Transcript:

Brian Keating:
For 50 years, dark matter explained why galaxies spin too fast.

Brian Keating:
Its rival, MOND, explained the same thing with no new particles at all. New data from a European spacecraft suggests both of them predicted the wrong curve.

Brian Keating:
I’m Brian Keating. I build telescopes that map the early universe and monitor distant astronomical objects for signs of cracks in relativity. 400 years ago, Johannes Kepler worked out how fast a planet should orbit. The farther out you go, the slower it moves. Galaxies refused to do that. Dark matter was one answer.

Brian Keating:
Modifying Newton’s equations was the other.

Brian Keating:
Then Gaia measured a billion stars in our own galaxy, and the number it got back was the one nobody expected.

Brian Keating:
So, start with Kepler. The solar system gave him the familiar picture. Mercury moves much faster than Earth, and Earth moves much faster than Jupiter. Neptune moves with the urgency of a teenager that you’ve asked to empty the dishwasher. The farther away you get from the Sun, the slower it orbits— not directly proportional, but actually proportional to 1 over the square root of the radius from the Sun. Good ol’ Johannes worked this out over 4 centuries ago. Now Kepler had 3 laws. For a circular orbit, which most of the planets nearly follow, the speed that the planet orbits is determined by the gravitating matter enclosed within that orbit.

Brian Keating:
In fact, the equation is circular speed squared equals Newton’s constant times the enclosed mass divided by radius. Newton actually proved mathematically why Kepler’s laws are correct. Measure an orbital speed, and after assuming a geometry— basically circular— you can infer the gravitational force that’s pulling on the orbiting planet. If the enclosed mass—within the orbital radius—stops increasing, the radius in the denominator keeps growing, but the numerator stays nearly fixed. Therefore, the speed must fall. Now let’s replace the Sun with a galaxy containing only its visible gas and stars. Far outside the bright disk, almost all of that baryonic mass is entirely enclosed. The mass term becomes approximately constant, so the predicted velocity falls off like 1 over the square root of radius.

Brian Keating:
And we’ve seen that far, far out in many galaxies. Now here on the slide, the gray curve is the visible matter only prediction. If galaxies behaved like enlarged solar systems with all of the mass essentially being at the center, that would be the end of the story. The universe, though, has other plans, and a larger budget for the invisible accounting that dark matter seems to require. What astronomers actually found, dating back to Vera Rubin and her collaborators, was the blue curve. The outer velocity remains approximately constant. And if circular speed stays constant while radius increases, the enclosed those gravitating masses must keep increasing in roughly proportion to their radius. The luminosity of the galaxy fades away, but the gravitational influence does not.

Brian Keating:
And that mismatch is one of the clearest reasons dark matter became central to modern astrophysics. It’s not the only reason, and it’s not merely that galaxies spin too fast— it’s that their radial pattern of motion implies more gravitating mass at larger radii than the visible mass can provide. Flat rotation curves map where the missing gravity appears to live. The standard explanation surrounds the visible disk with a much larger dark matter halo. The halo contributes little light, but it keeps adding enclosed mass as we move outward. Combine the disk with the halo and the rotation curve can remain essentially flat. That’s what was observed. So where is the extra gravity coming from? These questions are not exactly identical, but there is some commonality between them, and the rotation curve addresses the second one.

Brian Keating:
The extra gravity. Now measuring our galaxy has one disadvantage: we’re inside of it. This beach ball shows the perspective of God outside of it, but we’re inside of it looking out. So it’s like trying to infer the shape of a football stadium from inside the bleachers. Gaia gave us these exquisite measurements of stellar positions and their motions, but Gaia doesn’t provide a button labeled the true Milky Way rotation curve, click here. That was easy. So we have to begin with proxies. We measure stellar positions and their velocities.

Brian Keating:
We correct for their distances. It’s really good that Gaia is capable of doing that. We have to choose a model and correct for the asymmetric drift of stars that add peculiar effects. And we have to assume something about the equilibrium and symmetry of the physics of the problem. And then we can correct for a circular velocity and any biases that we may have induced. The instrument Gaia provides the data, and the pipeline tells us what we think those data points mean. Revolutionary claims need us to keep those chapters together. And one of the most important things is that stars do not travel on perfectly circular tracks.

Brian Keating:
Just like planets, they’re not perfectly ellipticity-free, but they also have wobbles. They wobble radially and vertically, and stellar populations’ average azimuthal speed is therefore lower than the circular speed of the gravitational field. That difference is called by professional astronomers asymmetric drift. Recovering the circular velocity requires a model of that random motion. Unfortunately, the correction matters most in the outer galaxies where stars become sparse, and that’s the most important part because you have most of the enclosed mass within you the farther out you go. And there is where the disputed decline becomes interesting. In this analysis, the inferred speed would fall by about 30 kilometers per second between 19.5 to 26.5 kiloparsecs from the center. The fitted outer slope is -0.47± 0.15.

Brian Keating:
Even though it sounds close to -0.5, which would be 1 over square root of radius, a declining outer curve looks increasingly plausible. A precisely Keplerian decline is more debatable. Converting it into an extraordinarily low galactic mass is more model-dependent even still. If the circular velocity really fell as 1 over the square root of radius, then the velocity squared falls as 1 over radius. Now if you insert that into the circular velocity equation and the enclosed spherical equivalent mass becomes You move outward but infer surprisingly little additional gravitating mass, which is awkward for a large extended halo whose enclosed mass should keep growing. And that’s the dominant paradigm for the dark matter picture, where galaxies are formed and held together and their rotation is driven by the enclosed mass within their visible light radius. But notice the phrase I just used— spherical equivalent. The Milky Way contains a disk, gas, a bulge, a warp, and a 3-dimensional halo.

Brian Keating:
Turning one curve into a mass Really requires a lot of geometrical insight. So where do we go next? The dramatic analysis produces an average total mass estimate of about 2.6× 10^11 solar masses. That’s a lot— 260 billion equivalent solar masses. So this isn’t actual stars, but it’s stars, gas, and dust. That’s below many independent estimates, which are closer to a trillion solar masses. The number comes from fitting the measured rotation curve and extending a mass model well beyond the region directly constrained by the stars alone. So this value is very interesting, but its precision should not hide the assumptions that produce it, as all good models have to incorporate. The Gaia-based rotation curve is constrained over roughly 9 to 27 kiloparsecs.

Brian Keating:
A Milky Way halo, though, may extend to something like 200 kiloparsecs. So when data extending nearly 30 kiloparsecs produce a total halo mass, most of the mass is supplied by that fitted model rather than that traced directly by the stars in that curve. Extrapolation is therefore unavoidable. But observed and extrapolated aren’t synonyms. Inside, Gaia constrains the dynamics. Outside, we have to make theoretical choices to do most of the work. Now, at this point, when you start to hear that the paradigm of dark matter may have failed to reproduce the dynamics, you might start to celebrate if you’re a MOND advocate like my past guest Stacy McGaugh or the founder of the MOND paradigm, Mordecai Milgrom himself. MOND proposes that below a characteristic acceleration, the effective dynamics depart from Newtonian relationships.

Brian Keating:
In the MOND region, the acceleration is approximately the square root of the Newtonian acceleration times the MOND scale, which is known as a0. For an isolated baryonic mass, this changes the expected orbital behavior without surrounding the galaxy with a conventional particle halo. So MOND has achieved real predictive successes at galactic scales, including the tight relationship between baryonic structure, and the observed acceleration. So if the dark matter paradigm’s curve has a problem, does MOND just win? Now this is where it becomes deliciously inconvenient for both scenarios. How does MOND’s predictions relate to what Gaia has observed? So in this low acceleration limit required for structure to ever form and not have too high a velocity dispersion, the velocity to the 4th power equals Newton’s constant times the baryonic masses times this constant a0, this baseline acceleration. So what’s missing from this equation? Radius. There’s no radius in there. And that’s why MOND produces an asymptotically flat rotation curve for an isolated galaxy.

Brian Keating:
That was one of the great attractions— no pun intended— that Mordecai and others were drawn in by. But now it’s part of its vulnerability. It might be part of its downfall if these data are reproducible. If the Milky Way’s outer curve is Keplerian, MOND is also expecting something flatter too, but it didn’t find that. Dark matter and MOND arrive at the flat outer rotation curves through completely different physics. Dark matter says there’s an additional gravitating mass. MOND says the low acceleration dynamics are different themselves. A robust Keplerian decline would challenge the simplest extended halo expectation and the deep MOND asymptotic behavior.

Brian Keating:
The question becomes not which of these 2 camps won, but why we’re both expecting the wrong curve. So bad news for everybody is Often excellent news for science. I usually say that flaws lead to new laws. That’s what I teach my students. When you find a crack, when you find something unexpected, as Einstein did with Newton’s gravity, for example, and as MOND may have done with the dark matter paradigm, and as inflation did with the Big Bang paradigm, these are exciting times for scientists. A Keplerian decline would not instantly falsify every version of MOND. MOND is nonlinear, so an external gravitational field can influence a galaxy’s internal dynamics and modify the Milky Way’s outer behavior. The external field effect can generate a decline.

Brian Keating:
So the defensible conclusion is not that Gaia killed MOND. A robust Keplerian curve would instead create tension with the isolated prediction and require that the external gravitational field or another refinement do substantial quantitative work. The scientific test is whether the theory fits the measured curve with independent, justified parameters, not whether or not we can tell a cool story after seeing it. Now here’s where I have to insert A warning. This is where experimentalists like me get interested, excited, but also a little bit nervous. Distance errors will alter both the star’s inferred position and its tangential velocity. Any asymmetric drift corrections depend on the tracer density, the gravitational field, and the velocity dispersion— how much these stars are moving independently of the gravitational force of dark matter or MOND. Selection effects can change which stars enter the sample.

Brian Keating:
The warp violates simple disk geometry. Sagittarius and the Large Magellanic Cloud also drive non-circular motion— they’re like outer gravitating masses. These tracers become sparse at great distances, and you have to question whether or not the stars are at actual equilibrium. Now, in the Gaia analyses, neglected dynamical terms and the systematic error budget grow towards the outermost radii. They increase. It gets harder and harder to do, and you get more and more contamination from external gravitating masses like the LMC. None of this proves the decline is false, by the way. It’s a brilliant result.

Brian Keating:
It means that the blue curve we showed earlier may conceal a messy galaxy. Maybe that teenager’s to blame. The more revolutionary the inference, the more carefully we have to distinguish between what Gaia measured from what we, or proponents of MOND or dark matter, would like to interpret.

Brian Keating:
Now, before you declare a winner, MOND has one more move. It isn’t a linear theory, which means a galaxy sitting inside someone else’s gravitational field doesn’t behave like one sitting by itself. And the Milky Way sure ain’t lonely.

Brian Keating:
As I said, the Milky Way is not some isolated, perfect galaxy that’s relaxed in a laboratory just hanging out. The Sagittarius Dwarf Galaxy, nearby but not part of our galaxy, has reportedly crossed and perturbed our Milky Way’s disk. The Large Magellanic Cloud is massive, it’s nearby, and it’s dynamical— it’s rotating, it’s doing its own thing too. Together with the Milky Way’s galactic warp, these interactions can produce ripples, star streams, and north-south asymmetries between the upper and lower halves of the galaxy. These motions are valuable, but they’re not necessarily indicative of equilibrium circular motion. So you wouldn’t expect Kepler’s law to actually hold in that sense. Force a disturbed population into a steady axisymmetric model, and the reconstructed curve will absorb the disturbance and present it as a modification to gravity. Sometimes the galaxy is telling us about dark matter, sometimes it’s telling us that it recently had a close encounter of the third kind.

Brian Keating:
So where does it leave us? At this point, there’s 3 possibilities that I would say remain viable. First, the decline is real, but it’s moderate. The Milky Way has a lighter or more concentrated halo than some older models suggested. Dark matter and MOND both can adjust their parameters, tune them, and survive. Second, the decline is real, but it’s exaggerated. It’s affected by systematics and disequilibrium which were implicitly assumed in the models. It’s the least glamorous answer, which is why scientists have to take it seriously. Third possibility: the outer disk is sufficiently disturbed that the reconstructed curve can never be assumed to be equilibrium and circular and represent the Keplerian profile at all.

Brian Keating:
So we have one pattern and 3 possible physical stories that explain it. The evidence that we have doesn’t uniquely constrain or select between the 3 of them. So what would actually settle the tie, if you will? But there are different objects we can use. Young stars called Cepheids are dynamically colder, Stellar streams can probe objects farther out, and globular cluster satellites can test at larger radii. That’s in fact how we knew the galaxy had a certain size from the beginning with the Shapley debate of the 1920s. Future Gaia releases improve their astrometry, the position and velocity. We’ll also get radio astronomical surveys that will supply different tracers, typically of the gas. And better theoretical models can include the warp, the Sagittarius mini dwarf galaxy effect, and the LMC’s effects as well explicitly.

Brian Keating:
If we combine those methods with different assumptions and different systematics, and we recover the same decline, then we’ll have to listen. It’ll go from 3 sigma to many, many sigma in that case, potentially. But our galaxy may be asking a nastier question. Not did dark matter lose, not did MOND win, but rather, are we expecting the wrong curve? So, what do you think is more preferable given the evidence we’ve presented today? MOND? dark matter, or something else entirely? Leave your comment below, give the video a thumbs up, exercise your thumb, and don’t forget to share this like invisible dark matter throughout your own universe. I’m Brian Keating, Chancellor’s Distinguished Professor of Physics at the University of California San Diego, and I’ll see you next time on the channel.

Brian Keating:
And I’d like to conclude this video by thanking my good friend Alessandro Melchiorri and his collaborator Ruchika. They produced the paper that inspired this. It came out in August, it’s still a preprint, but it’s called The Rotation Curve of the Milky Way: State-of-the-Art The Keplerian Decline Debate and Implications for Dark Matter. It’s a brilliant paper and anyone can understand it. They summarize the field, the history, and the controversy, so make sure you check that out. I’ll leave a link in the description below. Kepler said that the outer stars should slow down. For 50 years, our galaxy said otherwise, and we invented an invisible halo to explain it.

Brian Keating:
Now our galaxy may be taking it back. If that changes how you think about what we actually know, subscribe and tell me which one you prefer. And don’t forget to watch my interviews with Stacey McGaugh and with Mordecai Milgrom.