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In the Dark: What's the Matter?

Sunday, Jan. 14, 2007:

I've been reading a bit about the latest theories cooked up by the cosmologists. These brainy folks peer at distant galaxies and attempt to understand the origins and eventual fate of the universe in which we live. Since they can't visit distant galaxies, their observations are, of necessity, limited in scope. Large deductions have to be made based on the slimmest shreds of evidence.

Based on the best available evidence, it appears that galaxies aren't spinning the way they ought to. This is deduced from a well-known phenomenon called the red shift, which enables you to measure the velocities of stars by looking at the light coming from them.

Galaxies spin, rather than flying apart, because of gravitation. The stars in a galaxy all orbit the center of mass of the galaxy. The relationship of orbital speed to the mass of the object being orbited is well understood, because we've been able to study our own solar system in considerable detail. The details are embodied in a formula called Kepler's Third Law of Motion. Kepler figured out why, or at least described how, the outer planets orbit more slowly than the inner planets.

Trouble is, the stars in distant galaxies don't seem to be obeying Kepler's Third Law. The stars farther from the center of the galaxies ought to be travelling more slowly than those near the center, because they're further from the galaxy's center of mass -- but that's not what the red shift indicates. In many cases, the stars at the outer edges of galaxies seem to be travelling much too fast.

This would happen if the galaxy were actually a lot larger than it seems to be. If the outer stars were orbiting within much of the aggregate mass of the galaxy, they would behave as they seem to be behaving.

By measuring the total amount of light coming from a galaxy and making certain assumptions about the average mass of individual stars, astronomers can figure out how much mass there ought to be in a distant galaxy. Trouble is, they're not seeing nearly enough mass, nor is what they're seeing spread out enough.

The solution that has been proposed is something called "dark matter." Without getting too deep into particle physics (if you care about this topic at all, you probably know a lot more about it than I do), the idea is that the universe contains quite a lot of elementary particles called Weakly Interacting Massive Particles (or WIMPs, for short). These particles could be passing through your body in droves right now, and you'd never know it, because they don't interact. They don't reflect light, they don't have an electrical charge, they can pass through ordinary atoms as if the atoms weren't even there.

But the WIMPs have mass, so they respond to gravity, and they attract other, ordinary matter by means of gravity.

If a galaxy were surrounded by a halo of this dark matter, the mystery of how it spins would be solved. Galaxies may be composed of between 50% and 80% dark matter. Or at least, that's the theory.

This theory reminds me a bit of phlogiston. Phlogiston was an invisible substance proposed by physicists a couple of hundred years ago in order to explain combustion. The idea was that objects that could burn had phlogiston in them, and when they were burned the phlogiston escaped. The existence of phlogiston was supported by the fact that if you carefully weighed the ashes after burning something, you'd find that they weighed less than the original unburned substance had. Clearly, that was because the phlogiston was gone.

But then (I'm dredging up a 40-year-old memory here, and may have the details wrong) it was discovered that a few things were heavier after they were burned than before. Today we understand that this is because the process of burning created new chemical compounds that bonded atmospheric oxygen in solid form. But in the 18th century, physicists had to scramble to explain how phlogiston could sometimes weigh less than nothing.

When modern chemistry was born, the phlogiston theory passed into history. But I can't help thinking dark matter is the 21st century equivalent of phlogiston. It's an invisible substance that's proposed in order to account for phenomena that are observed but poorly understood.

So I asked myself (this is the kind of thing my brain comes up with when it's the middle of the night and I'm wide awake), if our own galaxy were embedded in a halo of dark matter particles, what would be the visible result?

To begin with, these particles have to be responding to gravitation. If they weren't, they'd fly serenely away. The whole universe would be full of a uniformly distributed "fog" of dark matter. Because it was uniformly distributed, its effects would cancel out, and its existence would be undetectable and explain nothing. The whole point of the theory is that dark matter congregates around galaxies (or else, that galaxies form where dark matter is already congregating, which amounts to much the same thing).

Individual WIMPs, therefore, have velocities that are less than the escape velocity of the galaxy around which they orbit. We don't know what their average velocity may be, but the escape velocity of the galaxy is an upper limit.

As they whiz around and through a galaxy, some of them will pass close to individual stars. At that point, those whose velocity is less than the escape velocity of the star will be drawn into an orbit around the star. I don't know much about orbital dynamics, but I have the impression that the gravity of a planet can cause a "braking effect" on a smaller body, drawing the smaller body into an orbit around the star that the planet orbits. So a particle that might otherwise enter a star's gravitational field, whiz through it, and exit on the other side may sometimes be sucked in and kept because it happens to pass close to a planet.

Over the course of billions of years, then, we should expect that a significant percentage of the dark matter in a galaxy would come to reside in invisible halos around individual stars, just as it's hypothesized to reside in halos around galaxies.

But there's a problem here: If there were a halo of dark matter around the Sun, Kepler never would have been able to formulate his Third Law, because the orbits of the outer planets would have been affected by the gravitational field of the halo. They would be orbiting faster than they're observed to orbit.

I'm just a layman, but it seems to me that at this point the theory of dark matter shoots itself in the foot. Dark matter is presumed to exist in the galaxy, but is also presumed not to exist in the neighborhood of the Sun.

Phlogiston, anyone?