In the Dark

“The universe is not only stranger than we imagine, it is stranger than we can imagine.”

I had seen this quote attributed to Sir Arthur Eddington, but this seems to have been a mistake. It was J. B. S. Haldane, and what he actually wrote was, “The universe is not only queerer than we suppose, but queerer than we can suppose.” Eddington was an astronomer and astrophysicist, Haldane an evolutionary biologist.

At the moment Eddington would have been more apropos. This line came to mind because I’ve been reading a bit about dark matter. Or perhaps I should say, I’ve been reading a bit about the theory that proposes the existence of dark matter. After explaining it (in vague and probably inaccurate terms), I’m going to give myself a pat on the back, so put on your wading boots and we’ll get started.

The problem faced by astrophysicists and cosmologists is, galaxies aren’t rotating the way they’re supposed to.

The law of gravitation (which was worked out by Sir Isaac Newton and later tweaked by Einstein) tells us that the further you are from a mass, the weaker the force of gravity with which that mass pulls on you. The force varies inversely with the square of the distance.

If you (“you” being a planet) are in orbit around a star, the further you are from the star, the weaker the star’s gravity. In consequence, you travel more slowly in your orbit. This can be clearly seen in our solar system. The outer planets take a lot longer to travel around the sun. The inner planets, Mercury, Venus, and Earth, are just whizzing along. If the outer planets were traveling as fast as the inner ones, they’d fly away into interstellar space. They stay in their orbits because their velocity exactly balances the weaker pull of the sun.

Stars travel in orbits around the center of a galaxy. That’s what galaxies are — they’re vast bundles of stars orbiting around. They aren’t orbiting around anything in particular. It’s their own combined mass (the mass of the whole galaxy) that creates a gravitational field. This field is what keeps the stars spinning around. It’s what keeps galaxies from flying apart.

Not too many years ago, astronomers developed some improved methods of studying the speed with which the stars in other, nearby galaxies are circling their galactic centers. Embarrassingly, it turned out that galaxies spin too fast. The stars at the outer edges of galaxies are whipping around at pretty much the same speed as stars near the centers of the galaxies. And yet, galaxies don’t fly apart.

This obviously violates Newton’s laws of gravitation. Einstein’s modifications of Newton’s laws don’t explain it either.

Someone cooked up a cute theory to explain it. The theory is, galaxies are embedded in vast haloes of invisible dark matter. We can’t see it, because it neither radiates nor absorbs light. So the total mass of a galaxy, which includes the dark matter, is much larger than you would expect from counting the number of stars in it and multiplying that number by the average mass of a star.

As theories go, this has always seemed a bit too clever to me, a bit too convenient. It reminds me of the theory of phlogiston, which was popular among scientists in the 18th century. But I’m not a physicist, and we know that the universe is a very strange place indeed (see above).

There are other theories that address the issue of galactic spin. I rather like the MoND (Modified Newtonian Dynamics) theory. This theory, which is looked on with scorn by a lot of physicists, postulates that Newton’s equations for gravity simply don’t predict what happens with the extremely low centripetal accelerations of things that are orbiting at galactic distances. (For details, see the MoND pages. Also good is this article, which talks about how MoND successfully explains the movements of nearby dwarf galaxies.)

I’m not a physicist. The MoND partisans may have been smoking too much hashish, for all I know. But they’re bright guys, and they know lots of equations, so they’re not out of the game quite yet.

There are two main ideas about dark matter. It may be baryonic or non-baryonic. “Baryonic” means “made up of ordinary particles of the kind we know, like neutrons and protons.” The dark matter might, in other words, be rocks, comets, black holes, or spinning balls of ice the size of Jupiter. If it’s non-baryonic, it might be made up entirely of stuff that we know nothing about … other than that it exerts a gravitational pull and doesn’t interact with light.

Current thinking is that dark matter — or at least, most of it — can’t be baryonic. If it were, the early Universe wouldn’t have formed nearly as much deuterium as we observe. This is all purely speculative, of course. We have no idea what the early minutes of the Universe were actually like. All we have is a bunch of extremely complicated equations that purport to tell us about it. Be that as it may, non-baryonic dark matter is looking good by comparison.

But the more I thought about the vast halo of dark matter within which each galaxy is supposedly spinning, the more puzzled I became. First of all, it’s a reasonable guess that non-baryonic dark matter is itself subject to gravitation. That is, it doesn’t just exert a gravitational pull, it responds to gravity. If it didn’t, why would a cloud of dark matter remain condensed into a spherical halo? Why wouldn’t it just dissipate? It’s possible that the particles of dark matter attract one another, and thus remain in the same neighborhood, by means of some other, non-gravitational force whose existence we don’t even suspect, a force that doesn’t affect baryonic matter. But that’s a pretty wacky hypothesis. Not provably wrong, since nobody has any idea what dark matter is, but physicists don’t like theories that require them to posit yet more basic universal forces. They’re trying to unify their theories, not add still more jerry-rigged assumptions. So let’s go with gravity. Dark matter responds to gravity.

But that idea raises what appears to me to be an awkward problem: Why is it, if the galaxy is permeated by a halo of dark matter, that the sun hasn’t gathered in its own private halo of the stuff?

If particles of non-baryonic dark matter are zipping around us all the time, unsuspected, they will have various velocities. We can suppose that their maximum velocity, on average, is less than the escape velocity of the galactic halo, because if it were greater, the dark matter would dissipate. We can also suppose that there will be some variation in the velocity of individual particles of dark matter. Some will be going faster, some slower.

We don’t know if they bump into one another. They may pass through one another, which would mean that their velocities are not affected by collisions. Collisions would slow some of them down. Nonetheless, it would be perilous to assume that all of them are traveling at exactly the same velocity relative to the galactic center. Remember, if Newtonian gravity holds true out to the edge of the dark matter halo, the particles at the outer edge will be traveling very slowly compared to those in the inner part of the cloud. And they’ll be in elliptical orbits, so they’ll be speeding up as they move inward toward the galactic core, and slowing down as they move outward.

So there will, inevitably, be some slower-moving particles of dark matter that will pass near the sun. The sun is moving on its own orbit through the galaxy, so some of the dark matter particles will be on more or less parallel orbits (meaning they’ll have less relative velocity compared to the sun.) And the sun, like every other star, has a powerful gravitational field. Over the course of billions of years, then, we would expect that stars would accrete their own haloes of dark matter — denser regions of dark matter within the galactic halo. As time passed, these stellar haloes of dark matter would grow.

The trouble is, if that were true, Newtonian orbital mechanics wouldn’t work at the level of the solar system either. Our outer planets (Saturn, Uranus, Neptune) would be orbiting faster, because they’d be embedded in a relatively thick cloud of dark matter.

I don’t even think it matters whether the dark matter is baryonic or non-baryonic. The same thing would happen in either case.

I know almost nothing about any of this stuff. So yesterday I emailed Andrew Zimmerman Jones, who writes the physics blog for I asked him, “Why hasn’t the sun accreted a halo of dark matter?”

This is the part where I pat myself on the back. He replied to my email. He said (not a direct quote, but close): “That’s a good question. I’ve never thought of it, and I should have.” So maybe in a few days he’ll come back to me with the current thinking on the subject — or write a blog post about it.

Or maybe I just let the air out of the tires of a major theory of cosmology. Nah, I’m not that smart. Those clever physics lads will have an answer. More likely, five or six answers, all of which they thought of five years ago and none of which can yet be verified experimentally.

They don’t know what’s going on, you see. They have these vast and dazzling edifices of sophisticated mathematics, and they haven’t got the least idea how the Universe actually works. They’re as thoroughly in the dark as I am.

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