Speaker
Description
Nearly collisionless self-gravitating systems far from equilibrium, such as merging galaxies, rapidly relax toward virialized equilibria through violent relaxation. I will present a framework for predicting the equilibria of violent relaxing systems that combines Lynden-Bell statistical mechanics and the time evolution of the system’s Casimir invariants [1]. The Casimirs evolve because finite-$N$ effects break the conservation of phase-space volume on a timescale given by the dynamical time multiplied by a logarithmic factor in $N$, the number of particles. This (relatively) fast dissipation arises due to gravitational turbulence, in which large-scale fluctuations in the gravitational field drive chaotic mixing of the distribution function in six-dimensional phase space. This turbulence obeys universal scaling laws below the Jeans scale for the fluctuation spectra of the gravitational field and the distribution function, which can be derived from a phenomenological scaling theory. The scale separation (in $\log N$) between the dynamical and dissipation timescales enables systems to relax "adiabatically" through a sequence of Lynden-Bell equilibria, each with nearly fixed Casimirs. In the long-time limit, the system tends toward its "ground state": a Lynden-Bell equilibrium that is both the maximum-entropy and minimum-energy state corresponding to the system’s late-time Casimirs. This framework is corroborated by 1D N-body simulations of violent relaxation and may be able to explain the universal equilibria of galaxies and dark matter halos. I will also discuss connections with turbulent relaxation in nearly collisionless plasmas [2, 3].
[1] Nastac, M. L., Ginat, Y. B., Ewart, R. J., Barnes, M. & Schekochihin, A. A. 2026 Violent relaxation redux, in preparation.
[2] Ewart, R. J., Nastac, M. L., Bilbao, P. J., Silva, T., Silva, L. O. & Schekochihin, A. A. 2025 Relaxation to universal non-Maxwellian equilibria in a collisionless plasma, PNAS 122, e2417813122.
[3] Nastac, M. L., Ewart, R. J., Juno, J., Barnes, M. & Schekochihin, A. A. 2025 Universal fluctuation spectrum of Vlasov-Poisson turbulence, e-print arXiv:2503.17278.