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COLD DIFFUSION
by Kathleen Ricker, NCSA Science Writer

In the interstellar medium--the vast, low-density regions of space between the stars--churn molecular clouds, turbulent masses of magnetized hydrogen gas and dust that ultimately produce new stars. Molecular clouds are extremely cold nebulae, with temperatures ranging from about -440 to -370 degrees Fahrenheit and consist mostly of hydrogen molecules.

When parts of a molecular cloud eventually collapse because of gravitational instability, they create a dense region warmer than the surrounding interstellar medium. This region, called a protostar, continues to increase in pressure and temperature until thermonuclear reactions at its core transform it into a new star.

But why, despite the mass and temperature of hundreds of observed molecular clouds in a given galaxy, don’t more of them simply collapse and form massive starbursts? "That would mean we would see much higher star formation rates in the galaxy than we actually observe," explains Fabian Heitsch, an astrophysicist at the University of Wisconsin at Madison (UWM). Heitsch says that, given the number of molecular clouds, one might expect to observe 200 newly forming stars per year, but actual observations only average around three per year.

Molecular clouds have been thought to be stable because of, among other things, the presence of magnetic fields, which, if sufficiently strong, could prevent the molecular clouds from collapsing under their own gravity. The interaction of magnetic fields with charged fluids (in this case, hydrogen) is called magnetohydrodynamics (MHD). In previous simulations, Heitsch, together with Mordecai-Mark Mac Low, Pakshing Li and Michael L. Norman, investigated the role of turbulence and magnetic fields in preventing the collapse of molecular clouds, relying heavily on NCSA's SGI Origin2000.

In his current work, Heitsch and his collaborators, Ellen Zweibel at UWM and Adrianne Slyz at the University of Oxford, are investigating how magnetic fields might diffuse in a turbulent environment, ultimately leading to the collapse within the molecular cloud. Heitsch recently ran two-dimensional simulations on NCSA's now-retired SGI Origin2000 and is currently preparing to run three-dimensional simulations on Copper, the center's IBM p690.

WHEN THE NUMBERS DON'T ADD UP

In the interstellar medium, the magnetic field is essentially frozen to the gas--a property referred to as flux freezing--such that the field strength would be expected to increase on average if the gas is compressed. How long the magnetic field can support the cloud depends on the strength of the field. "If the field is very strong, it supports the cloud indefinitely," says Heitsch, "and although the gas can move along the (straight) field lines, it can not move perpendicular to them because of flux freezing, so we get a sheetlike structure." But if the field is weak, Heitsch says, "the cloud would collapse directly."

The magnetic field isn't necessarily homogeneous throughout the cloud. It can be more intense in some regions of the clouds than in others, and especially, it can be highly tangled by the turbulent motions of the cloud's gas.

According to the laws of physics, when the cloud, or part of the cloud, collapses on itself, its mass should remain the same. The volume decreases, while the density increases in proportion to the decrease in volume. As for the magnetic flux, as the volume decreases, the magnetic lines are also concentrated over a smaller area. Thus, the magnetic field should increase with two-thirds power, along with the density.

However, says Heitsch, "observations of the magnetic field strength correlated with the density in the interstellar medium show the relationship as very flat. The magnetic field doesn’t change with increasing density." This suggests that the magnetic flux-to-mass ratio in the molecular cloud is actually decreasing, rather than holding steady.

How to explain the decrease? Of course, one could assemble molecular clouds by gas flows along the field lines, in which case no correlation between the magnetic field strength and the density would be observed. However, to reach gas densities typical for molecular clouds, gas would have to be carried over huge distances. The observed magnetic fields would be simply too weak to make such an organized flow structure possible. Heitsch offers another possibility, ambipolar diffusion, which causes charged particles to drift gradually out of the cloud.

This answer by itself is not entirely adequate, though.

A SLOW LEAK

Within the molecular clouds are ions, which respond to magnetic fields, and neutral atoms and molecules, which do not. Nevertheless, "if the medium is not fully ionized, the neutral [particles] can feel the magnetic field’s interaction with the [charged] particles," explains Heitsch, "so the ions collide with the neutrals and drag the neutrals around."

It is these neutral particles, however, that cause the collapse of the cloud. When the ionization decreases, and ions become fewer and fewer, "they don’t collide with the neutrals anymore, and the neutrals start to decouple from the ions and start to slip through the field lines," says Heitsch. This process is known as ambipolar diffusion and, by itself, could result in the collapse of the cloud.

Ambipolar diffusion, however, doesn’t happen quickly enough to explain the loss of the magnetic field strength. The timescale required for it to occur naturally and completely is anywhere between 100 million to a billion years, which, according to Heitsch, is "far longer than any timescale on which molecular clouds could form."

But, Heitsch wondered, could ambipolar diffusion operate at a faster rate than is conventionally accepted? And if so, how?

ENTER TURBULENCE

The answer may lie in the molecular cloud's turbulence, which helps to provide pressure in the absence of heat, but is also responsible for the gravitational collapse of parts of a molecular cloud. This turbulence is supersonic, often measuring at Mach 10, because the speed of sound in the dense interstellar medium is extremely low. "As a result, the cloud is uneven throughout, with higher concentration of gas in some regions, and, although the turbulence might prevent the global collapse of the cloud, it promotes collapse locally," explains Heitsch.

In addition to providing the pressure necessary to maintain the cloud's stability, turbulence can, however, also increase the ambipolar diffusion rate by mixing the field to small scales. Heitsch simulated a two-dimensional section of a molecular cloud to find out whether turbulence would indeed have such an effect on diffusion and discovered that this was indeed the case. "We can [now] diffuse the flux-to-mass ratio at a rate a factor of 10 or 100 higher than the standard diffusion rate, Heitsch says. "This would explain the weak correlation between magnetic field strength and density in the interstellar medium."

Heitsch has been using an extension of a gas-kinetic flux-splitting method developed by Xu and Tang Xu in 1999 and 2000, which is especially useful for investigating MHD problems including diffusive processes. A bit daunted by the prospect of porting his code to a new machine when the Origin2000 neared retirement, he was in for a pleasant surprise when he did his first test run. "I was so impressed that I could take the code and compile it on the IBM p690 and it ran--that has never happened to me. That's the first time a code ran quickly for me, which was very nice."

Heitsch is attempting to make his simulations progressively more and more realistic. "The models so far are restricted because they're only two- dimensional--the magnetic field is perpendicular to the flow plane, which is the easiest, most tractable case." The next step, he says, is to create a three-dimensional model. "I'm looking forward to the time when that will happen, because that will be computationally very expensive--and very exciting."

Funding statement

This research is funded by the National Science Foundation.

For further information: http://lcd-www.colorado.edu/~heitsch/research.html#mhdturb.