Secular dynamics of long-range interacting particles on a sphere in the axisymmetric limit

Fouvry, Jean-Baptiste; Bar-Or, Ben; Chavanis, Pierre‐Henri

doi:10.1103/physreve.99.032101

Cited by 17 publications

(22 citation statements)

References 31 publications

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“…Similar results were found later for axisymmetric distributions of 2D point vortices when the profile of angular velocity Ω(r, t) is monotonic [31][32][33][34][35][36] and for 1D systems with long-range interactions such as the HMF model [37,38] and classical spin systems with anisotropic interaction (or equivalently long-range interacting particles moving on a sphere) [39][40][41][42]. In the context of the HMF model, it was first believed that the relaxation time was anomalous, scaling with the number of particles as N 1.7 t d [43].…”

Section: Introductionsupporting

confidence: 81%

“…As it must originate from perturbations to the system's dynamics of increasing order in 1/N , it is natural to expect that the timescale for the collisional relaxation of a 1D homogeneous system would scale like N 2 t d . Indeed, this N 2 t d scaling of the dynamics was observed for 1D plasmas [8][9][10], or for long-range coupled particles on the sphere [19,20]. In the case of the HMF model, differents scalings proportional to N 1.7 t d [11,12], or even e N t d [14] were reported.…”

Section: Introductionmentioning

confidence: 77%

“…(E4) cannot always be computed analytically. One has to resort to numerical evaluations, e.g., following the method presented in Appendix D of [20]. We illustrate this method in Fig.…”

Section: Figmentioning

confidence: 99%

“…Yet, for 1D homogeneous systems, such kinetic equations exactly vanish, i.e. two-body encounters are unable to lead to an overall relaxation of the system, as highlighted in the context of 1D plasmas [8][9][10], the 1D Hamiltonian Mean Field (HMF) model [11][12][13][14][15][16], the dynamics of long-range coupled particles on the unit sphere [17][18][19][20], or even the dynamics of point vortices [21]. All these systems are said to being undergoing a kinetic blocking.…”

Section: Introductionmentioning

confidence: 99%

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Kinetic theory of one-dimensional homogeneous long-range interacting systems sourced by 1/N2 effects

2019

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The long-term dynamics of long-range interacting N -body systems can generically be described by the Balescu-Lenard kinetic equation. However, for 1D homogeneous systems, this collision operator exactly vanishes by symmetry. These systems undergo a kinetic blocking, and cannot relax as a whole under 1/N resonant effects. As a result, these systems can only relax under 1/N 2 effects, and their relaxation is drastically slowed down. In the context of the homogeneous Hamiltonian Mean Field model, we present a new, closed and explicit kinetic equation describing self-consistently the very long-term evolution of such systems, in the limit where collective effects can be neglected, i.e. for dynamically hot initial conditions. We show in particular how that kinetic equation satisfies an H-Theorem that guarantees the unavoidable relaxation to the Boltzmann equilibrium distribution. Finally, we illustrate how that kinetic equation quantitatively matches with the measurements from direct N -body simulations.

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Section: Introductionsupporting

confidence: 81%

Section: Introductionmentioning

confidence: 77%

“…(E4) cannot always be computed analytically. One has to resort to numerical evaluations, e.g., following the method presented in Appendix D of [20]. We illustrate this method in Fig.…”

Section: Figmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Kinetic theory of one-dimensional homogeneous long-range interacting systems sourced by 1/N2 effects

2019

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“…There are, at least, two possible venues to quantify such relaxation time: (i) One could use direct time integrations of the equations of motion to get the equilibrium distributions, a goal already pursued in Kocsis & Tremaine (2015). Building upon Fouvry et al (2020), one can expect that efficient multipole methods may be designed to perform such direct numerical simulations with a computational complexity scaling linearly with the total number of particles; (ii) In the limit of sufficiently symmetric orbital distributions, e.g., axisymmetric (Fouvry et al 2019a), one could alternatively derive an explicit kinetic theory for the cluster, from which the relaxation time would naturally follow. Interestingly, we report that the axisymmetric equilibrium recovered in Fig.…”

Section: Discussionmentioning

confidence: 99%

Orbital alignment and mass segregation in galactic nuclei via vector resonant relaxation

Magnan,

Fouvry,

Pichon

et al. 2021

Preprint

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Supermassive black holes dominate the gravitational potential in galactic nuclei. In these dense environments, stars follow nearly Keplerian orbits and see their orbital planes relax through the potential fluctuations generated by the stellar cluster itself. For typical astrophysical galactic nuclei, the most likely outcome of this vector resonant relaxation (VRR) is that the orbital planes of the most massive stars spontaneously self-align within a narrow disc. We present a maximum entropy method to systematically determine this long-term distribution of orientations and use it for a wide range of stellar orbital parameters and initial conditions. The heaviest stellar objects are found to live within a thin equatorial disk. The thickness of this disk depends on the stars' initial mass function, and on the geometry of the initial cluster. This work highlights a possible (indirect) novel method to constrain the distribution of intermediate mass black holes in galactic nuclei.

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Kinetic theory of stellar systems: A tutorial

Hamilton,

Fouvry

2024

Physics of Plasmas

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Stellar systems—globular and nuclear star clusters, elliptical and spiral galaxies and their surrounding dark matter haloes, and so on—are ubiquitous characters in the evolutionary tale of our Universe. This tutorial article is an introduction to the collective dynamical evolution of the very large numbers of stars and/or other self-gravitating objects that comprise such systems, i.e., their kinetic theory. We begin by introducing the basic phenomenology of stellar systems, and explaining why and when we must develop a kinetic theory that transcends the traditional two-body relaxation picture of Chandrasekhar. We then study the individual orbits that comprise stellar systems, how those orbits are modified by linear and nonlinear perturbations, how a system responds self-consistently to fluctuations in its own gravitational potential, and how one can predict the long-term evolutionary fate of a stellar system in both quasilinear and nonlinear regimes. Though our treatment is necessarily mathematical, we develop the formalism only to the extent that it facilitates real calculations. Each section is bolstered with intuitive illustrations, and we give many examples throughout the text of the equations being applied to topics of major astrophysical importance, such as radial migration, spiral instabilities, and dynamical friction on galactic bars. Furthermore, in the 1960s and 1970s, the kinetic theory of stellar systems was a fledgling subject which developed in tandem with the kinetic theory of plasmas. However, the two fields have long since diverged as their practitioners have focused on ever more specialized and technical issues. This tendency, coupled with the famous obscurity of astronomical jargon, means that today relatively few plasma physicists are aware that their knowledge is directly applicable in the beautiful arena of galaxy evolution, and relatively few galactic astronomers know of the plasma-theoretic foundations upon which a portion of their subject is built. Yet, once one has become fluent in both Plasmaish and Galacticese, and has a dictionary relating the two, one can pull ideas directly from one field to solve a problem in the other. Therefore, another aim of this tutorial article is to provide our plasma colleagues with a jargon-light understanding of the key properties of stellar systems, to offer them the theoretical minimum necessary to engage with the modern stellar dynamics literature, to point out the many direct analogies between stellar- and plasma-kinetic calculations, and ultimately to convince them that stellar dynamics and plasma kinetics are, in a deep, beautiful and useful sense, the same thing.

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Secular dynamics of long-range interacting particles on a sphere in the axisymmetric limit

Cited by 17 publications

References 31 publications

Kinetic theory of one-dimensional homogeneous long-range interacting systems sourced by 1/N2 effects

Kinetic theory of one-dimensional homogeneous long-range interacting systems sourced by 1/N2 effects

Orbital alignment and mass segregation in galactic nuclei via vector resonant relaxation

Kinetic theory of stellar systems: A tutorial

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