Why isn’t the interior of the solar system spinning faster? Old riddle has possible new solution

The motion of a tiny number of charged particles could solve a long-standing mystery about thin disks of gas spinning around young stars, according to a new study by Caltech.

These features, called accretion disks, last tens of millions of years and are an early phase in the evolution of the Solar System. They contain a small fraction of the mass of the star they are orbiting; Imagine a Saturn-like ring as big as the solar system. They are called accretion disks because the gas in these disks slowly moves inward toward the star.

Scientists have long recognized that this inward spiral should cause the radially inner portion of the disk to spin faster, according to the law of conservation of angular momentum. To understand conservation of angular momentum, think of figure skaters spinning: when their arms are extended, they spin slowly, but when they retract their arms, they spin faster.

Angular momentum is proportional to velocity times radius, and the law of conservation of angular momentum states that angular momentum in a system remains constant. So if the skater’s radius is decreasing because he’s tucking his arms in, then the only way to keep angular momentum constant is to increase spin speed.

The accretion disk’s inward spiraling motion is similar to a skater retracting his arms – and as such, the inner portion of the accretion disk should spin faster. In fact, astronomical observations show that the inner part of an accretion disk spins faster. Oddly enough, however, it’s not spinning as fast as the law of conservation of angular momentum predicts.

Over the years, researchers have explored many possible explanations for why the accretion disk’s angular momentum is not conserved. Some friction between the inner and outer rotating parts of the accretion disk could slow down the inner section. However, calculations show that accretion disks have negligible internal friction. The leading current theory is that magnetic fields create something called “magnetorotational instability” that creates gas and magnetic turbulence – effectively creating friction that slows the rotation speed of the inwardly spiraling gas.

“That worried me,” says Paul Bellan, a professor of applied physics. “People always want to blame turbulence for phenomena they don’t understand. There is currently a large cottage industry arguing that turbulence is responsible for getting rid of angular momentum in accretion disks.”

A decade and a half ago, Bellan began investigating this question by analyzing the orbits of individual atoms, electrons, and ions in the gas that forms an accretion disk. His goal was to determine how the individual particles in the gas behave when they collide with each other and how they move between collisions, to see if the loss of angular momentum can be explained without introducing turbulence.

As he has explained over the years in a series of articles and lectures focused on “basic principles” – the basic behavior of the components of accretion disks – charged particles (i.e. electrons and ions) are influenced by both gravity and magnetic fields , while neutral atoms are only affected by gravity. That difference, he suspected, was key.

Caltech graduate student Yang Zhang attended one of these lectures after attending a class that taught him how to create simulations of molecules as they collide with each other to explore the random distribution of velocities in ordinary gases like air, which we breathe to create. “I reached out to Paul after the lecture, we talked about it and finally decided that the simulations could be extended to charged particles colliding with neutral particles in magnetic and gravitational fields,” says Zhang.

Ultimately, Bellan and Zhang created a computer model of a spinning, super-thin, virtual accretion disk. The simulated disk contained about 40,000 neutral and about 1,000 charged particles that could collide with each other, and the model also accounted for the effects of both gravity and a magnetic field. “This model had just the right amount of detail to capture all the essential features,” Bellan says, “because it was large enough to behave like trillions and billions of neutral particles, electrons, and ions colliding, forming a star in one Set up magnets orbit.”

The computer simulation showed that collisions between neutral atoms and a much smaller number of charged particles would cause positively charged ions or cations to spiral inward toward the center of the disk, while negatively charged particles (electrons) spiraled outward toward the edge. Meanwhile, neutral particles lose their angular momentum and, like the positively charged ions, spiral inward towards the center.

A careful analysis of the underlying physics at the subatomic level – particularly the interaction between charged particles and magnetic fields – shows that angular momentum is not conserved in the classical sense, although something called “canonical angular momentum” is in fact conserved.

The canonical angular momentum is the sum of the original ordinary angular momentum plus an additional quantity that depends on a particle’s charge and the magnetic field. For neutral particles, there is no difference between ordinary angular momentum and canonical angular momentum, so worrying about canonical angular momentum is unnecessarily complicated. But for charged particles – cations and electrons – canonical angular momentum is very different from ordinary angular momentum because the extra magnetic quantity is very large.

Since electrons are negative and cations are positive, the inward movement of ions and the outward movement of electrons caused by collisions increase the canonical angular momentum of both. Neutral particles lose angular momentum through collisions with the charged particles and move inward, offsetting the increase in canonical angular momentum of the charged particles.

It’s a small difference, but makes a big difference throughout the solar system, says Bellan, who argues that this subtle calculation satisfies the canonical angular momentum conservation law for the sum of all particles in the entire disk; only about one in a billion particles needs to be charged to explain the observed loss of angular momentum of the neutral particles.

In addition, Bellan says, the inward movement of cations and the outward movement of electrons causes the disk to become something of a giant battery, with a positive terminal near the center of the disk and a negative terminal at the edge of the disk. Such a battery would drive electric currents flowing away from the disk both above and below the plane of the disk. These currents would propel astrophysical jets ejecting out of the disk in both directions along the disk’s axis. In fact, jets have been observed by astronomers for over a century and are known to be associated with accretion disks, although the force behind them has long been a mystery.

Bellan and Yang’s work was published in The Astrophysical Journal on May 17th.

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