff in the universe and gain their characteristic properties at a particular temperature of the universe as it cools down, and then stays that way more or less forever. As the linked analysis spells out, the analysis is a bit involved from a basic level and equally important relies upon model dependent assumptions.

But the fact actual kinetic temperature is model dependent doesn't really matter when you are just using "temperature" as a convenient tool for comparing different dark matter particle models on an apples to apples basis, or crudely estimating when in a Big Bang cosmology you would expect thermal relic dark matter to emerge, rather than trying to calculate anything observable from it.

 

[snorkack]

For example, 1 bar of air at 290 K has the same density that 1 bar of hydrogen at 20 K would have. If what you observe is density, its distribution and local gravitational potential, you cannot tell apart warm air from cold hydrogen - but you can measure the expression T/M.
For dark matter, do we observationally know the value of T/M in solar neighbourhood, and its distribution around Milky Way?

 

[Orodruin]

No.