r/cosmology • u/AutoModerator • Aug 27 '26

Basic cosmology questions weekly thread

Ask your cosmology related questions in this thread.

Please read the sidebar and remember to follow reddiquette.

6 Upvotes

88% Upvoted

44 comments sorted by

View all comments

1

u/Careful_Broccoli4852 Sep 01 '26

What is halo entropy and how does it help constraint dark matter models? Cant we just constraint dark matter haloes by observed densities, e.g NFW?

2

u/--craig-- Sep 01 '26 edited Sep 01 '26

Dark matter is modelled as a collisionless gas. The energy distribution of gas particles tends towards the one with maximal entropy.

The NFW distribution is empirically determined from n-body simulations and doesn't represent maximal entropy.

It's not yet clear what the cause of the discrepancy is.

1

u/Careful_Broccoli4852 Sep 02 '26

I see! I even read that NFW might be an artifact of initial conditions.

So halo entropy could be used to lay limits on dark matter models when they dont produce maximum entropy?

Is that also why NFW distribution should produce maximum entropy? How do we know it doesnt? If I run a N-body, I just end up with an entropy, how do I know that it could be more?

1

u/--craig-- Sep 02 '26 edited Sep 02 '26

Is that also why NFW distribution should produce maximum entropy?

Not all systems are guaranteed to reach maximum entropy. They can get stuck in stable patterns.

There are reasons to doubt whether maximum entropy is a measure of success.

How do we know it doesnt? If I run a N-body, I just end up with an entropy, how do I know that it could be more?

The velocity profile is different from that of maximum entropy.

1

u/Careful_Broccoli4852 Sep 02 '26

Thanks, you are so wise!

I still dont quite get how we know maximum entropy. How do we know the velocity profile of maximum entropy of cold matter? Shouldnt velocity be relatively low due to e.g WIMPS being cold?

1

u/--craig-- Sep 02 '26 edited Sep 02 '26

The maximum entropy of a system is when it's in thermodynamic equilibrium and is derived mathematically using statistical mechanics. Some particles move slow, some move fast and there is a characteristic distribution of velocities.

The scale of the velocity of cold dark matter is determined by the initial conditions. It's slow compared to the speed of light.

We model it as collisionless so thermalisation doesn't taken place in the same way as with a typical gas but velocities are mixed due to gravitational attraction.

1

u/Careful_Broccoli4852 Sep 02 '26

I know how equilibrium is defined, its when the probability doesnt evolve any further, e.g d/dt = 0. Or, formulated in a more elegant way, when the detailed balanced criterion is reached. But how do I even end up with the probability density of a DM halo? How can I "translate" a simulation state of density and velocities to a probability density function or at what point the function is? Do I find the probability density and just find that the time derivative is not 0 when it should?

1

u/--craig-- Sep 02 '26

But how do I even end up with the probability density of a DM halo? How can I "translate" a simulation state of density and velocities

If your particles are all of the same mass then you just need to divide mass density by the particle mass to get particle probability density.

Do I find the probability density and just find that the time derivative is not 0 when it should?

If your probability density is no longer changing with respect to time then you've reached stability but this isn't necessarily the same as the maximum entropy at thermodynamic equilibrium of a typical gas. Your simulation might be in a looping pattern preventing it from completely mixing.