Beyond Boltzmann

Unraveling Non-Thermal Distributions

The origins of Member Uddipan Banik's latest research project in the School of Natural Sciences can be traced back over 200 years, to the groundbreaking work of Austrian physicist Ludwig Boltzmann.

“When considering the colliding gas particles in a room, for example,” explained Banik, “Boltzmann asked how these particles would move and, importantly, at what speeds they might be moving. He found that such particles tend towards ‘thermal equilibrium,’ where the distribution of particle speeds follows a universal mathematical pattern.” This pattern is known as a Maxwell-Boltzmann distribution.

Not all systems exhibit a Maxwell-Boltzmann distribution, however. Examples of this include collisionless plasmas like the solar wind, a constant stream of charged particles that flows away from the Sun. Satellites that monitor the solar wind, such as the Parker Solar Probe, have found that it exhibits a universal “non-thermal tail,” meaning that a subset of its particles is moving at extremely high velocity with a universal power law distribution.

In a paper published in The Astrophysical Journal, Banik has offered a fundamental, first-principles explanation for this phenomenon. A key innovation in his approach is the incorporation of so-called “self-consistency.” Unlike previous studies, Banik's model accounts for how the velocity of each charged particle influences the forces acting upon it.

Banik found that slower particles get “shielded” by other charged particles, which reduces the force they feel. Faster particles, on the other hand, whizz around without getting shielded as much. They feel stronger forces and hence get kicked to even higher energies. Over time, this difference in energy boost creates the “non-thermal tail.”

Banik’s work has shown that self-consistency is an important ingredient in understanding the origin of non-thermal distributions in astrophysical systems.