# Why doesn't dark matter clump strongly in the center of galaxies, since it doesn't feel either radiation pressure or the Pauli exclusion effect?

Dark matter is described as being spread not only throughout a galaxy, but also around it in a halo of some sort that extends far beyond the visible parts of the galaxy...

In fact, dark matter haloes are often described as being twice or more the diameter of the visible galaxy, with a slightly higher, not lower density, towards the outer edge, which is why they are called haloes, not spheres...

But if dark matter is not (necessarily) affected by the Pauli Exclusion Principle or radiation pressure, nor any other effect or force that might keep the alleged particles from cramming together due to gravity, why is it not much more heavily concentrated in the centers of large masses (galaxies, clusters of galaxies, etc.)?

• This is actually a pretty good question, so I'm reluctant to downvote it, but it really needs to lose the editorializing in the final paragraph. "I don't understand it, so it must be wrong" really is a bad look. Commented Jul 13, 2022 at 15:54

The reason is the fact that dark matter is non collisional. The dark matter particles interact only gravitationally, they feel no pressure, right, but they also feel no drag! No drag, no friction, means that they can't dissipate energy.

Imagine a cloud of dark matter that starts very large and diffuse. Initially it has a very small kinetic energy $$K$$ and small negative potential energy $$U$$. If you let it evolve, initially gravity will make it collapse, but the virial theorem tells us that it will reach an equilibrium where $$U=-2K$$. This equation, plus the conservation of energy $$U+K=const$$ uniquely determines $$U$$ and $$K$$, as well as the radius of the cloud, that will be of the order of $$R \approx GM^2/U$$.

If dark matter could dissipate energy, the total energy would change and the cloud would shrink further, but since it can't, it is locked in viral equilibrium for the time being (or until it evaporates, but this is out of the scope of the question)

Regarding the actual density profile of the dark matter halo, which you suspect has been fitted to the data, the profile is often inferred from N-body simulations of dark matter. One famous example is the Navarro-Frenk-White profile

$$\rho(r)={\rho_0 \over {r \over R_s} \left(1+ {r\over R_s}\right)^2}$$

So, the shape is determined from simulation, while the two free parameters $$\rho_0$$ and $$R_s$$ must be instead fitted, because they vary for each halo. Mind that this is no "cheating", it is akin to fitting a law to the experimental data, which is done in every field of physics.

• Assuming no evaporation, would a dark matter cloud (very, very) slowly lose kinetic energy over time due to gravitational waves, and spiral in, like the process conjectured behind binary black hole merges?
– orlp
Commented Jul 13, 2022 at 23:49
• Great answer, I hope the OP accepts (!).
– pela
Commented Jul 14, 2022 at 8:36
• @orlp - You may well need a theory of quantum gravity to answer that. The gravitational wave losses would be so small that they might be quantum excluded. Commented Jul 14, 2022 at 10:24
• The big question in my mind, is how non-interacting dark matter gets gravitationally bound to galaxies in the first place (rather than staying diffuse or clumping independently). But since we don't know what "dark matter" is, that can't yet be answered. Commented Jul 14, 2022 at 11:37
• @nigel222 I think it's the other way around. Its not that dark matter is attracted to galaxies, but rather dark matter does its thing, clumping where it pleases, and then normal matter falls in the gravitational potential well of dark matter and forms galaxies. Without a dark matter halo keeping it together, a galaxy could not form Commented Jul 14, 2022 at 11:41