A New Test of Dark Matter vs. Modified Gravity: Who Wins?

"The best way to escape from a problem is to solve it." -Alan Saporta

One of the greatest puzzles in the Universe today is just why the Universe is structured the way it is.

Image credit: Robert Gendler / Hubble Legacy Archive.

For the individual galaxies that we see, the puzzle is why they rotate at the speeds they do. If the only matter in these galaxies were normal matter (made out of protons, neutrons, electrons, etc.), the outskirts of these galaxies would rotate around their centers much more slowly than they actually do.

Image credit: Victor Andersen, University of Alabama, KPNO, retrieved from APOD.

For clusters of galaxies, the above puzzle is not only there for each of the individual galaxies in the cluster, but there's another one on top of it: these galaxies move through the cluster far more quickly than expected!

Based on what we know about matter and gravity, if all that were in these clusters were protons, neutrons, and electrons obeying the laws of gravity, galaxies moving at these high speeds would escape from the cluster!

Image credit: N. Benitez, T. Broadhurst, H. Ford, M. Clampin, G. Hartig, G. Illingworth, ACS Science Team, ESA, NASA.

But galaxies aren't escaping from their clusters.

So what is going on? Well, something's got to give, and the two ideas that are always considered are:

  1. Either there's more mass out there than the stuff we can conventionally detect,
  2. or the laws of gravity need to be modified.

Any one observation, of course, could always be fit well by either of these options. The modifying gravity option does a little better at the individual galaxies, while having extra mass -- known as dark matter -- does better for the clusters. The key test, though, is whether we can fit all the observations with just one thing.

So what are some other observations we can make?

Image credit: ESA, NASA, K. Sharon and E. Ofek.

We can look to gravitational lensing, which is how general relativity was first confirmed in our Solar System! How is the light from background objects bent by the gravity of objects -- like galaxies and clusters -- that are in between us and the light source?

What else can we look for?

Image credit: NASA/STScI; Magellan/U.Arizona/D.Clowe et al.

We can find galaxy clusters in the process of colliding! Normal matter, as you can verify for yourself by trying to pass one hand through your other hand, interacts with other normal matter. When a proton, neutron, or electron runs into another one, they don't just pass right through one another, they exchange energy and momentum, and effectively experience friction. But not dark matter! There's no exchange of energy or momentum; dark matter simply coasts through both normal matter and other dark matter particles.

So we can look at X-ray emissions to see where the protons, neutrons, and electrons are (in pink, below), and gravitational lensing to search for overall mass and matter (blue, below). The results?

Image credit: as above, overlaid with X-ray: NASA/CXC/CfA/M.Markevitch et al.; and Lensing: NASA/STScI; ESO WFI; Magellan/U.Arizona/ D.Clowe et al.

So far, these (and other observations, like large-scale structure, clustering statistics and fluctuations in the cosmic microwave background) come down heavily in favor of dark matter, but it's always important to find new ways to test this.

In science, even when you're convinced that you know the right answer, you keep testing your understanding in new ways. You keep looking for phenomena that might do something different than what your best ideas and theories predict. As long as there's a Universe out there to investigate, science doesn't end.

So what else, if there's dark matter in these galaxy clusters, should we see?

Image credit: Steve Siegel, no relation.

Well, the deeper into a gravitational potential well you are, the more energy it takes to climb out! According to general relativity, that means the deeper you are towards the center of a galaxy, or in the case of a galaxy cluster, towards the center of the cluster, the lower the energy (and hence, the redder) your light will be.

If there is dark matter, you'd get one prediction.

Image credit: Large Synoptic Survey Telescope, of galaxy cluster CL0024.

But if there isn't dark matter, or if there's something else instead, you'd get a different prediction. While gravitational redshift has been tested and confirmed on our planet, in our Solar System and within our galaxy, we've never tested it for a galaxy cluster before.


A new paper published in Nature, by Radoslaw Wojtak, Steen H. Hansen & Jens Hjorth (arxiv version here), measures exactly this for the first time.

Image credit: Wojtak et al., 2011, as are the next two images.

First off, they took data (from the Sloan Digital Sky Survey and the associated Gaussian Mixture Brightest Cluster Galaxy catalogue), and tested whether you could see the effect of galaxies being gravitationally bound in the clusters. (After, that is, they subtracted out the overall Hubble flow; see the paper's supplemental section for more details.) If you couldn't, the above curves (showing the velocity distributions) would be flat, but the quasi-Gaussian shape of these curves shows, in fact, that these galaxies are gravitationally bound, as expected, in these clusters.

So then you ask, now that you know they're bound, what is their gravitational redshift? This is incredibly difficult to measure, as it's the departure of the data (in red) from those Gaussian curves (in black), which is tiny, but amazingly, measurable! And is that gravitational redshift consistent with General Relativity + Dark Matter + Dark Energy, or with its alternatives?

With the data collected to this point, General Relativity with dark matter (and dark energy) is the best fit, in red, above. One of the alternatives, f(R) gravity (which replaces dark energy, but not dark matter; if you heard otherwise, see here), is a slightly worse fit but isn't ruled out.

But TeVeS -- the relativistic generalization of MoND, which seeks to do away with dark matter -- is ruled out by this analysis!

The authors' conclusion from this?

The measurement agrees with the predictions of general relativity and its modification created to explain cosmic acceleration without the need for dark energy (f(R) theory), but is inconsistent with alternative models designed to avoid the presence of dark matter.

And there you have it. While this isn't a good measure of dark energy, it concludes that there's yet another independent test of dark matter, and the evidence not only supports it, it explicitly comes out against modified gravity as an alternative.

So how do you build the Universe, from the grand cosmic web down to individual galaxies?

Video credit: Fabio Governato and the N-Body Shop, University of Washingon.

You do it with dark matter.

More like this

There's one point I don't understand: You write "tested whether you could see the effect of galaxies being gravitationally bound in the clusters. If you couldn't, the above curves would be flat". But I thought the gravitational effect was only the small deviation from the Gaussian form that comes from the different doppler shifts. Wouldn't there still be a Gaussian curve without the gravitational redshift?

PS sorry if thats nonsense ... where i live, its way too late already :/


Take a look at that graph with the four Gaussians on it; note that the velocities shown there are in units of thousands of km/s. The black curves there are what they should follow, were there gravitational binding to clusters, but not with gravitational redshift.

If there were no clusters, you wouldn't have a Gaussian at all.

So those are galaxies zipping around with large speeds inside the cluster itself. Now, on top of those speeds, there should be the extra effect of gravitational redshift, which, as you can see from the next graph, is only an effect of around ten kilometers per second, or ~1% of the effect. But this effect should be entirely position dependent, based solely on how deep you are in the gravitational well of the cluster, and that should show up in the data as a deviation from the Gaussian shape, which (of course) is impossible to see with the naked eye, since it's occurring for speeds of ~10 km/s, while the graph is on the scale of 1,000 km/s.

Does that make sense? (Will it make more sense in the morning?)

I'm sorry, did you just tell us that we can measure velocity differences of 10 km/s on galaxies in clusters, oh, a billion light years away or so?

Pardon me while I go bumbadumbabumbdum with my lips for a while.

Sorry my solemn mood these days, but let me provoke you a little - maybe you even enjoy such:
If in a few weeks from now a TeVeS guy tells us that (just as a conceivable scenario without me knowing whether such even plays a role in these difficult analyses) relativistic frame dragging wasn't taken into account properly and that TeVeS is not excluded at all, apart from that surely not making it into Nature, will you present an equally grand post about that, with pictures and all? ;-)

So dark matter passes through itself and ordinary matter without friction? So its stress tensor wouldn't follow the equations for matter stress in General Relativity?

I'm still waiting for someone to admit that dark matter is being tested against other modifications of gravity; i.e., the theory of dark matter already does modify gravity by assuming the existence of an unknown type of gravitating substance.

Also, I don't understand how TeVeS can be considered ready for testing. It isn't off the drawing board yet. There are at least three big problems:

* A discontinuity between occupied and unoccupied regions of space.

* A term that does nothing but apologize for the speed of light.

* A dynamic assumed to be attractive, with no proof that such an attraction actually follows from the equation.

This doesn't mean TeVeS is wrong. But it means that until problems like these are fixed, it is "not even wrong".

Four data points, only one of which skews the analysis towards dark matter/dark energy. Looking at the error bars, they get their speed data to withing 5 km/s, but the distance maybe be off by a couple million lightyears.
Getting a paper by Nature's peer review must be easier than getting a thesis past my adviser, who always said if one more data point can invalidate the conclusion it's not a conclusion.

I am not surprised by this result because it is measuring radial derivative of the clock rate which in GR goes like 1+phi/c^2 (Newtonian gauge, phi = Newtonian potential). The gravitational lensing signal also measures the spatial derivative of phi. So for GR this result and lensing have to agree and they do.

Shorter version: I am not surprised that GR passes this test because it has passed all tests to date.

But more testing is always recommended.

Thanks for playing. By the way, "peer review" on the internet means people making fun of you for not being able to follow the last set of valid criticisms levied in the attempt to refute them.

Your posts lately are reminding me very much of Stephen Baxter novels (Xeelee Sequence). Its enjoyable to read them simultaneously.

By Schmutzli (not verified) on 12 Oct 2011 #permalink

First, just let me say I just started reading your blogs two weeks ago, and I love them.

Second. Wouldn't the presence of some form of Dark Matter that passes through normal matter without friction, is virtually undetectable on earth, and skews light from distant galaxies require a revised understanding of gravity? A particle-less cloud of matter that exerts a gravitational force on the space around it.

And if I'm being an idiot, it's because I dropped out of physics for music theory.

By Jon Jones (not verified) on 12 Oct 2011 #permalink

Re "frictionless", my understanding is that what keeps your hands from passing through each other when you clap are electro-magnetic forces (also what keeps your hands together in the first place). In other words, gravity has a negligible effect on (elementary) particle-to-particle interactions. Dark matter has no charge and no electro-magnetic interactions. True, if your hands were clouds of dark matter particles, some of them might collide (if there were any way to clap them), but this too would be a negligible effect because hands are mostly empty space. So for all practical purposes, dark matter hands would frictionlessly make the same sound as one hand clapping.

(Okay, actually you can make a sound with one hand by flapping your fingers against your palm, but for my purposes that is not defined as clapping.)

AJ @3: That's the power of statistics: when you have 50,000+ galaxies in thousands of clusters, you can tease an awful lot of information out of it.

Sascha @4: It depends on what else they have to give up to make that statement be true. For example, a few years ago, John Moffat came out with a variant of modified gravity (he called it MoG) that explained the Bullet Cluster without dark matter. Unfortunately, it also predicts Bullet Cluster-like effects for two galaxy clusters in a pre-collision phase headed towards one another, which, well, is wrong, and hence I wouldn't dare give it equal attention. Remember,

The equal treatment of unequals is the greatest injustice of all. -Edmund Burke

Collin @5 and Jon Jones @10, friction is an electromagnetic interaction, not a gravitational one. Rubbing your cold hands briskly together works just as well in zero-gravity as it does on Earth. But shooting a kilogram's worth of dark matter into the center of the Earth works pretty much the same as shooting a kilogram's worth of neutrinos into the center of the Earth: they'll simply pass through it and come out the other side. The difference is, a tiny fraction of your neutrinos will interact (through the weak interaction) on the way through; dark matter may not do even that.

Mu @6, those four data points you deride are actually binned data from 50,000+ data points; I'm familiar with Steen Hansen (second author)'s work, and he knows how to do proper statistical analysis.

Ned @7, those who treat dark matter as being no better than modified gravity need to be reminded of these facts. Because they are misrepresentatively vocal about their claims, I feel a duty to tell the truth, vocally, about successes like this.

I understand the electromagnetic force.

We are talking about something that makes up 83% of the matter in the universe. Yet, it can only interact with other matter through inferred gravitational affects and gravitational lensing? Unlike, Neutrinos which have mass and interact(even if it is occasionally) with other particles, we have never observed this for dark matter. So I don't find it fair to compare the two, because we have the ability to fire beams of neutrinos, we cannot for dark matter.

Now, if I were making observations and my observations for what I could see were wrong unless I was missing 83% of the world in front of my eyes, I might consider getting my eyes checked. Then you want to claim the evidence is based on almost immeasurable redshift from galaxy clusters millions to billions of lightyears away. If dark matter has such an effect on light perhaps our measurements are wrong?

By Jon Jones (not verified) on 12 Oct 2011 #permalink

@Ethan Siegel

But shooting a kilogram's worth of dark matter into the center of the Earth works pretty much the same as shooting a kilogram's worth of neutrinos into the center of the Earth: they'll simply pass through it and come out the other side.

That assumes that the remarkably puny >6 GeV Invisible Dark Matter particles apparently detected by DAMA and CoGeNt is the only kind of DM that exists.

Isnât a far more substantial and far more gravitationally powerful form of DM needed to explain the behaviour of galaxies and galactic clusters? I donât see how DM particles of only about >6 GeV would come close to being sufficient, no matter how many there are.

If a form of DM particle exists that is comparable in size to baryonic matter then such a particle would probably be unable to penetrate the Earthâs surface, assuming that such a DM particle is really impelled to collide with baryonic matter in the first place.

Setting that aside, any respectable gevatron should be able to easily separate into its constituent parts a DM particle as small and insignificant as >6 GeV. Has such an event ever happened?

Any chance dark matter may simply be the effect of many, many neutrinos when viewed from a large enough scale?

By StreetScooby (not verified) on 13 Oct 2011 #permalink

But isn't it nice that even with countless beautiful galaxies and stars to shine for us we also get gravitational lensing to multiply even that vast number for us to view upon. Any magician would be proud.


By jesuslives (not verified) on 13 Oct 2011 #permalink


Why is that when anyone questions the validity of dark matter or dark energy they are immediately written off and attacked? Wouldn't the existence of large amounts of brown dwarfs and vast neutrino clouds give the same effect? Sorry if I offended whoever felt the need for this ridiculous post but it seems to be standard procedure in the astrophysics community. I met a girl doing work over at the University of Florida a few weeks ago who got so offended she left the party when I questioned the validity of these measurements. No one is questioning evolution or if the Earth is round. We are talking about an unproven, debatable, and undetectable form of matter.

By Jon Jones (not verified) on 13 Oct 2011 #permalink

I don't see anyone "attacking" you here. Disagreeing, yes, and vocally so, but attacking?

I'm curious about something. Dark matter, as I'm just now finding out, appears to pass through itself? Would that mean that dark matter can form singularities far easier than normal matter? I'm curious about how often large "clumps" of it just collapse down to a single point through gravity. It sounds like you could find clumps of the same size but of vastly different masses due to this incredible compression potential.

By Dark Jaguar (not verified) on 13 Oct 2011 #permalink

"But galaxies aren't escaping from their clusters."

No, but why do we know that? Dark energy should not allow that.

We don't have time to wait for any distance changes in clusters moving mutually. We simply cannot observe at that scale objectively. Our timespan measuring a change in distances is too small.

But we DO know that on a smaller scale the Milky Way is colliding with Andromeda.

And we also know that other big galaxies are colliding with other small ones and therefore are still growing in size.

Strange isn't it?

In this view the biggest galaxies should be at a moderate age of the universe (40+ years in a human life as a comparison) and a tendency to expand in the future.

No growth of galaxies by merging events should be expected. "Coldness" should be more easily achieved thermo-dynamically in an expanding accelerated universe also.

It would be increasingly difficult to create heat/entropy.

If an expansion of this universe is logical we have no alternative than to a introduce "dark energy" and "dark matter" obviously.

Otherwise this assumption of an expanding universe would be wrong.

Are we observing (after 13+ billion years after the Big Bang) that there is a tendency to "order" or low entropy?

No, there is a tendency observed to disorder in this universe currently, which corresponds to a higher state of entropy.

Well the new evidence is nice and may hold up.

Either way, dark matter is a very strong hypothesis.

But the problem hasn't been solved; because the particles responsible for the observations have not been detected or a reasonable process involving known particles has not been explained.

Now for a fairytale:
Archimedes walks into a room and find only twelve people to shakes hands with; he rightly concludes that the room has thirteen people. Then Archimedes puts the whole room and its occupants on a balance beam and determines that the mass of the room plus occupants is equal to the mass of the room plus 100 occupants. Archimedes has found conflicting evidence.

Over the millennium more and more test are consistent with the "87% of people are invisible hypothesis". In the 20th century airplanes are built to accommodate the 87% invisible people hypothesis. Not only must the planes have extra lift but they must be equipped with full sized reclining seats with legroom or the planes just will not fly.

Of course people argue forever whether "87% of people are invisible" or "only apparently" 87% of people are invisible. Other hypothesis are also put forward, such as a hypothesis that gravity must be modified to account for the number of people in a given volume. Theologians piously explain that souls of the departed do indeed have mass.

Furthermore the "87% of people are invisible hypothesis" best fits most of the physics data. But chemists can find no evidence; nor can biologist, sociologists, psychologists or even psychics.

Now this fairytale has no explanation. Sorry to disappoint you but in my story the scientists have not yet discovered the cause of their inexplicable observations. Careful examination has always found experimental observational integrity. No tricks, no flaws.

Now the "dark matter hypothesis" is very much a case of conflicting evidence just like the fairytale's "87% of people are invisible hypothesis".

"Dark matter observations" are that profound a mystery. Jumping for joy at our collective and consistent ignorance is not my way. Naming a profoundly inexplicable mystery is not the same as solving it. The " dark matter observations" are not understood.

Thank you Ethan for your clear explanation of the evidence.

Oh one more thought; excellent tour de force analysis of the "dark matter observations". Really excellent science whether the cluster redshift data holds up or not.

Today I read an article in New Scientist magazine, It Discussed the idea that the universe was born spinning.
It was suggested that this was the reason for the disparity between the amount of matter and dark matter.
Could this be the reason for the higher than predicted roatational speeds of these galaxies?

@Jon Jones. Jesuslives looks like one of those automatic spam messages. Just ignore it.

By https://me.yah… (not verified) on 16 Oct 2011 #permalink

I must second Mu there, it is a insecure conclusion you are offering as "evidence".

Mu @6, those four data points you deride are actually binned data from 50,000+ data points; I'm familiar with Steen Hansen (second author)'s work, and he knows how to do proper statistical analysis.

So why exactly don't we see the 50 000 data points or a subset of it together with the derived data points ? Just asking and yes, you *can* do that in a plot !

In fact, with your string of argumentation I can "prove" with the data that *all* theories are invalid because while point 1, 2 and 4 have steadily decreased, point 3 has visibly jumped up ! Instead of going down, down, down we have down, up, down.
No theory predicted a zig-zag pattern, so all theories are refuted !

Scientists wouldnt say that ? Ok, then explain why the zig-zag pattern is ok with the theories and still the data refutes TeVeS !

You can't that because you very well know that the up-point is an artifact of a big statistical error. The measurement, while in fact favoring the GM curve, is too insensitive and is therefore (currently) not able to refute TeVeS.

The errorbars have 68% confidence, so the probability that TeVeS fits the data is more than 1% if the data has no systematic errors.

at 33and 1/3 of rotaton if more bodys spin will the d f increase and u can escape a black hole it obseved most days gravity depeneds on motion speed uni dose not exist

By william fulton (not verified) on 16 Oct 2011 #permalink


It rules out TeVeS at nearly (but just under) the 3-sigma level. Which means that TeVeS fits the data at < 1% confidence, but > 0.3%.

The typical standard for statistical errors is we start taking it very, very seriously once it hits 4-sigma in astrophysics, 5-sigma in particle physics.

The Bullet Cluster rules out no dark matter at 12-sigma confidence, FWIW.

what is the summary of this article. Its alittle confusing.

By christian (not verified) on 17 Oct 2011 #permalink

Christian, Sorry my post was confusing. This was because I'm not a scientist, just an interested layman. Given the significance of the research, and the apparent in depth knowledge of the responders to this post, I thought they would be aware of it. I only mentioned it in the hope of learning something. It seemed to me that the article might be of interest and relevant to the post. In that it may be an alternative explanation,to the two suggested, for the anomalous rotational speeds of the galaxies.

A very brief summary of the article would be: Whilst its generally acknowledged that the Universe is expanding and this expansion is accelerating. Michael Longo at the University of Michigan, thinks that it is spinning too!!.
He suggests that this could be the answer to the puzzling question of why matter exists at all.

"Its to do with the law of the conservation of parity. In 1956,The Physicists Chein-Shuing Wu and Tsung-Dao Lee.
were studying the radioactive beta decay of spinning Cobalt-60 Nuclei. Assuming parity conservation, the nuclei should have emmitted a beta particle or electron, just as often along the direction of spin as in the opposite direction.
But they didn't. They found that 70% more electrons were emitted against the nuclear spin. This insight was crucial in establishing the standard model of particle Physics. They were awarded the Nobel Prize the following year. "

Longo, has suggested that if parity conservation was violated on a small scale, might it also be violated on large scales or even the very largest.

He used data bases of cosmological observations to test this hypothesis. He found that there was a statistically significant difference in the direction of rotation (clockwise/anti-clockwise) of spiral galaxies. He followed this up with direct observations in both the northern and southern hemispheres.

He found the same assymetry. He says that If this assymetry is real, it means that the universe has a net angular momentum. Angular momentum, like energy cannot be destroyed, therefore it means that it must have been born in spin. Only that would explain why galaxies along one line , the universe's own spin axis, received an extra kick to make most of them spin in the same direction.

This may also explain the anomalous rotational speeds of these galaxies.

He also suggests that, "an initially spinning universe, brought on a parity violating asymmetry in gravity, that allowed matter to triumph over its anti-matter rival".The process left two marks behind, the axis of evil in the cosmic background radiation , and the inconspicuous alignment of galaxies that Longo has identified.

Apologies if the summary isn't perfect, I'm no expert, Look it up for yourself.

Ananthaswamy, A, 2011. Original Spin. New Scientist Magazine. Reed Business information Ltd, England. Vol 212 No 2834.

Fascinating! But how did they determine the axis? It looks as if there's a row of bright patches going slightly downward from the far right. I thought that would be the axis?

Also, does this lend credence to the torus ("doughnut") universe theory?

By https://me.yah… (not verified) on 18 Oct 2011 #permalink

Thanks Ethan.

Whilst the U of Michigan press office may have over egged the pudding (its the nature of such people).In the article, Longo acknowledges the limitations of his data so far. As you observed, its an extremely interesting even exiting observation, but the absolute proof(nasty word) is severely lacking.

What's interesting about the article, is that it discusses work by three other researchers, that tentatively supports the notion of a CP violating process on a universal scale..

e.g Andre Sakharov who in 1967, "showed that a hugely CP violating process, at work in the early universe, when matter and anti-matter were being produced, could explain why the one won out over the other".

As I said I'm not a scientist, just an interested layman.
Perhaps you could answer a slightly tongue in cheek,query of mine.
I've only recently started reading serious texts on Quantum Physics, Cosmology etc, and visiting science blogs.I've found myself engrossed and fascinated, but honest about my ignorance.

The thing that puzzles me (I may be mis-quoting), is that I read that Richard Feynman said that no-one understands Quantum Mechanics, and I think I read somewhere else, that another famous scientist said at the time, that only seven people in the world, really understand the theories of Einstein. A true understanding still seems to be beyond my grasp(although I do try).

Yet when I visit Internet Science Blogs, There seem to be numerous posters who apparently write with the authority that can only come from a deep and understanding knowledge. Where did all these geniuses, suddenly appear from? LOL

Kind Regards