# 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. Aug 10 '18 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. Aug 10 '18 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. Aug 10 '18 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. Aug 11 '18 at 11:41
• I'd be kind of concerned if dark matter could pass through black holes. That might allow us to "X-ray" the hole and find out what sort of structure is inside the event horizon. That's supposed to be impossible. Like to see some numbers on how fast a black hole should be gaining mass from the dark matter it sucks in. -Different question, that I'm not going to ask here. Aug 13 '18 at 23:00

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? Aug 11 '18 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. Aug 12 '18 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. Aug 12 '18 at 10:41
• @VaneVoe - I describe the consequences of standard physical models. Aug 12 '18 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. Aug 12 '18 at 16:20

I want to clarify a part of this question that some people may not understand. If dark matter literally were only affected by gravity, then you would not expect to see it collecting at the center of neutron stars. As a dark matter falls towards the center of a neutron star, it picks up speed until it passes on through the neutron star and starts to slow down. But when it leaves the vicinity of the neutron star it will have the same speed that it had when entering the vicinity. In order to collect dark matter, the neutron star has to slow it down somehow. This is what Anders Sandberg meant when he mentioned the interaction cross-section of dark matter. That refers to the probability of interactions that might slow down the dark matter particles enough for them to be trapped.

To put it a little differently, suppose a particle were far enough away from the neutron star so that the neutron star's gravity is can basically be ignored. Imagine that the particle is drifting towards the neutron star, so that eventually it will pass through it. Then, by the time the particle reaches the neutron star, it is mathematically guaranteed to be above escape velocity. The definition of escape velocity is the velocity that a particle will have if it falls from infinitely far away. The neutron star cannot trap anything because anything that drifts by is guaranteed to pick up precisely enough speed falling in so that, by the time it gets back out to the same distance it was before, it's moving away at the same speed it was moving in before.

To be fair, there is one caveat here. If the particles had significant gravity, so they could strongly influence each other, then they could interact in such a way that one particle flies out even faster, and the other one is trapped in orbit around (maybe also passing through) the neutron star. Some of Jupiter's moons may have been captured that way. But dark matter particles are thought to have negligible mass.

I am not saying anything different from Anders Sandberg here, but I just want to emphasize the importance of his statement that "most particles will just swoop on past."

• If dark matter was literally only affected by gravity, then I still don't see why what you're saying would be such a huge constraint. Gravity within a sphere is linear, though I don't know if that holds for the immense case of a neutral star, especially with a density gradient. In order for a particle to not be trapped, its linear velocity would have to exceed escape velocity of the neutral star entirely, otherwise at the very least there should be a cloud of dark matter surrounding neutron stars that oscillate about its center. Dec 16 '18 at 2:06
• I added a new paragraph. Does it help? The point is, if the particle was from far away, then its linear velocity is guaranteed to exceed escape velocity. And if it was already nearby and moving below escape velocity, then it was already in orbit and doesn't count as a particle being newly trapped. That orbit will continue forever - the particle won't get sucked in so it stays inside the neutron star, just like the sun doesn't suck in the planets. Feb 1 '19 at 4:32
• Just to say that if you have a two body system however, dark matter could be captured without any non gravitational interactions, simlarly to the way the Voyager spacecraft used boosts from Jupiter to escape the solar system, so if relative velocity to our solar system is not too great, there could be a small population of dark matter in our solar system maintained by occasional dark matter particles captured by a similar trajectory in the opposite direction (and lost on Voyager like paths). But accumuluation in a neutron star is still impossible, at most it just orbits or swoops in / out. Apr 3 '21 at 23:18
• Robert Walker - I think your comment is what my next-to-last paragraph is trying to get at. Apr 4 '21 at 3:38

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. Aug 10 '18 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. Aug 10 '18 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. Aug 10 '18 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. Aug 10 '18 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. Aug 11 '18 at 5:22

Why aren't neutron stars full of dark matter?

Because dark matter doesn't consist of particles. There's something of a myth that it does, which I think comes from particle physicists who have never actually read Einstein's original material. I also think science is something of a competitive business, and there's a tendency for advocates to promote their own theory (eg WIMPs) and claim that a competitor theory (eg MOND) is flawed.

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.

Remember that we have good scientific evidence for flat galactic rotation curves and other phenomena. These suggest that either a) there's some unseen "dark matter" around somewhere, or b) that gravity doesn't work quite the way that people think. However the evidence does not actually say dark matter is made out of particles and falls down.

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

Because we do not live in some Chicken Little world where the sky is falling in. I'm referring to Gullstrand-Painlevé coordinates which model a gravitational field as a place where space is falling down. Einstein rejected the idea, but some contemporary physicists take it seriously, see this for example.

Image credit Andrew Hamilton

Why is this relevant? Because in his 1916 Foundation of General Relativity Einstein said “the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy”. This is spatial energy, and it isn't made of particles. The energy density of space near the Earth is greater than the energy density of space further away from the Earth. Because of this, there's a gravitational effect. This is why "gravity gravitates". Einstein also described a gravitational field as a place where space is "neither homogeneous nor isotropic". So dark matter might simply be inhomogeneous space. Don't forget that as per the raisin-cake analogy, the space between the galaxies expands whilst the space between the galaxies does not. Conservation of energy tells me that this will surely lead to an inhomogeneous spatial energy density. And that an older galaxy will be surrounded by a bigger/steeper halo of inhomogeneous space than a younger galaxy, so it will look like there's more dark matter present.

What Einstein said means that there's "dark matter" of sorts in the room you're in, right in front of your face. Only it isn't made of particles, and it isn't falling down. Instead it's made of space. Don't forget that space is dark, and there's a lot of about.

• Unhelpful to appeal to ancient authority. If MOND is correct then GR is wrong. You can call dark matter an "energy field" if you like, but energy fields are quantised and have particles associated with this quantisation - e.g. Higgs field/Higgs boson. I have no idea what the reference to G-P coordinates is about Aug 29 '18 at 17:51
• @Rob Jeffries : referring to the Einstein digital papers is not "appealing to ancient authority", the gravitational field is not quantised, and the Gullstrand-Painlevé coordinates are a reference to the waterfall analogy, which is not correct. A gravitational field is a place where space is inhomogeneous, not infalling. The energy density of this space is not uniform, hence a gravitational field itself causes gravity, and it isn't made of WIMPs. Aug 30 '18 at 7:21
• You should make it clear to (perhaps) inexperienced readers that you are pursuing your own ideas. The need for dark matter was established in the 1950s, irrespective of whether Newtonian or GR perspectives are used to consider gravity. Dark matter is the explanation compatible with GR. We (including you) don't know what that dark matter could be. Only certain parts of parameter space have yet been excluded. Aug 30 '18 at 7:35
• Except that GR fails to explain the rotation curves of galaxies, gravitational lensing, cluster velocity dispersions etc., without the presence of dark matter! Aug 30 '18 at 17:24
• Or are you claiming that dark matter is not required because GR explains everything and disagreeing with absolutely everyone, both dark matter and MOND enthusiasts alike? If your argument is just about whether dark matter is made of particles, then -1 for your first sentence because you don't know (if dark matter is required) whether it is made of particles or not, and neither does anyone else, and then another -1 for obfuscating the issue with irrelevancies about G-P coordinates and what Einstein said in 1916, when dark matter wasn't even a thing. Aug 30 '18 at 17:27