arXiv subjects

Jean-Baptiste Fouvry

Publications and source records attributed to Jean-Baptiste Fouvry.

At least 19 recordsLinked to original sources

arXiv2026

Very long-term relaxation of harmonic 1D self-gravitating systems

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.

astro-ph.GA↗

arXiv2026

From Landau Equation and Large Deviations to Efficient Simulations of Dynamical Fluctuations

The (deterministic) Landau equation captures the mean long-term evolution of dynamically hot long-range interacting finite-$N$ systems. Though successful, this kinetic equation fundamentally ignores dynamical fluctuations. Building upon Large Deviation Theory, we present a physically-consistent system of Langevin equations that simultaneously recovers the mean Landau dynamics and accurately captures the corresponding fluctuations among different realizations. We show in particular how these Langevin equations can be derived from Rostoker's principle in the limit of weak two-body deflections. We extensively validate these equations against tailored direct $N$-body simulations, showing an exquisite level of agreement.

cond-mat.stat-mech↗

arXiv2026

Vector Resonant Relaxation and Statistical Closure Theory. II. One-loop Closure

We use stellar dynamics as a testbed for statistical closure theory. We focus on the process of "Vector Resonant Relaxation," a long-range, non-linear, and correlated relaxation mechanism that drives the reorientation of stellar orbital planes around a supermassive black hole. This process provides a natural setting to evaluate the predictive power of generic statistical closure schemes for dynamical correlation functions, in the fully non-linear and non-perturbative regime. We develop a numerical scheme that explicitly implements the seminal "Martin-Siggia-Rose" formalism at one-loop order via an iterative fixed-point approach, thereby improving upon the bare order from the "Direct Interaction Approximation." Using this framework, we quantitatively validate the ability of the formalism to predict (i) the two-point two-time correlation function; (ii) the renormalised three-point interaction vertex; (iii) the three-point three-time correlation function. These predictions are compared to direct measurements from numerical simulations. We conclude by discussing the limitations of this approach and presenting possible future venues.

cond-mat.stat-mech↗

arXiv2025

Thermodynamic blocking in self-gravitating systems

Building upon a thermodynamic formalism, we show that self-gravitating systems in hydrostatic equilibrium with a uniform density are maximal entropy states when submitted to perturbations which are slow on dynamical timescale. We coin this phenomenon "thermodynamic blocking", given its similarity with the more general "kinetic blocking". This result underlines the importance of the thermodynamic formalism which proves useful when kinetic equations break down.

astro-ph.GA↗

arXiv2025

Kinetic theory of two-dimensional point vortices at order $1/N$ and $1/N^{2}$

We investigate the long-term relaxation of a distribution of $N$ point vortices in two-dimensional hydrodynamics. To focus on the regime of weak collective amplification, we embed these point vortices within a static background potential and soften their pairwise interaction on small scales. Placing ourselves within the limit of an average axisymmetric distribution, we stress the connections with generic long-range interacting systems, whose relaxation is described within angle-action coordinates. In particular, we emphasise the existence of two regimes of relaxation, depending on whether the system's profile of mean angular velocity (frequency) is a non-monotonic [resp. monotonic] function of radius, which we refer to as profile (1) [resp. profile (2)]. For profile (1), relaxation occurs through two-body non-local resonant couplings, i.e. $1/N$ effects, as described by the inhomogeneous Landau equation. For profile (2), the impossibility of such two-body resonances submits the system to a ``kinetic blocking''. Relaxation is then driven by three-body couplings, i.e. ${1/N^{2}}$ effects, whose associated kinetic equation has only recently been derived. For both regimes, we compare extensively the kinetic predictions with large ensemble of direct $N$-body simulations. In particular, for profile (1), we explore numerically an effect akin to ``resonance broadening'' close to the extremum of the angular velocity profile. Quantitative description of such subtle nonlinear effects will be the topic of future investigations.

cond-mat.stat-mech↗

arXiv2025

Vector Resonant Relaxation and Statistical Closure Theory. I. Direct Interaction Approximation

Stars orbiting a supermassive black hole in the center of galaxies undergo very efficient diffusion in their orbital orientations: this is "Vector Resonant Relaxation". Such a dynamics is intrinsically non-linear, stochastic, and correlated, hence bearing deep similarities with turbulence in fluid mechanics or plasma physics. In that context, we show how generic methods stemming from statistical closure theory, namely the celebrated "Martin-Siggia-Rose formalism", can be used to characterize the correlations describing the redistribution of orbital orientations. In particular, limiting ourselves to the leading order truncation in this closure scheme, the so-called "Direct Interaction Approximation", and placing ourselves in the limit of an isotropic distribution of orientations, we explicitly compare the associated prediction for the two-point correlation function with measures from numerical simulations. We discuss the successes and limitations of this approach and present possible future venues.

astro-ph.GA↗

arXiv2025

On the long-term evolution of razor-thin galactic discs: Balescu-Lenard prediction and perspectives

In the last five decades, numerical simulations have provided invaluable insights into the evolution of galactic discs over cosmic times. As a complementary approach, developments in kinetic theory now also offer a theoretical framework to understand statistically their long-term evolution. The current state-of-the-art kinetic theory of isolated stellar systems is the inhomogeneous Balescu-Lenard equation. It can describe the long-term evolution of a self-gravitating razor-thin disc under the effect of resonant interactions between collectively amplified noise-driven fluctuations. In this work, confronting theoretical predictions to numerical simulations, we quantitatively show that kinetic theory indeed captures the average long-term evolution of cold stellar discs. Leveraging the versatility of kinetic methods, we then offer some new perspectives on this problem, namely (i) the crucial impact of collective effects in accelerating the relaxation; (ii) the role of (weakly) damped modes in shaping the disc's orbital heating; (iii) the bias introduced by gravitational softening on long timescales; (iv) the resurgence of strong stochasticity near marginal stability. These elements call for an appropriate choice of softening kernel when simulating the long-term evolution of razor thin discs and for an extension of kinetic theory beyond the average evolution. Notwithstanding, kinetic theory captures quantitatively the ensemble-averaged long-term response of such discs.

astro-ph.GA↗

arXiv2024

Kinetic Theory of Stellar Systems: A Tutorial

Stellar systems - star clusters, galaxies, 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 study the orbits that comprise stellar systems, how those orbits are modified by perturbations, how a system responds self-consistently to fluctuations in its gravitational potential, and how one can predict the long term fate of a stellar system in various dynamical regimes. Though our treatment is necessarily mathematical, we develop the formalism only to the extent that it facilitates real calculations. We give many examples throughout the text of the equations being applied to topics of major astrophysical importance. 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. 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 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 and beautiful and useful sense, the same thing.

astro-ph.GA↗

arXiv2024

Non-resonant relaxation of rotating globular clusters

The long-term relaxation of rotating, spherically symmetric globular clusters is investigated through an extension of the orbit averaged Chandrasekhar non-resonant formalism. A comparison is made with the long-term evolution of the distribution function in action space, measured from averages of sets of $N$-body simulations up to core collapse. The impact of rotation on in-plane relaxation is found to be weak. In addition, we observe a clear match between theoretical predictions and $N$-body measurements. For the class of rotating models considered, we find no strong gravo-gyro catastrophe accelerating core collapse. Both kinetic theory and simulations predict a reshuffling of orbital inclinations from overpopulated regions to underpopulated ones. This trend accelerates as the amount of rotation is increased. Yet, for orbits closer to the rotational plane, the non-resonant prediction does not reproduce numerical measurements. We argue that this mismatch stems from these orbits' coherent interactions, which are not captured by the non-resonant formalism that only addresses local deflections.

astro-ph.GA↗

arXiv2023

Predicting the linear response of self-gravitating stellar spheres and discs with LinearResponse.jl

We present LinearResponse.jl, an efficient, versatile public library written in julia to compute the linear response of self-gravitating (3D spherically symmetric) stellar spheres and (2D axisymmetric razor-thin) discs. LinearResponse.jl can scan the whole complex frequency plane, probing unstable, neutral and (weakly) damped modes. Given a potential model and a distribution function, this numerical toolbox estimates the modal frequencies as well as the shapes of individual modes. The libraries are validated against a combination of previous results for the spherical isochrone model and Mestel discs, and new simulations for the spherical Plummer model. Beyond linear response theory, the realm of applications of LinearResponse.jl also extends to the kinetic theory of self-gravitating systems through a modular interface.

astro-ph.GA↗

arXiv2023

Dynamical large deviations for long-range interacting inhomogeneous systems without collective effects

We consider the long-term evolution of an inhomogeneous long-range interacting $N$-body system. Placing ourselves in the dynamically hot limit, i.e. neglecting collective effects, we derive a large deviation principle for the system's empirical angle-averaged distribution function. This result extends the classical ensemble-averaged kinetic theory given by the so-called inhomogeneous Landau equation, as it specifies the probability of typical and large dynamical fluctuations. We detail the main properties of the associated large deviation Hamiltonian, in particular how it complies with the system's conservation laws and possesses a gradient structure.

cond-mat.stat-mech↗

arXiv2023

Kinetic blockings in long-range interacting inhomogeneous systems

Long-range interacting systems unavoidably relax through Poisson shot noise fluctuations generated by their finite number of particles, $N$. When driven by two-body correlations, i.e. ${1/N}$ effects, this long-term evolution is described by the inhomogeneous Balescu-Lenard equation. Yet, in one-dimensional systems with a monotonic frequency profile and only subject to 1:1 resonances, this kinetic equation exactly vanishes: this is a first-order full kinetic blocking. These systems' long-term evolution is then driven by three-body correlations, i.e. ${1/N^2}$ effects. In the limit of dynamically hot systems, this is described by the inhomogeneous ${1/N^2}$ Landau equation. We investigate numerically the long-term evolution of systems for which this second kinetic equation also exactly vanishes: this a second-order bare kinetic blocking. We demonstrate that these systems relax through the "leaking" contributions of dressed three-body interactions that are neglected in the inhomogeneous ${1/N^2}$ Landau equation. Finally, we argue that these never-vanishing contributions prevent four-body correlations, i.e. ${1/N^{3}}$ effects, from ever being the main driver of relaxation.

cond-mat.stat-mech↗

arXiv2023

Constraining intermediate-mass black holes from the stellar disc of SgrA*

Stars evolving around a supermassive black hole see their orbital orientations diffuse efficiently, a process called "vector resonant relaxation". In particular, stars within the same disc, i.e. neighbors in orientations, will slowly diffuse away from one another through this stochastic process. We use jointly (i) detailed kinetic predictions for the efficiency of this dilution and (ii) the recent observation of a stellar disc around SgrA*, the supermassive black hole at the centre of the Milky-Way, to constrain SgrA*'s unobserved stellar cluster. Notably, we investigate quantitatively the impact of a population of intermediate mass black holes on the survivability of the stellar disc.

astro-ph.GA↗

arXiv2023

Astrophysics with the Laser Interferometer Space Antenna

The Laser Interferometer Space Antenna (LISA) will be a transformative experiment for gravitational wave astronomy, and, as such, it will offer unique opportunities to address many key astrophysical questions in a completely novel way. The synergy with ground-based and space-born instruments in the electromagnetic domain, by enabling multi-messenger observations, will add further to the discovery potential of LISA. The next decade is crucial to prepare the astrophysical community for LISA's first observations. This review outlines the extensive landscape of astrophysical theory, numerical simulations, and astronomical observations that are instrumental for modeling and interpreting the upcoming LISA datastream. To this aim, the current knowledge in three main source classes for LISA is reviewed; ultracompact stellar-mass binaries, massive black hole binaries, and extreme or intermediate mass ratio inspirals. The relevant astrophysical processes and the established modeling techniques are summarized. Likewise, open issues and gaps in our understanding of these sources are highlighted, along with an indication of how LISA could help making progress in the different areas. New research avenues that LISA itself, or its joint exploitation with upcoming studies in the electromagnetic domain, will enable, are also illustrated. Improvements in modeling and analysis approaches, such as the combination of numerical simulations and modern data science techniques, are discussed. This review is intended to be a starting point for using LISA as a new discovery tool for understanding our Universe.

gr-qc↗

arXiv2022

Milankovitch equations with spinors

We investigate the use of spinors to describe the secular evolution of quasi-Keplerian systems. Evaluating their Poisson brackets, we show that the components of a properly-chosen spinor are canonical variables. We illustrate this formalism with a satellite's motion around an oblate body.

physics.class-ph↗

arXiv2022

Kinetic theory of one-dimensional inhomogeneous long-range interacting $N$-body systems at order $1/N^{2}$ without collective effects

Long-range interacting systems irreversibly relax as a result of their finite number of particles, $N$. At order $1/N$, this process is described by the inhomogeneous Balescu--Lenard equation. Yet, this equation exactly vanishes in one-dimensional inhomogeneous systems with a monotonic frequency profile and sustaining only 1:1 resonances. In the limit where collective effects can be neglected, we derive a closed and explicit $1/N^{2}$ collision operator for such systems. We detail its properties highlighting in particular how it satisfies an $H$-theorem for Boltzmann entropy. We also compare its predictions with direct $N$-body simulations. Finally, we exhibit a generic class of long-range interaction potentials for which this $1/N^{2}$ collision operator exactly vanishes.

cond-mat.stat-mech↗

arXiv2022

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

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.

astro-ph.GA↗

arXiv2022

Long-term relaxation of ${1D}$ self-gravitating systems

We investigate the long-term relaxation of one-dimensional (${1D}$) self-gravitating systems, using both kinetic theory and $N$-body simulations. We consider thermal and Plummer equilibria, with and without collective effects. All combinations are found to be in clear agreement with respect to the Balescu-Lenard and Landau predictions for the diffusion coefficients. Interestingly, collective effects reduce the diffusion by a factor ${\sim 10}$. The predicted flux for Plummer equilibrium matches the measured one, which is a remarkable validation of kinetic theory. We also report on a situation of quasi kinetic blocking for the same equilibrium.

cond-mat.stat-mech↗