According to a new study from Caltech, the movement of a small number of charged particles may solve a long-standing mystery about thin disks of gas orbiting young stars.
These functions, called accretion disks, last for tens of millions of years and represent an early stage in the evolution of the solar system. They contain a small fraction of the mass of the star they orbit; imagine a Saturn-like ring the size of the solar system. They are called accretion disks because the gas in these disks slowly spirals inward toward the star.
Scientists long ago realized that when this inward spiral occurs, the radially inner part of the disk should spin faster, according to the law of conservation of angular momentum. To understand the conservation of angular momentum, think of spinning figure skaters: When their arms are straight, they spin slowly, but when they pull their arms in, 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 decreases because he has drawn his arms inward, the only way to keep the angular momentum constant is to increase the spin rate.
The inward spiraling motion of the accretion disk is similar to a skater pulling its arms inward – and as such, the inner part of the accretion disk should spin faster. Indeed, astronomical observations show that the inner part of an accretion disk spins faster. Oddly, though, it doesn’t spin as fast as predicted by the law of conservation of angular momentum.
Over the years, researchers have explored many possible explanations for why the accretion disk’s angular momentum is not conserved. Some thought that friction between the inner and outer rotating parts of the accretion disk could slow down the inner region. However, calculations show that accretion disks have negligible internal friction. The leading current theory is that magnetic fields create what’s called “magnetorotational instability” that generates gas and magnetic turbulence — effectively creating friction that slows the rotational speed of inwardly spiraling gas.
“That worries me,” said Paul Bellan, professor of applied physics. “People always want to blame turbulence on phenomena they don’t understand. There’s a big cottage industry right now claiming that turbulence is the cause of getting rid of angular momentum in accretion disks.”
A decade and a half ago, Bellan began exploring the 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, and how they move between collisions, to see if the loss of angular momentum can be explained without creating turbulence.
As he explained over the years in a series of articles and lectures focused on “first principles” – the fundamental behavior of the constituent parts of accretion disks – charged particles (i.e. electrons and ions) are affected by both gravity and magnetic fields, while neutral atoms are only affected by gravity. This difference, he guessed, was the key.
Caltech graduate student Yang Zhang attended one of those lectures after taking a course in which he learned to make simulations of molecules as they collide with each other to produce the random distribution of velocities in ordinary gases, such as the air we breathe. . “I approached Paul after the conversation, we discussed it and finally decided that the simulations could be extended to charged particles colliding with neutral particles in magnetic and gravitational fields,” Zhang says.
Finally, 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 took into account 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 upon trillions of colliding neutral particles, electrons and ions orbiting a star in a magnetic field.” .”
The computer simulation showed 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) spiral outward toward the edge. Neutral particles meanwhile lose their angular momentum and, like the positively charged ions, spin inward toward 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 indeed conserved.
Canonical angular momentum is the sum of the original ordinary angular momentum plus an additional amount that depends on the charge on a particle 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 – the canonical angular momentum is very different from the ordinary angular momentum, because the extra magnetic amount is very large.
Since electrons are negative and cations positive, the inward movement of ions and outward movement of electrons, which are caused by collisions, increase the canonical angular momentum of both. Neutral particles lose angular momentum due to collisions with the charged particles and move inward, which compensates for the increase in the canonical angular momentum of charged particles.
It’s a small difference, but makes a huge difference at the solar system scale, says Bellan, who argues that this subtle accounting satisfies the law of conservation of canonical angular momentum for the sum of all the particles in the entire disk; only about one in a billion particles needs to be charged to account for the observed loss of angular momentum of the neutral particles†
In addition, Bellan says, the inward movement of cations and outward movement of electrons results in the disk becoming something like a giant battery with a positive terminal near the disk center and a negative terminal at the disk edge. Such a battery would drive electric currents flowing away from the disc both above and below the plane of the disc. These currents would power astrophysical jets that shoot from the disk in both directions along the disk axis. Indeed, jets have been observed by astronomers for over a century and are known to be associated with accretion disks, although the power behind them has long been a mystery.
Bellan and Yang’s article was published in The astrophysics magazine on May 17.
Yang Zhang et al, Neutrally charged particle collisions as the mechanism for accretion disk Angular Momentum Transport, The astrophysics magazine (2022). DOI: 10.3847/1538-4357/ac62d5
California Institute of Technology
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