Heat is an abstract thermodynamic concept that does not depend on the particle species. For instance, the leading class of theory of dark matter is called "cold dark matter", and this literally refers to the temperature of the dark matter.
>The different theories on dark matter (cold, warm, hot) refer not to the temperatures of the matter itself, but the size of the particles themselves with respect to the size of a protogalaxy
That article is wrong. (More generally, phys.org cannot be trusted.) The cold/warm/hot absolutely refers to temperature, specifically whether the typical thermal speed is much less than (cold) or comparable to (hot) the speed of light.
Thermal speed depends on the mass of the particle at a given temperature, correct? Like a volume of hydrogen has a much higher thermal speed than the same volume of radon at the same temperature.
The article from Symmetry Magazine says the same thing as the Phys.org article:
>Light, fast particles are known as hot dark matter; heavy, slow ones are cold dark matter; and warm dark matter falls in between.
The dark matter in the early universe would have been at the same temperature whether of the "warm" or "cold" type, it is just that the speed of the "warm"/non-heavy types would have been too fast to have caused the clumping we see. Or at least that's how I understood it. But that Symmetry article is a good one as well.
If a heavy species and a light species are in thermal equilibrium in the early universe and decouple from everything else (because the interaction rate falls due to expansion) at the same time (i.e., same temperature), the heavy species cools faster with the expansion of the universe than the light one does. This is because the temperature of a relativistic gas cools like ~1/a while the temperature of a non-relativistic gas cools like ~1/a^2, where a is the expansion factor. Thus, in that simplified case, the heavier one really is colder, not just moving slower.
Now, it turns out there's an opposing effect where, depending on how the DM couples to normal matter, the heavier particle decouples earlier (and thus at a hotter temperature) because creation/annihilation have to stop once the temperature drops below the energy scale associated with the rest mass, and this effect can often dominate the previous one.
The thing that actually matters, functionally, (and thus the thing that is used to classify DM types) is the thermal velocity relative to the speed of the Hubble flow during structure formation. It is of course true that, as you say, at fixed temperature a species of low mass will have higher velocity than a species of high mass, but CDM and HDM are not at the same temperature due to the opposing expansion and decoupling effects mentioned above (among other things).
My original point, in response to andsoitis, was that heat is an abstract thermodynamic concept that does not depend on the particle species. The names "hot" and "cold" were not metaphorical, even if the boundaries between CDM and HDM are not literally drawn using a threshold temperature. For instance, per the symmetry article:
> “Even though the universe was very hot at the time, axions would have been very cold at birth and would stay cold forever, which means that they are absolutely cold dark matter.” Even though axions are very light, Graham says, “because they exist at close to absolute zero, the temperature where all motion stops, they are essentially not moving. They’re kind of this ghostly fluid, and everything else moves through it.”
This is why it's wrong for phys.org to say that "cold", "warm", and "hot" do not refer not to the temperatures of the matter itself. Likewise, even if "hard" and "soft" cheeses are formally defined by whether they are dried and aged (such that there could be a few "hard" cheeses that are softer than the hardest "soft" cheeses), it would be wrong to say "'hard' and 'soft' do not refer to the firmness of the cheese itself".
