One point of evidence in support of dark matter is the way in which the speed of stars, gas and dust in a galaxy varies with their distance from the center of the galaxy, known as the galactic rotation curve. Most of the visible matter of a galaxy is concentrated near the center of a galaxy, so we would expect that more central stars should move much faster than stars on the outer rim. Thus the rotation curve should decrease with distance. However most galaxies have a fairly flat rotation curve, meaning outer stars move about as fast as inner stars. This and other evidence as led us to develop the theory of dark matter. But new research on galactic rotation curves has found an odd correlation, and it could mean that dark matter is wrong after all. 

The rotation curve for M33, also known as the Triangulum galaxy. Credit: Wikipedia

The orbital speed of stars in a galaxy depends upon the gravitational pull of a galaxies mass. The more strongly a star is pulled toward galactic center, the greater its radial acceleration, and the faster it needs to move to overcome that pull. This is similar to the planets in our solar system. Mercury is close to the Sun, and therefore has a large radial acceleration due to the Sun’s gravity. Distant Pluto has only a small radial acceleration. So Mercury zips around the Sun at 48 km/s, while Pluto chugs along at less than 5 km/s. According to the dark matter model, a galaxy’s mass isn’t concentrated in its center. Most of the visible matter is, but a galaxy is surrounded by a halo of dark matter. Most of a galaxy’s mass is dark matter, and most of it is in the halo.

There’s a lot of other evidence to support dark matter, but there have also been alternative models such as Modified Newtonian Dynamics (MoND). In this model, the radial acceleration of a star deviates very slightly from that predicted by Newtonian physics and general relativity. The difference is too small to notice on the scale of our solar system, but on a galactic scale that difference adds up, producing a galactic rotation curve just as we observe. MoND and related theories can accurately describe rotation curves, but they fail to describe other effects such as large scale galactic clustering and the mass distributions of colliding galaxies, so dark matter is the dominant model in astrophysics. But new research on the radial acceleration of stars could bring MoND back into favor.

The correlation between radial and gravitational accelerations is pretty strong. Credit: McGaugh, et al.

The researchers looked at the observed rotation curves for 153 galaxies, and calculated the radial acceleration at various distances in each galaxy. They then compared these results to the gravitational acceleration as predicted by the distribution of visible matter within a galaxy (technically the distribution of baryonic mass). They found a strong correlation between the two. When the gravitational acceleration was stronger, so was the radial acceleration, and when one was weaker, so was the other. What’s interesting is that this relation holds up in a range of galaxies. It didn’t matter whether most of the visible matter was clustered in the center or not, the relation still held. It’s also a purely empirical correlation, so there is no strong theoretical component to make it work.

So what gives? The researchers propose three possibilities. The first is that the correlation could be due to the dynamics of galaxy formation. It’s not clear how this would occur, but there are aspects of galactic evolution we don’t fully understand. The second is that the distribution of dark matter and baryonic matter within a galaxy are correlated. This would require some new kind of dark matter physics that makes dark matter clump in the same way that regular matter does. The third and perhaps most intriguing idea is that it really is due to some kind of modified dynamics.

The correlation between radial acceleration and mass distribution is strong enough that it points to baryonic matter being the source of the acceleration. A relation such as this is exactly the kind of thing MoND models would predict, and it contradicts current dark matter models. If this result is replicated, dark matter will have some explaining to do if it wants to remain the dominant theory. But the challenge for MoND is also just beginning. To succeed in the end it will have to account for things like large scale clustering, where it currently fails miserably.

The game between dark matter and MoND just got a bit more interesting.

Paper: Stacy McGaugh, et al. The Radial Acceleration Relation in Rotationally Supported Galaxies. arXiv:1609.05917 [astro-ph.GA] (2016)

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So I last talked about two approaches to explaining the motion of stars in a galaxy, MOND and dark matter.  Now I finish answering the question about which model I favor, and why.

When we left our story we, had two proposed models:  MOND, which posits that for very small forces, the acceleration of an object doesn’t quite go to zero, and dark matter, which introduces an invisible “something” that makes up most of a galaxy’s mass.  Neither one of these seem particularly appealing, so why (as I stated yesterday) do I favor dark matter as a solution?

Let’s start by looking at MOND again.  Yesterday I said its weaknesses were that it was a bit of a kludge, and in its simple form it violates conservation momentum. Both of these are valid criticisms, but neither is enough to just discard the theory. Early quantum theory was also a kludge, and it violated the fundamental tenets of physics.  It also happened to be true.  MOND is still a young model, so being kludgy is to be expected.  There is also the fact that more sophisticated versions of MOND have been proposed that are relativistic, and don’t violate momentum.

That said, any model must make clear predictions, and MOND does.  One of the big predictions MOND makes is that for very small forces the acceleration of an object levels off to about 10 trillionths of a gee (1 gee is the gravity we feel on Earth).  This is a very tiny force, but in 2007 an experiment was done that tested Newton’s theory down to accelerations 5000 times smaller than the limit proposed by MOND.  What they found was that to the limits of their measurements Newton’s theory worked perfectly.  Strike one for MOND.  This is also a bit of a win for dark matter, which assumes that Newtonian gravity should hold even for small accelerations.

Supporters of MOND have noted that this 2007 experiment looked at inertial forces, not gravitational forces.  MOND models usually assume that they apply for all small accelerations, but one could also propose that MOND only applies to gravitational forces (hence the 2007 experiment wouldn’t apply).  But if MOND only applies to gravity, then it violates Einstein’s theory of general relativity, which we know works very well.  Again, this isn’t a deal-breaker, but it does mean more kludgy fiddling with the model to make it work.

So now let’s look at dark matter a bit.  Proposing invisible undiscovered particles to fix your problem is a dangerous path to tread, but let’s look at what dark matter predicts.  The 2007 experiment is nice to have, but it isn’t really a prediction.  It would be better to have a prediction we can test.  This can be found through an effect called gravitational lensing.

In general relativity, gravity is described as a curvature of space and time.  Matter warps space around it, which produces the appearance of a force we call gravity.  This warping of space also means that light near a mass will be deflected slightly.  As a result, light passing near a galaxy is focused by the galaxy’s mass, similar to the way a lens focuses light.  We’ve observed this effect around lots of galaxies.  The more mass a galaxy has, the more the light will be deflected, so we can use gravitational lens measurements to determine the mass of a galaxy.

This leads us to a dark matter prediction.  If dark matter really does exist, and it makes up most of the mass of a galaxy, then the mass measured by gravitational lensing should be much higher than the visible mass we see in a galaxy.  This is in fact exactly what we find.  The visible matter in a galaxy seems to be a small fraction of the total mass.  Mark this as a win for dark matter.

Our initial MOND model predicted that the mass should be mostly visible.  But our first experiment required that MOND apply only to gravity (and violate general relativity).  If that is true, then MOND might also deflect light, which would give the appearance of extra mass that isn’t really there.  MOND can still be made to work.  But continually tweaking a theory to match new data isn’t the way science works.  Having your model agree with past observation is necessary, but not sufficient.  Ideally your model should make a solid prediction before the outcome is known.

So at this point we have two experimental findings.  Dark matter agrees with the first and predicted the second.  MOND made the wrong prediction for the first, didn’t predict the second, but can be modified to agree with both.  Dark matter seems to be winning, but it still predicts a new type of “something” that 1) isn’t regular matter 2) hasn’t been observed.  As the saying goes, extraordinary claims require extraordinary evidence.  Just because it works better than the alternative doesn’t mean we should accept dark matter.

It would be nice if we could have a prediction that is unexpected.  Preferably one that contradicted MOND.  It turns out we have just such a thing in colliding galaxies.

Let’s assume for a moment that dark matter exists.  This would mean that two approaching galaxies would have both regular matter and dark matter.  As the galaxies collide, the regular matter (stars, gas, dust) interact with each other, which slows them down.  But the dark matter would only weakly interact with matter, so it shouldn’t slow down.  Instead the dark matter from the two galaxies should pass through each other and keep going.  This means that in a galactic collision the regular matter should bunch up in the middle while the dark matter passes through to the other side.  *If* that is true, then the distribution of visible mass should be different than the distribution of dark matter as measured by gravitational lensing.  This is a radical idea, and it completely contradicts MOND.  According to MOND, the distribution of visible mass should agree with the distribution seen by gravitational lensing.

For this experiment, dark matter wins big time.  The first colliding galaxies where the two distributions were compared is known as the Bullet Cluster.  The results were published in 2004, and they showed a clear difference between the visible mass and lensing mass distributions.  In 2008, another pair of colliding galaxies (known as MACS J0025.4) showed the same difference.  You can see this one in the figure below.  The red shows the distribution of visible mass, while the blue shows the mass distribution seen by gravitational lensing.  MOND predicts the two should overlap.  Dark matter predicts that it should be red in the center and blue on either side.  Which result do you see?

So what have we found?  Out of three experimental results, dark matter agreed with the first outcome and predicted the other two correctly.  MOND on the other hand incorrectly predicted the first and third.  It seems like every time we get new data, MOND has to go back to the drawing board for revisions.  A scientific model lives or dies based on the evidence, and the evidence doesn’t look good for MOND.

This is why I’m in the dark matter camp.  It has made accurate predictions, and it agrees with observation without wild tweaking.  It also agrees with our understanding of cosmology.  When we make computer models of cosmic evolution, the ones with dark matter agree with observation, while the ones without don’t.  So dark matter is actually on a pretty strong footing, which is why most astrophysicists are in the dark matter camp.

Of course dark matter still has a serious challenge.  It predicts a new kind of matter that we haven’t seen in the lab.  It would be nice to make a direct detection of dark matter.  This is actually an active area of research.  So far there are some interesting hints, but nothing conclusive.

In the end, the data will have the final say.  Until then, if you have other astrophysics questions, ask away.

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As part of an “Ask an Astrophysicist” project, I was asked whether I’m in the Dark Matter or MOND camp.  Before answering that, let’s talk about about what these two camps are.

Both MOND and dark matter were introduced to address a problem with the way galaxies behave.  At a basic level, the stars in a galaxy such as ours orbit the galactic center in roughly circular orbits.  The speed of a star in its orbit should be governed by Newton’s law of gravity.  So, using Newton’s gravitational theory, we can predict a star’s speed given its distance from the center and the distribution of matter in our galaxy.  The dotted line in the figure below gives the result of that prediction.  We can also measure the speeds of stars in our galaxy and plot them as a function of their distance from the center.  The result of those measurements are given by the dots on the figure below.

As you can see, Newton’s beautiful theory doesn’t agree with the experimental data.  The two are not even close. We see the same type of discrepancy in other galaxies, so it isn’t just that our galaxy is weird.  Our theory is somehow very, very wrong.

One solution to this problem is that somehow we haven’t accounted for all the mass in our galaxy.  We can measure the mass in the galaxy by looking at all the stars and nebulae in it.  This is relatively easy because they give off light.  Of course there is also dust and gas in the galaxy that doesn’t give off light.  This “dark” material is harder to measure, so it is quite possible that we’ve underestimated the amount of matter in a galaxy.  The problem with this idea is that our prediction isn’t just a little off, it’s way off.  To make our theory agree with observation, most of the matter in a galaxy would have to be “dark.”  If there were that much dust and gas in the galaxy we would see it, and we don’t.  So we might be a little off in our measurement of “dark” material, but not off that much.  The missing mass can’t be regular gas and dust.

Perhaps the missing matter could be something like neutrinos, which don’t interact with light and would therefore be invisible?  Nope.  Neutrinos move too fast to be held by the regular matter of the galaxy, so that can’t be it.  Maybe there’s some still unobserved type of particle similar to neutrinos, but with more mass so they could be held by regular matter.  We’ll call them WIMPs, or Weakly Interacting Massive Particles.  Maybe there are very tiny black holes swarming the galaxy, or some other strange mass.

It seems like we’re really reaching here, so let’s just lump all these possible solutions into a broad term we’ll call “dark matter.”  Given our experimental data, dark matter must have two properties:  1) it can’t interact with light very much, otherwise we would be able to see it directly.  2) it must have mass and interact with regular matter gravitationally.  Any candidate for dark matter must have these properties to agree both with observation and Newton’s theory of gravity.  There’s one more fact we know from astronomical observations, and that is if dark matter exists, it must make up about 95% of the mass in our galaxy.

To make a long story short, to make Newtonian gravity match our observational data, we have to introduce a new type of invisible material, and this invisible stuff must make up the majority of our galaxy’s mass.  There is, of course, an alternative.  Our theory could be wrong.  This seems much more reasonable. After all, we know that Newtonian gravity doesn’t work for large masses and high speeds.  Even the orbit of Mercury deviates a bit from Newton’s predictions, so we already know it’s “wrong.”  It could also be wrong on galactic scales.  If it is, then maybe we don’t need to make up invisible undetected “dark matter.”

Enter MOND, or MOdified Newtonian Dynamics.  MOND proposes a correction to Newton’s Laws of motion by noting that for stars in a galaxy the force of gravity is very tiny.  Newton’s Laws of motion state that the rate at which an object speeds up or slows down (its acceleration) is directly proportional to the force of gravity applied to the object.  MOND proposes that the force of gravity is proportional to a function of acceleration.  On the scales we normally see on Earth, this function is about equal to the acceleration itself, so motion would be just as Newton predicts, but for really small forces the function levels off to a small constant (about 10 trillionths of gravity on Earth).  By making this modification to gravity, we have a theory that agrees with observation.

There are two big downsides to MOND however.  The first is that MOND violates conservation of momentum, which is one of the fundamental principles of physics.  So if MOND is correct, then it isn’t just gravity but most of physics that has to be modified.  The second is that, unlike general relativity, MOND is not derived from a fundamental theoretical concept, but it is introduced specifically to make predictions agree with experiment.  An analogy would is that MOND is much like epicycles added to the beautiful theory of circular orbits, rather than Kepler’s revolutionary proposal that planets move in elliptical orbits.

It seems we have two pretty pathetic alternatives:  propose that our galaxy is mostly made up some kind of yet undetected, unknown, invisible stuff, or propose a kludgy new theory of gravity that would require us to rewrite most of physics.  Neither one seems particularly appealing.  The only good news in all this is that our observational data is solid.  We know what is happening, even if we don’t know why.

Having said all that, which of these camps am I in?  I’m in the dark matter camp. To learn why, you’ll have to wait for my next post.

In the meantime feel free to ask more questions.

The post Beautiful Theory, Ugly Data appeared first on One Universe at a Time.

I’ve been writing quite a bit about gravity lately, specifically about how astronomical observations confirm general relativity (and Newtonian gravity as an approximation to GR). But there are also cases were things don’t seem to add up. A case in point is the motions of stars in our galaxy.

Using the Doppler effect and a few other tricks we can measure the speeds of stars in our galaxy. If you plot a star’s speed vs its distance from the center of our galaxy, you get the result shown in the figure below, which is very, very strange. The dots represent the speeds we observe, while the dotted line represents the speed we expect according to our understanding of gravity. As you can see, the stars far way from galactic center move much faster than we would expect. Something is seriously wrong.

Stellar speed vs distance from galactic center.

If we measure the stellar speeds of other galaxies, we find the same type of discrepancy. Stars near the core of a galaxy move at the speeds we would expect, but stars far from the center move much faster than we would expect. So it isn’t the case that our galaxy is strange. All galaxies seem to behave the same way. This means that either our understanding of gravity is wrong, or something is causing the stars to move faster.

If our understanding gravity is wrong, then it can only be wrong on a galactic scale. We have seen that Newtonian gravity and general relativity work exceptionally well on the scale of our solar system, and it also works for binary stars, neutron stars and even other solar systems. One model that tries to take this into account is Modified Newtonian Dynamics, or MoND. The MoND model proposes a very small extra bit of acceleration due to gravity, about a tenth of a nanometer per square second. This extra term would be so small that we’d only notice it on the galactic and cosmic scales. If you calculate stellar speeds using MoND, you can get the theory to match observations pretty well.

The alternative is to suppose that something else must be going on. If our understanding of gravity is correct, then there must be more matter in the galaxy than we think. But this matter can’t be regular matter. If it were stars or gas or dust then we could observe it. This extra matter must be something that doesn’t emit light or block light. It must be an invisible form of matter known as dark matter. Dark matter seems like a crazy idea. To fix our broken model, let’s introduce an invisible something that can’t be regular matter (protons, neutrons, electrons), but otherwise still acts like regular matter. But it isn’t any more crazy than adding an extra acceleration term just to fit observation.

So how could we test either of these models? It turns out there is one way in which MoND and dark matter models differ. Since MoND proposes an extra term to gravity, the center of mass for a galaxy should be the center of mass we observe. In the dark matter model, the distribution of dark matter can be different than the distribution of regular matter, so the two types of matter can have different centers of mass. It is this latter case that has been observed in a colliding cluster of galaxies known as the Bullet Cluster. (You can see an animation of this collision here). Dark matter it is.

There have been proposed corrections to MoND to account for the Bullet Cluster observations, but so far it looks like dark matter is real. By latest estimates dark matter makes up about 27% of our universe. Of course the big mystery is what dark matter actually is. We know it isn’t regular matter. It has to be something different.

I guess you could say we’re still in the dark on this one.

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