# Why aren't neutron stars full of dark matter?

Dark matter interacts with the gravitational force right? Well, unlike black holes, neutron stars are actually visible, and they're an enormous gravitational sink, so dark matter should collect to them.

But if all that is true, which it seems to be, why haven't astronomers detected or used neutron stars to detect dark matter?

• Recent observations are being analyzed to determine whether a neutron star's radial density is consistent with (or not consistent with) the possible existence of dark matter at the core. It's an open question. – Carl Witthoft Aug 10 at 13:20
• I might add that "Dark matter" is simply a term applied to stuff that we don't know what it is, or if it even exists. It's still possible that our current understanding of forces is incomplete. – Carl Witthoft Aug 10 at 13:20
• Neutron stars may not be big enough to slow down dark matter particles to the point where they are gravitationally captured. OTOH, they might be. Last I looked we had little idea of the velocity profile (hot vs cold) of dark matter, if it exists. – Wayfaring Stranger Aug 10 at 15:18
• "they're an enormous gravitational sink" -- Not really; neutron stars have masses of a few times that of the Sun, so they're no more of a "gravitational sink" than many stars are. – Peter Erwin Aug 11 at 11:41
• And "dark matter should collect to them" -- only if the dark matter particles were not moving themselves. – Peter Erwin Aug 11 at 11:46

## 2 Answers

Yes, neutron stars might actually accumulate weakly interacting dark matter and this allows some observational constraints on its nature. Basically, the temperature and continued existence of neutron stars places bounds on the density and interaction cross-section of dark matter.

A dark matter particle that does not interact with matter will just have its trajectory bent by the gravity field of a heavy object, so most unbound particles will just swoop past on a hyperbolic trajectory. But as discussed in (Adams & Laughlin 1997), if there is some matter-dark matter interaction then the particle may scatter from a matter particle and now have less than escape velocity. This way white dwarfs and neutron stars would indeed accumulate dark matter in their cores. The rate of accumulation is proportional to $\rho v \sigma$ where $\rho$ is the dark matter density, $v$ the average relative velocity and $\sigma$ the cross section. Adams & Laughlin estimate that a white dwarf star would accumulate its own mass in $10^{25}$ years, but this is going to be depend on the cross section (if it is too small the dark matter will pass through) which is at present unknown.

Were this accumulation the only thing happening it would eventually make white dwarfs and later neutron stars implode. However, dark matter is plausibly a mix of particles and antiparticles that annihilate each other at a rate $\sim \rho^2$; in an enriched environment like a white dwarf core this would produce energy from emitted photons heating things up. Adams & Laughlin estimate the luminosity as to about $10^{-12}L_\odot$, which is imperceptible in the current era but would eventually keep white dwarfs at 63 K in the far future (until the dark matter halo runs out).

Other, more elaborate, calculations lead to accretion estimates that are higher. If the rate were high enough, then we would not see any cool dense objects - so white dwarf and neutron star cooling gives some bounds on the possible density and cross sections, albeit not very strict ones. For example, one model suggests that neutron stars would level out at 10,000 K. Cool star observations can also already rule out some dark matter models.

There are even some arguments that super-earth planets in dense dark matter halos might be heated significantly, although this may require unrealistically dense halos and big cross sections. The current heath flow of Earth does give some constraints on how strongly it can interact.

So neutron stars are not directly giving us dark matter detection, but they (and planets and white dwarfs) are giving us some information.

• So now dark matter is made even more complex by offering virtual pairs. As Hawking radiation suggests however, pairs don't necessarily retain their symmetry, so why aren't black holes growing at unprecedented rates? Furthermore, the Casimir effect shows that a force arising from such pairs should be quantifiable, especially with the Cavendish experiment made decades and decades ago before the high tech equipment of today, so why wouldn't the presence of mere objects then be projected to affect differentials in the permeation of dark matter itself of not massive stellar objects? – Vane Voe Aug 11 at 22:21
• @VaneVoe - Assuming WIMPS to be a mix of particles and antiparticles (or self-antiparticles) is the most symmetric assumption. I don't see why this has anything to do with Hawking radiation or Casimir forces? Black hole capture cross-sections for dark matter are pretty tiny - $(27/4)\pi R_s^2$, so their overall absorption is minimal. The existence of low-mass particles will have some effect on the Hawking particle spectrum and presumably the Casimir force, but so does neutrinos and any mass-less particle. – Anders Sandberg Aug 12 at 8:37
• If the process wasn't symmetric, then it should be detectable. You're going to have a hard time arguing why it couldn't be detectable when there's centuries old documents measuring the gravity of a hand-held ball of matter. "Why" is there any reason to believe these virtual particles wouldn't be symmetric given the precedent of symmetric pairs as already proven? These pairs are shown to have a measurable force via the Casimir effect and they are theorized to affect black holes. You however are making the assumption dark matter exists in order to argue it exists!! That doesn't make sense. – Vane Voe Aug 12 at 10:41
• @VaneVoe - I describe the consequences of standard physical models. – Anders Sandberg Aug 12 at 10:50
• Wrong again, you've described an aspect of the standard model, and then without any evidence, carelessly assumed that it applies in the exact same manner to an unconfirmed particle of circumstance that can be accounted for by other theories. It's already known there's missing mass, but there's no known reason to assume it could only be dark matter, it doesn't predict anything that can't be equally accounted for by other models that carelessly trend fit. I could make up right now that there's simply space dust beyond current instrument measurement and fit it to missing mass just as easily. – Vane Voe Aug 12 at 16:20

I have never seen any discussion of the interaction between any of the various Dark Matter candidates and neutron star matter. But we can still say something useful about the prospect.

First, remember that we don't know what Dark Matter (DM) is. We do have a number of theories that are reasonable extensions of the Standard Model which contains particles which behave sorta-kinda like we think DM behaves, but not only do we not have any good evidence for any of them, we have looked for most of them and have failed to find anything. The negative evidence falls well short of certain, but also suggests that there is something important we don't know yet.

At any rate, you're correct that DM ought to be attracted by the neutron star's (NS's) gravity, and it seems plausible that the DM would react with the NS's dense matter. But the only interactions that I'm aware of would release a bit of heat and a bit of electromagnetic radiation at the point of interaction. (DM particles aren't hugely energetic, and DM isn't very dense.) This would be promptly absorbed and result in an ultra-minuscule heating of the NS.

And neutron stars are far away. It is very difficult to see how we could hope to observe any effects of whatever interaction may be taking place.

• If we have yet to find any evidence of dark matter, why do so many people obsessed over it as opposed to simply modifying general relativity over galactic scales or finding alternatives of real matter like space dust that is only detectable at very low or very high frequencies? Those all seems more likely than a bunch of invisible stuff that makes up most of the universe but that no one sees, that sounds literally like a religion. – Vane Voe Aug 10 at 11:06
• @VaneVoe: You misunderstood what MarkOlson wrote. There is plenty of evidence for dark matter, even a wikipedia page dedicated to it. The answer however said that the theories that explain DM don't have any other evidence backing them up. So if a theory can only explain DM, but has no other connection to reality it is problematic, because it can't be tested then. – AtmosphericPrisonEscape Aug 10 at 11:45
• The only "evidence" for dark matter specifically is unaccounted for mass which can still be accounted for by any number of other means. Scientists simply trend-fitted the allegedly "missing" mass in the universe for their assumption of dark matter. The same exact thing could be said for one of the many alternative theories where the gravitational constant varies over distance, so I still see no particular reason to pay attention to dark matter. People obsessed over string theory, and then it failed to generate its biggest evidence at the LHC and it now string theory remains dead or dormant. – Vane Voe Aug 10 at 11:58
• @Vane Voe OK. Not believing in Dark Matter can be a perfectly reasonable position if taken for sensible reasons. I think the reason most physicists believe in DM is that there is pretty solid observational evidence which we can't explain using our current theories. A DM extension to the Standard Model does no violence to what we already understand, accounts for the anomalies, and anyway, some sort of extension is expected. Modified gravity theories also work, but do violence to General Relativity which is well-tested and (unlike the Standard Model) difficult to tweak. – Mark Olson Aug 10 at 21:17
• @VaneVoe Many people have done exactly that and continue to work on it. MOND (modified newtonian dynamics) and TeVeS (tensor-vector-scalar) are some of the more well-known modifications. So far they have not fared very well at handling observations: they might predict galaxy rotation rates well, but then fail noticeably at galaxy cluster dynamics, or galaxy mergers, etc. As long as searches for explanations via particles come up empty, some people will keep at it. And as long as formula tweaks come up short, other people will keep looking for particles. – zibadawa timmy Aug 11 at 5:22