Very long-term relaxation of harmonic 1D self-gravitating systems
- 1Observatoire Astronomique de Strasbourg, CNRS UMR 7550
- 2Institut d’Astrophysique de Paris, CNRS and Sorbonne Université, UMR 7095
- 3Kyung Hee University, Department of Astronomy & Space Science
Abstract
One-dimensional self-gravitating systems admit genuine thermodynamical equilibria. For systems with a strictly monotonic orbital frequency profile, the Landau and Balescu–Lenard theories predict a relaxation time that scales linearly with the number of particles, N , in agreement with simulations. These theories become ill-posed for degenerate frequency profiles, as is the case in the harmonic potential, where all particles have the exact same mean orbital frequency. Using an exact collision-driven 1D integrator, we numerically investigated 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 high N, but transition to the linear non-degenerate behaviour for higher N . The larger the fraction of degenerate orbits, the higher the value of N at which this transition of dynamical regime occurs. Finally, we explored the dynamics of fully non-degenerate systems, but with finite radial support: we confirm that their relaxation time scales linearly with N , but with a substantially larger prefactor than in non-compact systems. Astrophysically, this investigation offers some new clues on the dynamics of density cores, as in the centre of dwarf galaxies.
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BibTeX
@article{tep2026very,
title = {{Very long-term relaxation of harmonic 1D self-gravitating systems}},
author = {Kerwann Tep and Jean-Baptiste Fouvry and Christophe Pichon},
journal = {Astronomy \& Astrophysics},
year = {2026},
month = oct,
doi = {10.1051/0004-6361/202659808},
url = {https://www.aanda.org/10.1051/0004-6361/202659808},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Very long-term relaxation of harmonic 1D self-gravitating systems
AU - Kerwann Tep
AU - Jean-Baptiste Fouvry
AU - Christophe Pichon
PY - 2026
DA - 2026/10/12
JO - Astronomy & Astrophysics
DO - 10.1051/0004-6361/202659808
UR - https://www.aanda.org/10.1051/0004-6361/202659808
AB - One-dimensional self-gravitating systems admit genuine thermodynamical equilibria. For systems with a strictly monotonic orbital frequency profile, the Landau and Balescu–Lenard theories predict a relaxation time that scales linearly with the number of particles, N , in agreement with simulations. These theories become ill-posed for degenerate frequency profiles, as is the case in the harmonic potential, where all particles have the exact same mean orbital frequency. Using an exact collision-driven 1D integrator, we numerically investigated 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 high N, but transition to the linear non-degenerate behaviour for higher N . The larger the fraction of degenerate orbits, the higher the value of N at which this transition of dynamical regime occurs. Finally, we explored the dynamics of fully non-degenerate systems, but with finite radial support: we confirm that their relaxation time scales linearly with N , but with a substantially larger prefactor than in non-compact systems. Astrophysically, this investigation offers some new clues on the dynamics of density cores, as in the centre of dwarf galaxies.
SN - 0004-6361
SN - 1432-0746
ER -