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Physicist here. It's roughly right, but it's kind of the picture we had 50 years ago. 50 years ago, dark matter and modified gravity were both reasonably equally good hypothesis. Then we got a treasure trove of astrophysical, galactic, and cosmological data from nearly a hundred distinct experiments.

The results of _all_ of these experiments do not fit with the naive theory. And they each can be fit perfectly by adding in dark matter. But that's not important; the crucial point is that all of them can be _simultaneously_ fit perfectly by adding in the _same_ amount of dark matter. That's practically the definition of what a good scientific theory should do. Put in a single parameter and explain a hundred observed results.

Meanwhile, modified gravity theories have fared extremely poorly -- they were originally designed specifically to fit galaxy rotation curves, and accordingly it is very difficult to massage them into fitting anything else. Usually if you get the rotation curves right, the astrophysics and cosmology come out disastrously wrong. You could probably get it right if you added a pile of ad hoc parameters, but that would be bad science.

Unfortunately every discussion of this subject ever just hyperfocuses on the nearly 100 year old galaxy rotation curve observations... probably because it's easy to understand.

> Is there any prediction that would prove the existence of dark matter?

If dark matter interacts in a non-gravitational way, and is present near the Earth, then the smoking gun would be directly detecting it in an terrestrial experiment. (People also work on indirect detection, by looking at possible products of its decay or annihilation elsewhere in the galaxy, but this is less definite because such products could be made by something else.) Of course in all these cases, the specific kinds of predictions depend on what you think dark matter is made of. Unfortunately, its good scientific properties (i.e. fitting a lot of data with remarkably little input) also mean that we have very little to go on here. Practically any kind of new "stuff" that interacts weakly electromagnetically could work.

Also a physicist here, this is correct. Some details for anyone interested https://arxiv.org/pdf/1006.2483.pdf

Sabine Hossenfelder seems to think dark matter has quite a lot more problems than is usually presented


Sorry for a tangent. But I must say I'm a fan of your answers on physics SE.

It's a great resource for people with basic undestanding of fundamental physics and some experience with math, along with John Rennie's

Nice to see you here. Keep up great job popularizing scince on a bit higher level. Kudos.

What is Physics SE? I really liked knzhou's explanation and would like to know where else answers like these are posted

Physics Stack Exchange: physics.stackexchange.com

> The results of _all_ of these experiments do not fit with the naive theory. And they each can be fit perfectly by adding in dark matter. But that's not important; the crucial point is that all of them can be _simultaneously_ fit perfectly by adding in the _same_ amount of dark matter. That's practically the definition of what a good scientific theory should do. Put in a single parameter and explain a hundred observed results.

Slightly off-topic, but can I ask if dark energy has anything like this going for it?

>But that's not important; the crucial point is that all of them can be _simultaneously_ fit perfectly by adding in the _same_ amount of dark matter.

Is that true? There are claims of galaxies with no dark matter, or tons of dark matter. It seems like dark matter is a parameterized value with lots of local anisotropy across the universe.

It's not that the dark matter distribution is isotropic (it's not, as you note). Think of it like this: locally for a given object in the universe, we can work out the amount of dark matter necessary to describe one of its anomalous properties under the DM model. That same amount will work to explain the other anomalous properties locally for that object. You can do this at any point in the observable universe, including the unusual cases like the DM-deficient galaxies, and the model still holds up. MOND and related theories struggle in this regard, which is why DM is viewed as a more likely explanation (whatever the underlying nature of DM might be).

"MOND and related theories struggle in this regard"

It's often said that mind has difficulty explaining bizzare galaxies but my understanding is that's not true. I thought the only thing that MOND cannot explain is the matter distribution in the early universe, which requires an anisotropy that MOND does not "give for free" like dark matter does.

MOND famously (notoriously?) cannot explain the observed motions of galaxies within groups and clusters (the oldest known evidence for dark matter). Even if you assume MOND is true, the galaxies are moving too fast, so you need an extra source of, well, dark matter.

> That's practically the definition of what a good scientific theory should do. Put in a single parameter and explain a hundred observed results.

[edit] bellow is wrong (dark matter uses free params), misread from wikipedia see child comment...

Conversely entropic gravity uses free parameters, which according to the crushing wikipedia definition is likely to be a product of wishful thinking.

A stark difference, although i'm definitely not suggesting this to be some absolute measure of truth - perhaps it is useful to consider the historical context this good scientific quality (which is generally good) emerged from, it's possible it may not be a good fit for theories grounded in emergence and chaos of the very small?

disclaimer - not a physicist, obvs.

I could be misunderstanding this sentence, but from the linked page:

> Importantly, [entropic gravity] also explains (without invoking the existence of dark matter and its accompanying math featuring new free parameters that are tweaked to obtain the desired outcome) why galactic rotation curves differ from the profile expected with visible matter.

I get that entropic gravity doesn't use free parameters.

Also, I don't think that free parameters are necessarily so damning. I happen to have more hammocks than usual in my house. Any theory about how hammocks are distributed will either fail to explain the concentration, or will predict that hammocks are more likely to be found near people who like them, and then will subsequently fail to provide a way to derive the location or distribution of those people. That failure would be a free parameter. It's not necessarily an indicator of wishful thinking. It could just be that the theory knows its limits.

> I get that entropic gravity doesn't use free parameters.

You are correct, my error in skim reading too fast.

> It could just be that the theory knows its limits.

Yes that's essentially what I meant by chaos, if you could know enough information you could predict where all your hammocks end up, but that requires vast and subtle knowledge about how you think and minutiae of your environment and how you interact with it that caused you to make arbitrary decisions... the interesting thing about chaos is that it _can_ be deterministic, in other-words, given initial conditions it can be computed - but even then in the context of such large systems that computation is infeasibly and irreducibly costly, in which case (i guess) you use free parameters in combination with what conceptually similar to statistical mechanics?

> I don't think that free parameters are necessarily so damning

Free parameters which significantly outpower the power of the observations are damning because there is no way to falsify the theory: if the theory can explain an extremely wide range of observations by tweaking the free parameters then it has much less predictive power and should be viewed extremely suspicously.

Oh yeah, depending on how they show up, they're a problem. I'm just saying that there are certain non-problematic cases where only a free parameter will do.

I think the trouble with dark-matter-as-WIMPs is that the free parameter (the location of those WIMPs) is overpowered:

You can say that the extra gravitation is caused by the presence of these particles and leave the details of how those particles got where they are out of your theory. But then when you add "oh, and they can't be detected by any other means" it becomes a problematic free parameter because wait a second, that's the very problem we were trying to solve in the first place. If you can't connect the causal agent to anything besides the problem that necessitated it, then it might as well be a ghost.

Explained much better than me, I've removed my reply!

I haven't seen any explanation for Dark Matter that explains its distribution. It's always "hey, if there's some stuff with this distribution it will explain this observation". An example would be a halo that fixes a rotation curve. If it interacts with visible matter gravitationally then why doesn't it take on the same distribution? That is never explained.

My other issue is that in discussions of rotation curves, I keep seeing reference to Kepler, which simply shouldn't apply. Where can I see the math behind the "expected" curve - I suspect an error.

"My other issue is that in discussions of rotation curves, I keep seeing reference to Kepler, which simply shouldn't apply. Where can I see the math behind the "expected" curve"

"Keplerian" in this context is an approximate term. It refers to the fact that most of a galaxy's visible mass is centrally concentrated, and so as you get further and further away, with virtually all of the mass inside whatever distance you're at, the rotation curve should converge on a true Keplerian one, because the difference between the effect of the true mass distribution and one where all the galaxy's (visible) mass is concentrated in a point at the center gets smaller and smaller.

Actual published fits to galaxy rotation curves always use the measured visible-mass distribution for a given galaxy to compute the non-dark-matter curve. No one working in this field is confused about this.

As long as physicists disagree on the explanation of anomalous physics, it is quite accurate to say that the physics community is in a state of doubt or confusion about the anomaly.

Note that this person explicitly asks for the dataset, and the computation of the expected curve, but hardly ever does anyone help such a person in such a direction, it is always taken as a suspected insult on the mental state of one camp of interpretation.

I too would love some kind of central register or portal for the most widely accepted anomalies (anomalous.physics/dark-matter/...), where people can get and inspect observation datasets, and competing models to fit the datasets.

Imagine Brahe & Kepler's, data & interpretation to be widely popular, but whenever someone asked for data or computations to compare circular orbits with elliptical ones, nobody would point them where to find such data and computations?

I apologize for the snark, but, really, you are both on the internet...


(The fourth link, for example -- http://astroweb.cwru.edu/SPARC/ -- has both observed rotation-curve data and computations of expected rotation curves.)

There is zero validity to treating galactic mass as a point mass. That is exactly one of the mistakes I suspect keeps being made. At best it is a misapplication of the divergence theorem. Disks dont behave like spheres and rings dont behave like uniform shells. Proximity matters.

It generally works a bit better if you say something like, "Hmm... it seems like this approach would be wrong, for this reason that just occurred to me. Am I missing something? Or: How do people in the field actually do it, so as to avoid this error?"

If, on the other hand, you assume they must all be stupider than you are and say things like "That is exactly one of the mistakes I suspect keeps being made", then you're basically saying, "I'll bet none of the hundreds or thousands of people working in this field for decades have ever thought of this one point that just occurred to me!" The latter is, shall we say, rather unlikely.

(In point of fact, Newton's shell theorem generalizes to the case of axisymmetric, flattened spheroids with homeoidal density distributions, a result that was derived by Laplace and others in the 18th and 19th Centuries. Which means that disks do behave somewhat like spheres.)

To get a sense of what's really involved, you could look at something like Brandt's 1960 paper, and then some of the papers that cite it (including some of the classic early papers by Vera Rubin and collaborators), to get an idea of how much more sophisticated than an simple Keplerian rotation curve:


what you say is obviously true, but could astronomers really be making this elementary kind of mistake? one would have to completely lose touch with elementary physics to make that mistake...

For modeling individual galaxies, that's more or less correct. (Of course, the same applied to things like MOND: "hey, if Newtonian acceleration is tweaked with this interpolation function and that free parameter, it will explain the observation".)

In a large-scale, statistical sense, the answer is: initial quantum fluctuations (as seen in the Cosmic Background Radiation) + gravitational collapse and fragmentation in an expanding universe. Simulations done under these assumptions have done an increasingly good job of describing the general distribution of dark matter, and the typical statistical distribution within galaxies.

This is why it's good to do independent fits of dark matter distributions to galaxies: it provides something you test the simulations against. After all, if the individual-galaxy fits say dark matter generally has distribution X, but the simulation say that gravitational collapse and mixing should almost always produce something different, then you know you've got a problem.

"If it interacts with visible matter gravitationally then why doesn't it take on the same distribution?" Because visible matter interacts with itself via radiation and hydrodynamics (e.g., gas pressure). So it gets pushed around in ways the dark matter can't. These forces can be much stronger than gravity in some circumstances (gravity, after all, is the weakest fundamental force), so the gas atoms, ions, electrons, etc. experience forces the dark-matter particles do not.

> If it interacts with visible matter gravitationally then why doesn't it take on the same distribution?

Because unlike visible matter, it does not interact in non-gravitational ways, even with itself.

Visible matter can clump to form planets and stars because when two particles of it are attracted enough to hit each other there is some interaction other than gravity, which helps eat some of their kinetic energy. In contrast, when that happens with two particles of dark matter, they just fly through each other, and if they were moving fast enough, never meet again.

There are non-gravitational interactions even at the galactic scale, even though they are very weak indeed compared to gravity. As our sun plows through space, the particles it's sphere of influence hits have a preferred range of velocities and directions, the "galactic rest". Over billions of years, this does influence where in the galaxy our sun is. Dark matter has no such influence on it.

Do we actually know that dark matter doesn't interact with itself or other matter, or do we just have an upper bound on how much it could potentially interact? And if so, roughly what is it?

Do we expect to observe it in specific places and we do not, or is it just "not illuminated" or "not radiating" in the same way that other matter is?

Dark matter is technically anything that doesn't radiate, but often it's meant to refer to WIMPs -- weakly interacting massive particles.

Now WIMPs are basically what it says on tin. We know they don't interact much, with themselves or anything else, because the rotation curves of the galaxies implies there are large halos. This means there's little to no friction, as otherwise the majority would fall down to the galactic cores, like normal matter does.

We assume they're a separate type of particle from anything we know, as otherwise that shouldn't be possible. We know they're massive, as otherwise we'd see them in particle accelerators... well, we'd see the missing mass at least.

Then, what are they? Well...

Probably a lot of things. The "dark matter sector" outweighs visible matter by a lot, and there's no reason that should be just a single particle.

But anyway, think of graph theory. You can map particles to nodes on a graph, and the fundamental forces to edges.

Not all particles are connected by way of all forces. Electrons lack color charge; neutrinos lack basically everything. (Even when there's a connection, connections can be of varying strengths.)

Dark matter is matter that lacks any connection to the other particles, except gravity.

(Could there be particles that are unconnected by gravity? That gets speculative, but probably not. Gravity is special.)

Ah, but-- there might be more than one dark matter particle, and forces connecting them that won't touch our type. For the most part we know this isn't true, since we know they don't interact with themselves either, but this is only to say that most dark matter can't be doing that.

There absolutely could be dark-matter stars, or stranger things.

... This is purely speculative, though. Good for fiction, but the only kind of dark matter we know exists is the WIMPs.

If WIMPs had forces between them, they’d form some kind of structure that would have been detected by other surveys for “dark” objects.

Dark Matter is a bit of a misnomer... it’s invisible, transparent.

They'd also have fallen to the center of the galaxy, probably following roughly the same mass distribution as visible matter.

What I'm suggesting is just that there might be multiple dark matter particles, some of which might have structure. At present that is basically untestable, of course.

To what extent are people confident dark matter WIMPs are not some sort of neutrino?

Not very much. https://www.forbes.com/sites/startswithabang/2019/03/07/how-... seems to cover the discussion fairly well.

It explicitly (almost) doesn't interact with normal matter, so it cannot be illuminated: it's dark because the light just goes right trough it, the same way space is dark because it doesn't scatter light.

However, for a long time the main competing theory for WIMPs was MACHOs (yeah, really), basically "familiar" dim, compact objects such as brown dwarfs and black holes, scattered around in the galactic halo. However, gravitational microlensing surveys have found that the observed density of MACHOs is far too low to make up a significant fraction of dark matter.

So what else is there besides rotational curves?


Short version:

* Distribution of stellar velocities in elliptical galaxies implies DM

* Mass distribution in clusters of galaxies implies DM

* Gravitational Lensing observations imply DM

* CMS anisotropy power spectrum matches DM

* Structure formation in early universe appears to require DM

* Bullet cluster observations imply DM

* Flatness of the universe implies DM

plus some other statistical measures which also imply DM.

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