Discrepancies between Chandrasekhar's theory of relaxation and N-body simulations
Abstract
Globular clusters are systems which are known to be particularly well described by two-body relaxation. In recent decades many studies have shown that Chandrasekhar's orbit-averaged theory is able to reproduce many features of numerical simulations. However, it has been claimed that differences between the theory and simulation remain, such as an amplitude mismatch of the rate of change of the distribution function. In this paper we compare the theoretical predictions of Chandrasekhar's theory for anisotropic clusters to precise N-body data. We show that more careful N-body measurements are able to reduce the claimed mismatch. Nevertheless, we observe a dependency of the remaining mismatch on both position and anisotropy. While the dependence on anisotropy may be understood qualitatively on theoretical grounds, the radial dependence implies that spatial inhomogeneities, and therefore collective effects, may become unavoidable to resolve the residual mismatch between theory and simulations.
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BibTeX
@misc{tep2026discrepancies,
title = {{Discrepancies between Chandrasekhar's theory of relaxation and $N$-body simulations}},
author = {Kerwann Tep and Douglas C. Heggie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.14844},
eprint = {2607.14844},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.14844},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Discrepancies between Chandrasekhar's theory of relaxation and N-body simulations
AU - Kerwann Tep
AU - Douglas C. Heggie
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2607.14844
UR - https://arxiv.org/abs/2607.14844
AB - Globular clusters are systems which are known to be particularly well described by two-body relaxation. In recent decades many studies have shown that Chandrasekhar's orbit-averaged theory is able to reproduce many features of numerical simulations. However, it has been claimed that differences between the theory and simulation remain, such as an amplitude mismatch of the rate of change of the distribution function. In this paper we compare the theoretical predictions of Chandrasekhar's theory for anisotropic clusters to precise N-body data. We show that more careful N-body measurements are able to reduce the claimed mismatch. Nevertheless, we observe a dependency of the remaining mismatch on both position and anisotropy. While the dependence on anisotropy may be understood qualitatively on theoretical grounds, the radial dependence implies that spatial inhomogeneities, and therefore collective effects, may become unavoidable to resolve the residual mismatch between theory and simulations.
ER -