A numerical method for the study of the gravothermal instability in star clusters

Bettwieser, E.

doi:10.1093/mnras/203.3.811

Cited by 23 publications

(24 citation statements)

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“…The idea of this model goes back to Hachisu et al (1978) and Lynden‐Bell & Eggleton (1980), who first proposed to treat the two‐body relaxation as a transport process as in a conducting plasma. They had been developed further by Bettwieser (1983), Bettwieser & Sugimoto (1984), Heggie (1984) and Heggie & Ramamani (1989). Their present form, published in Louis & Spurzem (1991), Giersz & Spurzem (1994) and Spurzem & Takahashi (1995) improves the detailed form of the conductivities in order to yield high accuracy (for comparison with N ‐body) and correct multimass models.…”

Section: Loss‐cone Accretion On To Massive Bhs: the Diffusion Modelmentioning

confidence: 99%

“…In the first case, stars on nearly circular orbits lose energy by distant gravitational encounters with other stars and, in the process, their orbits get closer and closer to the central BH. The associated energy diffusion time‐scale can be identified with the local stellar‐dynamical relaxation time generalized for anisotropy as in Bettwieser (1983): Here σ r and σ t are, respectively, the radial and tangential velocity dispersions (in the case of isotropy 2σ 2 r =σ 2 t ), ρ ⋆ ( r ) is the mean stellar mass density, N is the total particle number, G is the gravitational constant, m ⋆ is the individual stellar mass and is the Coulomb logarithm. We set γ= 0.11 (Giersz & Heggie 1994).…”

Section: Loss‐cone Accretion On To Massive Bhs: the Diffusion Modelmentioning

confidence: 99%

“…The cluster is modelled like a self‐gravitating, conducting gas sphere, according to the methods presented in Louis & Spurzem (1991) and Giersz & Spurzem (1994). These models improved earlier gas models of Bettwieser (1983) and Heggie (1984). Much as the structure of the numerical method is for the sake of computational efficiency on account of physical accuracy, it allows for all the most important physical ingredients that may carry out a role in the evolution of a spherical cluster.…”

Section: Introductionmentioning

confidence: 99%

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Accretion of stars on to a massive black hole: a realistic diffusion model and numerical studies

Amaro-Seoane

Freitag

Spurzem

2004

Monthly Notices of the Royal Astronomical Society

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We present a study of the secular evolution of a spherical stellar system with a central star‐accreting black hole (BH) using the anisotropic gaseous model. This method solves numerically moment equations of the full Fokker–Planck equation, with Boltzmann–Vlasov terms on the left‐hand side and collisional terms on the right‐hand side. We study the growth of the central BH due to star accretion at its tidal radius and the feedback of this process on to the core collapse as well as the post‐collapse evolution of the surrounding stellar cluster in a self‐consistent manner. Diffusion in velocity space into the loss cone is approximated by a simple model. The results show that the self‐regulated growth of the BH reaches a certain fraction of the total mass cluster and agrees with other methods. Our approach is much faster than competing ones (Monte Carlo, N‐body) and provides detailed information about the time‐ and space‐dependent evolution of all relevant properties of the system. In this paper we present the method and study simple models (equal stellar masses, no stellar evolution or collisions). None the less, a generalization to include such effects is conceptually simple and under way.

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Section: Loss‐cone Accretion On To Massive Bhs: the Diffusion Modelmentioning

confidence: 99%

Section: Loss‐cone Accretion On To Massive Bhs: the Diffusion Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Accretion of stars on to a massive black hole: a realistic diffusion model and numerical studies

Amaro-Seoane

Freitag

Spurzem

2004

Monthly Notices of the Royal Astronomical Society

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“…In real star clusters, this "catastrophe" is averted by the second process that governs star cluster evolution, namely short-range strong stellar encounters between individual stars and binaries (and higher-order stellar systems). Early star cluster simulations showed that including the effect of binaries as an energy source (and even a single massive binary) can allow the core to rebound out of this collapsing phase [8]. These models also predict a new phase of gravothermal oscillations, where the core bounces between collapsing and expanding due to the interplay between the diffusion of energy out of the core, due to two-body relaxation processes, and the input of energy to the core, from close encounters with binary stars.…”

Section: Dynamical Processing Of Stars and Planets Through Star Clustersmentioning

confidence: 99%

Dynamical Processing of Stars and Planets Through Star Clusters

Geller¹

2016

Proceedings of Frank N. Bash Symposium 2015 — PoS(BASH2015)

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Most stars are born in clustered environments that are far denser than the Solar Neighborhood.Yet, star clusters can be hostile locations, where close stellar encounters can be frequent and can have violent consequences, including direct stellar collisions. Such encounters can dramatically alter stellar and planetary systems, and can produce exotic stars that define new pathways in stellar evolution. Understanding how, and to what extent, such "dynamically processing" occurs in star clusters may be critical for our understanding of the architectures of today's observed stellar and planetary systems, as well as the origins of X-ray sources, blue stragglers, sub-subgiants, and other stellar exotica. In this contribution, I discuss the impacts of living in a star cluster on its inhabitants, through a review of observational and theoretical efforts to study these complex systems. Throughout, I assert that binary stars are intimately linked to both the dynamical evolution of star clusters and the effects that stellar encounters within these environments have on their stellar and planetary populations. I conclude that in order to properly interpret our present and future observations of stars and planets, both in star clusters and the field, and particularly if we attempt to use these observations to inform star and planet formation theory, we must first account for the imprint left by stellar encounters within a clustered birth environment.

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“…More than 35 yr ago, Hachisu et al (1978) and Lynden‐Bell & Eggleton (1980) proposed transport process in a self‐gravitating, conducting gas sphere as a way to mimic two‐body stellar relaxation. Later, Bettwieser (1983), Bettwieser & Sugimoto (1984), Bettwieser & Spurzem (1986), Heggie (1984), Heggie & Ramamani (1989) and Louis & Spurzem (1991) implemented anisotropy and Giersz & Spurzem (1994) and Spurzem & Takahashi (1995) added a multi‐mass distribution and improved the detailed form of the conductivities to have better accuracy. The resulting model is often called the AGM.…”

Section: Self‐gravitating Conducting Gas Spheresmentioning

confidence: 99%

Higher-order moment models of dense stellar systems: applications to the modelling of the stellar velocity distribution function

Schneider¹,

Amaro-Seoane²,

Spurzem³

2010

Monthly Notices of the Royal Astronomical Society

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Dense stellar systems such as globular clusters, galactic nuclei and nuclear star clusters are ideal loci to study stellar dynamics due to the very high densities reached, usually a million times higher than in the solar neighbourhood; they are unique laboratories to study processes related to relaxation. There are a number of different techniques to model the global evolution of such a system. We can roughly separate these approaches into two major groups: the particle‐based models, such as direct N‐body and Monte Carlo models, and the statistical models, in which we describe a system of a very large number of stars through a one‐particle phase‐space distribution function. In this approach we assume that relaxation is the result of a large number of two‐body gravitational encounters with a net local effect. We present two moment models that are based on the collisional Boltzmann equation. By taking moments of the Boltzmann equation one obtains an infinite set of differential moment equations where the equation for the moment of order n contains moments of order n+ 1. In our models we assume spherical symmetry but we do not require dynamical equilibrium. We truncate the infinite set of moment equations at order n= 4 for the first model and at order n= 5 for the second model. The collisional terms on the right‐hand side of the moment equations account for two‐body relaxation and are computed by means of the Rosenbluth potentials. We complete the set of moment equations with closure relations which constrain the degree of anisotropy of our model by expressing moments of order n+ 1 by moments of order n. The accuracy of this approach relies on the number of moments included from the infinite series. Since both models include fourth‐order moments we can study mechanisms in more detail that increase or decrease the number of high‐velocity stars. The resulting model allows us to derive a velocity distribution function, with unprecedented accuracy, compared to previous moment models.

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A numerical method for the study of the gravothermal instability in star clusters

Cited by 23 publications

References 0 publications

Accretion of stars on to a massive black hole: a realistic diffusion model and numerical studies

Accretion of stars on to a massive black hole: a realistic diffusion model and numerical studies

Dynamical Processing of Stars and Planets Through Star Clusters

Higher-order moment models of dense stellar systems: applications to the modelling of the stellar velocity distribution function

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