Beautiful Theory,
Ugly Data

26 October 2012

After a busy week finalizing the sendoff of the book to Cambridge, I finally have time to start answering some of the “Ask An Astrophysicist” questions. We’ll start off with one from Mark Bruce, who asks whether I’m in the Dark Matter or MOND camp. Before answering that, let’s talk about about what these two camps are.

Speed of hydrogen in the Milky Way. Brian Koberlein
Speed of hydrogen in the Milky Way.

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. Technically, not the stars, but rather hydrogen gas in interstellar space, which moves at basically the same speed. The result of those measurements are given by the dots on the figure. 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 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.