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I keep reading that cusps are one of the most "robust" predictions of N-body simulations of dark matter halos. But papers I've found on the topic make it sound like these simulations are complicated and slow and that the cusps are just an observed result of the simulations rather than that the cusps have some understandable physical origin. But my immediate reaction was that the cusps' origin is trivial (just the result of phase-space considerations) and that interaction-less dark matter simulations should be one of the easiest things in the world.

I remember writing a program to simulate non-interacting particles orbiting each-other with an inverse square law on an old PC over a decade ago, and I recall being able to get a pretty good picture of the density profile by tracing the paths of just a few particles. This only took a minute or two on a very slow PC. Indeed I remember something of a cusp being obvious, simply because the orbits of each particle tended to intersect near the CM, an effect that overrode the countervailing fact that individually each spent less time near the CM.

In fact, even without doing a simulation, I would assume this would be the case because Keplerian motion clearly indicates that the time spent near the CM drops close to linear in R while volume goes as R^3. Anyway, I'm just wondering if these observations are basically correct, or if the origin of the cusps is somehow more obscure/complicated.

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  • $\begingroup$ My N-bodies made a swarm! $\endgroup$ – Kevin Kostlan Nov 15 '13 at 19:37
  • $\begingroup$ So, is your question: What are the origins of cuspy dark matter halos? $\endgroup$ – astromax Dec 6 '13 at 21:19
  • $\begingroup$ @astromax: what about my question is unclear? I am asking about the origins of the cusps (as opposed to cores) in dark matter halos. Not about the origins of the halos themselves. As I say in my question, it seems like the cuspy prediction is naively obvious and shouldn't require difficult simulations. I'm wondering if this is true or if there is some complication I am not aware of. $\endgroup$ – user1247 Dec 6 '13 at 21:39
  • $\begingroup$ @user1247 Well, for one you don't actually ask a single question. Additionally, some of these simulations have millions or even billions of particles in them - why is it 'obvious' to you that you should be seeing cusps as opposed to cores. I may have a few answers once I know what you question is, because this is part of what I study. $\endgroup$ – astromax Dec 6 '13 at 21:49
  • $\begingroup$ @astromax: the last line of my post is a question. Additionally, I think I give a very detailed context in my post for exactly what I am asking, and why it is obvious to me that I should be seeing cusps. In fact, as I said in my post, I DID see cuspiness myself in my own small-N simulations trivially done on an old computer. Furthermore, in my post I mentioned a pretty trivial theoretical argument for cuspiness. My question, again, are the above observations correct, or not? If not, why not? $\endgroup$ – user1247 Dec 6 '13 at 22:06
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Wikipedia has this entry about the cuspy halo problem

"The cuspy halo problem arises from cosmological simulations that seem to indicate cold dark matter (CDM) would form cuspy distributions — that is, increasing sharply to a high value at a central point — in the most dense areas of the universe. This would imply that the center of the Milky Way, for example, should exhibit a higher dark-matter density than other areas. However, it seems rather that the centers of these galaxies likely have no cusp in the dark-matter distribution at all. "

I think the last sentence could be interpreted thus "... it seems from actual astronomical observations and interpretations/models based on observations that... there should not be a cusp in DM density at the centre of a galaxy".

Thus it seems to me that your simulation (for whatever reason) agrees with more sophisticated simulations in predicting a cusp whereas actual astronomical observations suggest that there should not be a cusp.

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  • $\begingroup$ The most popular explanation is that there is no cusp due to the presence of baryons which need hydrodynamic simulations to be accurately described. $\endgroup$ – Virgo Aug 26 '15 at 2:11
  • $\begingroup$ @physicsphile So baryons influence DM? $\endgroup$ – steveOw Sep 1 '15 at 13:34
  • $\begingroup$ Yes, via their gravitational attraction. $\endgroup$ – Virgo Sep 2 '15 at 0:55
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Cusps are an obvious consequence of the usual DM models to me too.

It seems that there are so many problems with dark matter theory that something is obviously wrong.

We have the cusp problem, the lack of DM in the nearby region of of our galaxy, the failure to find any in experiments, and more.

By far the biggest problem with DM though is the complete lack of its prediction, given that we have so many smart theoreticians! Ditto of course on the dark energy front.

I really like how observational astronomy is working on the third decimal place of DM abundance. To physics however there is not even an acknowledgment of any problem.

I thought I was commenting ...

To turn this into an answer,

There is no need for complicated models to model the cusps, they come about when making models for the entire matter -DM structure.

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  • $\begingroup$ I think those extra comments are not in line with stack exchange conventions and I suggest you remove them. $\endgroup$ – Virgo Sep 17 '14 at 2:38

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