Very long-term relaxation of harmonic 1D self-gravitating systems
Abstract
One-dimensional self-gravitating systems admit genuine thermodynamical equilibria. For systems with strictly monotonic orbital frequency profile, the Landau and Balescu-Lenard theories predict a relaxation time scaling linearly with the number of particles, N, in agreement with simulations. Yet, these theories become ill-posed for degenerate frequency profiles, as is the case in the harmonic potential, where all particles share the exact same mean orbital frequency. Using an exact collision-driven 1D integrator, we investigate numerically the self-consistent relaxation of 1D harmonic self-gravitating systems. We show that harmonic systems relax on a timescale that grows quadratically with N. We show that systems that are only partially degenerate display the same quadratic scaling for low N, but transition to the linear, non-degenerate behaviour for larger N. The larger the fraction of degenerate orbits, the larger the value of N at which this transition of dynamical regime occurs. Finally, we explore the dynamics of fully non-degenerate systems, albeit with finite radial support: we confirm that their relaxation time scales linearly with N, though with a substantially larger prefactor than in non-compact systems. Astrophysically, this investigation should offer some new clues on the dynamics of density cores, as in the center of dwarf galaxies.
Related
- Efficient numerical evolution of self-gravitating systems with dark-matter-baryon scattering
- Accurate dynamical mass and orbit determination of the M dwarf binary DG CVn using astrometric very long baseline interferometry
- The Peculiar Astrometric Behaviour and Radio Structure of the Quasar 1524-136 Revealed with Very Long Baseline Interferometry
- Very Long Baseline Interferometry with the SKA Observatory
- An RFSoC-based Backend and Timing System for the Balloon-borne Very Long Baseline Interferometry Experiment
BibTeX
@misc{tep2026very,
title = {{Very long-term relaxation of harmonic 1D self-gravitating systems}},
author = {Kerwann Tep and Jean-Baptiste Fouvry and Christophe Pichon},
howpublished = {HAL},
year = {2026},
month = aug,
eprint = {2603.11238},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05760118v1},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Very long-term relaxation of harmonic 1D self-gravitating systems
AU - Kerwann Tep
AU - Jean-Baptiste Fouvry
AU - Christophe Pichon
PY - 2026
DA - 2026/08/25
PB - HAL
UR - https://hal.science/hal-05760118v1
AB - One-dimensional self-gravitating systems admit genuine thermodynamical equilibria. For systems with strictly monotonic orbital frequency profile, the Landau and Balescu-Lenard theories predict a relaxation time scaling linearly with the number of particles, N, in agreement with simulations. Yet, these theories become ill-posed for degenerate frequency profiles, as is the case in the harmonic potential, where all particles share the exact same mean orbital frequency. Using an exact collision-driven 1D integrator, we investigate numerically the self-consistent relaxation of 1D harmonic self-gravitating systems. We show that harmonic systems relax on a timescale that grows quadratically with N. We show that systems that are only partially degenerate display the same quadratic scaling for low N, but transition to the linear, non-degenerate behaviour for larger N. The larger the fraction of degenerate orbits, the larger the value of N at which this transition of dynamical regime occurs. Finally, we explore the dynamics of fully non-degenerate systems, albeit with finite radial support: we confirm that their relaxation time scales linearly with N, though with a substantially larger prefactor than in non-compact systems. Astrophysically, this investigation should offer some new clues on the dynamics of density cores, as in the center of dwarf galaxies.
ER -