<p>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.</p>
<p>Imagine a cloud of dark matter that starts very large and diffuse. Initially it has a very small kinetic energy <span class="math-container">$K$</span> and small negative potential energy <span class="math-container">$U$</span>. If you let it evolve, initially gravity will make it collapse, but the <a href="https://en.m.wikipedia.org/wiki/Virial_theorem#In_astrophysics" rel="noreferrer">virial theorem</a> tells us that it will reach an equilibrium where <span class="math-container">$U=-2K$</span>. This equation, plus the conservation of energy <span class="math-container">$U+K=const$</span> uniquely determines <span class="math-container">$U$</span> and <span class="math-container">$K$</span>, as well as the radius of the cloud, that will be of the order of <span class="math-container">$R \approx GM^2/U$</span>.</p>
<p>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 <a href="https://en.m.wikipedia.org/wiki/Mass_segregation_(astronomy)" rel="noreferrer">evaporates</a>, but this is out of the scope of the question)</p>
<p>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 <a href="https://en.m.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_profile" rel="noreferrer">Navarro-Frenk-White profile</a></p>
<p><span class="math-container">$$ \rho(r)={\rho_0 \over {r \over R_s} \left(1+ {r\over R_s}\right)^2}$$</span></p>
<p>So, the shape is determined from simulation, while the two free parameters <span class="math-container">$\rho_0$</span> and <span class="math-container">$R_s$</span> must be instead fitted, because they vary for each halo. Mind that this is no &quot;cheating&quot;, it is akin to fitting a law to the experimental data, which is done in every field of physics.</p>

CC BY-SA 4.0
2022-07-13T23:49:08.233Z
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
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2022-07-14T08:36:16.460Z
Great answer, I hope the OP accepts (!).
pela
CC BY-SA 4.0
2022-07-14T10:24:22.107Z
@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.
Martin Bonner supports Monica
CC BY-SA 4.0
2022-07-14T11:37:33.590Z
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.
nigel222
CC BY-SA 4.0
2022-07-14T11:41:57.893Z
@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
Prallax
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2022-07-14T12:40:04.177Z
How does angular momentum factor into this virial equilibrium? Or is the assumption that the initial angular momentum is also very small?
Seb
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2022-07-14T12:45:19.157Z
@Seb Initial angular momentum might or might not be present for this reasoning to hold. In case of angular momentum, the resulting halo would not be spherical, but oblate. A ball of gas, that is able to dissipate and radiate away the energy, still cannot get rid of angular momemum and flattens to a disk perpendicular to the total angular momentum. That's how disk galaxies form
Prallax
CC BY-SA 4.0
2022-07-15T00:52:47.443Z
It seems to me that it ought to be possible for dark matter to dissipate energy by gravitationally coupling to normal matter. But I guess this would probably be a rather slow process.
Ilmari Karonen
CC BY-SA 4.0
2022-07-13T06:30:45.107Z
2022-07-14T00:53:18.760Z
2022-07-14T00:53:18.760Z
Prallax
<p>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...</p>
<p>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...</p>
<p>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.)?</p>

CC BY-SA 4.0
2022-07-13T15:54:33.843Z
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.
Nobody
<observational-astronomy><astrophysics><cosmology><dark-matter>
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?
Kurt Hikes
# 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?

(Asked by: username_0 on 2022-07-13)

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.)?

**Tags:** observational-astronomy, astrophysics, cosmology, dark-matter
> **Comments:**
> **username_1**: 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.  

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## 1 answers

### Answer by username_2 on 2022-07-13. Score: 34

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](https://en.m.wikipedia.org/wiki/Virial_theorem#In_astrophysics) 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](https://en.m.wikipedia.org/wiki/Mass_segregation_(astronomy)), 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](https://en.m.wikipedia.org/wiki/Navarro%E2%80%93Frenk%E2%80%93White_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.

> **Comments:**
> **username_3**: 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?  
> **username_4**: Great answer, I hope the OP accepts (!).  
> **username_5**: @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.  
> **username_6**: 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.  
> **username_2**: @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  
> **username_7**: How does angular momentum factor into this virial equilibrium? Or is the assumption that the initial angular momentum is also very small?  
> **username_2**: @Seb Initial angular momentum might or might not be present for this reasoning to hold. In case of angular momentum, the resulting halo would not be spherical, but oblate. A ball of gas, that is able to dissipate and radiate away the energy, still cannot get rid of angular momemum and flattens to a disk perpendicular to the total angular momentum. That's how disk galaxies form  
> **username_8**: It seems to me that it ought to be possible for dark matter to dissipate energy by gravitationally coupling to normal matter. But I guess this would probably be a rather slow process.  

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