5 research outputs found

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

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    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.Comment: Software available at https://github.com/michael-petersen/LinearResponse.j

    Évolution séculaire des amas stellaires

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    Stellar systems in the Universe are mainly driven by gravity, a long-range force affecting every massive object. Recent surveys have produced a formidable quantity of data capturing the kinetic properties of the Galaxy and its components (such as globular clusters and its nucleus). Decades of research have allowed the astrophysical community to reach a good understanding of the formation of gravitationally bound structures: the Λ-CDM model. Still, the long-term evolution of these systems remains an ongoing subject of research. My thesis is focused on the evolution of gravitational systems on such secular timescales. My triple objective is: (i) to understand the particular mechanisms which operate on these long timescales; (ii) to identify the origin of the observed differences depending on the nature of these objects (geometry, kinematics, composition, ...); (iii) to deduce diagnostics for dark matter experiments (e.g., the identification of populations of intermediate mass black holes). In practice, this thesis aims at describing the secular fate of isolated stellar clusters by relying on kinetic theory. The master equation describing self-gravitating clusters over many orbital times is the Balescu–Lenard diffusion equation. It captures perturbatively the effect of resonant interactions between noise-driven fluctuations within the system. In this thesis, I specifically study two approximations of the Balescu–Lenard equation: (i) the inhomogeneous Landau limit, in which collective amplification is neglected; (ii) the (orbit-averaged) Chandrasekhar limit, in which local, incoherent deflections dominate over long-range resonances. I apply these formalisms to a variety of systems. First, I study the Galactic nucleus, where I present a fiducial likelihood analysis to probe the presence of intermediate mass black holes around Sgr A⋆. Second, I consider globular clusters with kinematic anisotropy and ultimately rotation. I first apply the extended non-resonant approach, which I validate by using large sets of direct N-body simulations. This allows me to investigate the rate of core collapse and the diffusion of orbital inclinations. I also study the impact of resonant relaxation on the effective Coulomb logarithm which enters the non-resonant formulation. Finally, I probe the space of physical parameters of galactic discs which are prone to bi-symmetric instabilities. Using linear response theory, I study the onset of bars. This allows me to understand the lack of bars in galactic discs observed in current hydrodynamical simulations.Les systèmes stellaires de l’Univers sont principalement régis par la gravité, une force à longue portée qui affecte tous les objets massifs. Des études récentes ont permis de recueillir une quantité considérable de données sur la cinétique de la Galaxie et de ses composants (tels que ses amas globulaires et son noyau). Des décennies de recherche ont permis à la communauté astrophysique de parvenir à une bonne compréhension de la formation des structures gravitationnellement liées : le modèle Λ-CDM. Cependant, l’évolution à long terme de ces systèmes reste un sujet de recherche intense. Ma thèse se concentre sur l’évolution des systèmes gravitationnels sur ces échelles de temps séculaires. Mes objectifs sont triples: (i) comprendre les mécanismes particuliers qui opèrent sur ces échelles de temps longs ; (ii) identifier l’origine des différences observées en fonction de la nature de ces objets (géométrie, cinématique, composition, ...) ; (iii) déduire des diagnostics pour des expériences de matière noire (par exemple, l’identification de populations de trous noirs de masse intermédiaire). Cette thèse vise donc à décrire le destin séculaire des amas stellaires isolés en s’appuyant sur la théorie cinétique. L’équation maîtresse décrivant les amas autogravitants sur de nombreux temps orbitaux est l’équation de diffusion de Balescu–Lenard. Elle capture de manière perturbative l’effet des interactions résonantes entre les fluctuations issues du bruit au sein du système. Dans cette thèse, j’étudie deux approximations de l’équation de Balescu–Lenard : (i) la limite de Landau inhomogène, dans laquelle l’amplification collective est négligée ; (ii) la limite de Chandrasekhar (moyennée sur les orbites), dans laquelle les déviations locales incohérentes dominent sur les résonances à longue portée. J’applique ces formalismes à une variété de systèmes. Tout d’abord, j’étudie le noyau Galactique, où je présente une analyse de vraisemblance pour sonder la présence de trous noirs de masse intermédiaire autour de Sgr A⋆. Deuxièmement, je considère les amas globulaires avec une anisotropie cinématique et éventuellement de la rotation. J’applique d’abord une extension de l’approche non-résonante, que je valide en utilisant un jeu important de simulations directes à N-corps. Cela me permet d’étudier le taux d’effondrement du noyau et la diffusion des inclinaisons orbitales. J’étudie également l’impact de la relaxation résonante sur le logarithme de Coulomb effectif qui entre dans la formulation non-résonante. Enfin, je sonde l’espace des paramètres physiques des disques galactiques qui sont sujets à des instabilités bi-symétriques. En utilisant la théorie de la réponse linéaire, je quantifie le contexte propice à l’apparition des barres. Cela me permet d’expliquer l’absence de barres dans les disques galactiques observée dans les simulations hydrodynamiques actuelles

    Non-resonant relaxation of anisotropic globular clusters

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    Globular clusters are dense stellar systems whose core slowly contracts under the effect of self-gravity. The rate of this process was recently found to be directly linked to the initial amount of velocity anisotropy: tangentially anisotropic clusters contract faster than radially anisotropic ones. Furthermore, initially anisotropic clusters are found to generically tend towards more isotropic distributions during the onset of contraction. Chandrasekhar's "non-resonant" (NR) theory of diffusion describes this relaxation as being driven by a sequence of local two-body deflections along each star's orbit. We explicitly tailor this NR prediction to anisotropic clusters, and compare it with NN-body realisations of Plummer spheres with varying degrees of anisotropy. The NR theory is shown to recover remarkably well the detailed shape of the orbital diffusion and the associated initial isotropisation, up to a global multiplicative prefactor which increases with anisotropy. Strikingly, a simple effective isotropic prescription provides almost as good a fit, as long as the cluster's anisotropy is not too strong. For these more extreme clusters, accounting for long-range resonant relaxation may be necessary to capture these clusters' long-term evolution

    Non-resonant relaxation of anisotropic globular clusters

    No full text
    Globular clusters are dense stellar systems whose core slowly contracts under the effect of self-gravity. The rate of this process was recently found to be directly linked to the initial amount of velocity anisotropy: tangentially anisotropic clusters contract faster than radially anisotropic ones. Furthermore, initially anisotropic clusters are found to generically tend towards more isotropic distributions during the onset of contraction. Chandrasekhar's "non-resonant" (NR) theory of diffusion describes this relaxation as being driven by a sequence of local two-body deflections along each star's orbit. We explicitly tailor this NR prediction to anisotropic clusters, and compare it with NN-body realisations of Plummer spheres with varying degrees of anisotropy. The NR theory is shown to recover remarkably well the detailed shape of the orbital diffusion and the associated initial isotropisation, up to a global multiplicative prefactor which increases with anisotropy. Strikingly, a simple effective isotropic prescription provides almost as good a fit, as long as the cluster's anisotropy is not too strong. For these more extreme clusters, accounting for long-range resonant relaxation may be necessary to capture these clusters' long-term evolution

    Mapping the Galactic centre’s dark cluster via resonant relaxation

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    International audienceSupermassive black holes in the centre of galaxies dominate the gravitational potential of their surrounding stellar clusters. In these dense environments, stars follow nearly Keplerian orbits, which get slowly distorted as a result of the potential fluctuations generated by the stellar cluster itself. In particular, stars undergo a rapid relaxation of their eccentricities through both resonant and non-resonant processes. An efficient implementation of the resonant diffusion coefficients allows for detailed and systematic explorations of the parameter space describing the properties of the stellar cluster. In conjunction with recent observations of the S-cluster orbiting SgrA*, this framework can be used to jointly constrain the distribution of the unresolved, old, background stellar cluster and the characteristics of a putative dark cluster. Specifically, we show how this can be used to estimate the typical mass and cuspide exponent of intermediate-mass black holes consistent with the relaxed state of the distribution of eccentricities in the observed S-cluster. This should prove useful in constraining supermassive black hole formation scenarios
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