Spin control: how does swirling interstellar gas slow down enough to drain into a cosmic sink?

Natural History, March, 2007 by Charles Liu

If our Sun turned into a black hole tomorrow, would Earth and the other planets suddenly fall into it? Nope, no way. Black holes, weird as they are, don't "suck" matter. They're gravitational sinkholes, like any other object with mass, so from a distance they're no more destructive than any other lump of matter with an equivalent mass. As long as Earth maintains its angular momentum around the Sun (the product of its mass, orbital velocity, and distance from the Sun), our planet will stay serenely where it is.

Angular momentum is the key to all things spinning--from toy tops whirling on tables to giant planets revolving around distant suns to entire galaxies wheeling around a central black hole. You've doubtless seen figure skaters doing a scratch spin: starting with arms outstretched, they end up whirling dervishly as their arms are crossed close to their chests. One of the fundamental properties of physical systems is that (not counting friction) their angular momentum must stay the same. Thus, as their arms draw in (less distant mass), the skaters' spin velocities must increase.

The same relation holds for rotating liquids and gases. Take spiral galaxies, which look like cosmic pinwheels. The galaxy arms aren't solid. Rather, they're ephemeral patterns of gas flowing in the galaxy's disk; as the gas bunches up, it forms bright blue stars that outshine the regions between the arms. Any unprocessed gas stays in orbit, too, rather than funneling into the center--as long as it retains its angular momentum around the galaxy's center.

On Earth, friction is ubiquitous, and with time it bleeds angular momentum away from just about every spinning thing, making the spin slow down and eventually stop. Scientists who rely on spinning lab equipment--a gyroscope, a centrifuge--have to think hard about how to reduce friction to keep things spinning. We astronomers have the opposite problem. In outer space, friction is rare, so angular momentum rarely goes away; objects and systems spinning in space tend to keep spinning forever. So when things actually do stop spinning and fall into their center of gravity, we have to think hard to understand why.

But what makes stopping such a big deal? For a star to form, most of a vast, spinning disk of interstellar gas many billions of miles across must condense into a spherical blob less than a thousandth its original diameter. But if there's no way for the disk to shed much of its initial angular momentum, no star can form. In particular, if some of the angular momentum of the protostellar gas that formed our infant solar system more than 4 billion years ago hadn't dissipated, the gas would have kept spinning and never have collected in a ball. The Sun would never have been born, and we wouldn't be here today.

So what causes the matter swirling around a protostar to lose its angular momentum, fall in on itself, and form a star? According to one long-held idea, gas moving at various speeds caused turbulence in the swirling matter, which dissipated the angular momentum. Alas, that idea has just been dashed by a swirling canister of fluid slightly taller than a kitchen blender--and along with it, decades of astrophysical models have gone down the drain.

Of course, the aforementioned canister--designed and operated by a team of astronomers and plasma physicists led by Hantao Ji at Princeton University--is hardly your ordinary margarita-mixing machine. But forget that for a brief margarita moment, and think about what happens in an ordinary bar-top blender. The blender mixes the cocktail's ingredients because its rotating blades move its contents faster near the center and dower at the edge. That speed difference creates shear, which in turn creates turbulence--mini-whirlpools and eddies that interfere with the otherwise smooth-swirling flow. The turbulence sucks away the angular momentum of the protobeverage, which is mainly why the mixture stops spinning once the blades are stopped.

On Earth, the onset of turbulence depends on a quantity first defined by the English mathematician-engineer Osborne Reynolds. In 1883, while studying the flow of liquids in pipes, Reynolds determined that as flow speeds up and pipe diameters increase, so does the likelihood of turbulence; furthermore, the higher the density of the fluid--molasses, say, rather than water--the lower the likelihood of turbulence. He condensed all those factors into a single critical ratio, now known as the Reynolds number.

When fluid--liquid or gas--flows in a circular pipe at a Reynolds number greater than about 2,300, the flow is usually turbulent. In a see-through pipe, for instance, eddies and irregular flows would be clearly visible. So engineers design waterworks and gas pipeline systems with Reynolds numbers no higher than about 2,000.

Beyond Earth, fluid flows can dwarf terrestrial ones, and their Reynolds numbers do, too. The flow speeds of gas in a protostellar disk can be many thousands of miles an hour; the density of the gas is much less than a billionth that of water, and the channels of fluid flow can be millions of miles wide. Those factors push the Reynolds number up into the millions, billions, and even trillions. At first glance, then, you'd expect such a gas disk to have tremendous fluid turbulence, enough to drain the angular momentum rapidly out of the disk, causing the gas to pour into a single core.