Astrophysical flows from small kinetic scales to large hydrodynamic scales are non-linear and turbulent. And yet, order emerges from chaos. Matter tends to self-organize into universal distributions.
In neutral gases, the emergence of the Maxwellian distribution through particle collisions is well understood. By contrast, the origin of non-Maxwellian, power-law distributions observed in systems governed by long-range interactions, e.g., collisionless plasmas and self-gravitating systems, remains an open problem. In this talk, I will describe recent progress towards understanding how such universal distributions arise across astrophysical scales, using perturbative calculations in kinetic theory and hydrodynamics, as well as high-resolution numerical simulations.
I will begin by discussing how electron and ion distribution functions in weakly collisional plasmas relax towards specific power-laws (kappa distributions), and how this process may shed light on the long-standing problem of solar coronal heating. I will then turn to magnetized accretion disks, where I will present a theory for large-scale (magnetorotational) dynamo action that explains the origin of long-period cyclic behavior of magnetic fields (the famous butterfly diagram) in sheared rotational flows.
Finally, I will address the relaxation of self-gravitating systems. I will discuss how dynamical friction drives the inspiral and merger of black holes in galaxies, and how core-stalling and buoyancy can counteract this process. This has far-reaching implications for gravitational wave detections from such events with the Laser Interferometer Space Antenna and the Pulsar Timing Array. Then I will present a new first-principles theory for collisionless relaxation (virialization) that provides a physical explanation for the emergence of the universal Navarro–Frenk–White profile in cold dark matter halos, which has been a long-standing puzzle in structure formation. I will conclude by discussing some open problems in plasma astrophysics and gravitational dynamics that require particular attention from both theoretical and observational perspectives.