Dark Matter Has a Problem. So Does MOND.

Brian Keating (0:00)

For 50 years, dark matter explained why galaxies spin too fast. 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. On Brian Keating, I built 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. Modifying Newton's equations was the other. Then Gaia measured a billion stars in her own galaxy, and the number it got back was the one nobody expected.

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 at 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 one over the square root of the radius from the sun. Good ol Johannes worked this out over four centuries ago. Now, Kepler had three 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. In fact, the equation is circular speed squared equals Newton's constant times the enclosed mass divided by a 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 one over the square root of radius. 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 behave 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, gravitating mass must keep increasing in roughly proportion to the radius. The luminosity of the galaxy fades away, but the gravitational influence does not. 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, 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. We correct for their distances. It's really good. Gaia is capable of doing that. We have to choose a model and correct for the asymmetric drift of stars. They add peculiar effects. We have to assume something about the equilibrium and symmetry of the physics of the problem. 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 meet. Revolutionary claims need us to keep those chapters together. One of the most important things is that stars do not travel on perfectly circular tracks. Just like planets, they are 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.