Gravitational N-body problem and the validity of concepts of the gas model

Bettwieser, E.; Sugimoto, Daiichiro

doi:10.1093/mnras/212.1.189

Cited by 13 publications

(17 citation statements)

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“…This is appropriate for a standard gas, where the collision mean free path is much smaller than the system's size (Hensler et al 1995). Quite surprisingly, it still seems to be valid for a stellar cluster even though the radial excursion of a typical star is not "microscopic" (Bettwieser & Sugimoto 1985;Giersz & Spurzem 1994;Spurzem & Takahashi 1995). However, we discarded such an approach because, due to its continuous nature, integrating the effects of collisions in it seems difficult.…”

Section: Choice Of a Simulation Methodsmentioning

confidence: 99%

A new Monte Carlo code for star cluster simulations

Freitag

Benz

2001

A&A

111

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Abstract.We have developed a new simulation code aimed at studying the stellar dynamics of a galactic central star cluster surrounding a massive black hole. In order to include all the relevant physical ingredients (2-body relaxation, stellar mass spectrum, collisions, tidal disruption, . . . ), we chose to revive a numerical scheme pioneered by Hénon in the 70's (Hénon 1971b,a; Hénon 1973. It is basically a Monte Carlo resolution of the Fokker-Planck equation. It can cope with any stellar mass spectrum or velocity distribution. Being a particle-based method, it also allows one to take stellar collisions into account in a very realistic way. This first paper covers the basic version of our code which treats the relaxation-driven evolution of a stellar cluster without a central BH. A technical description of the code is presented, as well as the results of test computations. Thanks to the use of a binary tree to store potential and rank information and of variable time steps, cluster models with up to 2 × 10 6 particles can be simulated on a standard personal computer and the CPU time required scales as Np ln(Np) with the particle number Np. Furthermore, the number of simulated stars needs not be equal to Np but can be arbitrarily larger. A companion paper will treat further physical elements, mostly relevant to galactic nuclei.

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Section: Choice Of a Simulation Methodsmentioning

confidence: 99%

A new Monte Carlo code for star cluster simulations

Freitag

Benz

2001

A&A

111

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“…Bettwieser & Sugimoto (1985) compared N ‐body systems to gaseous models using a direct N = 1000 model. Even though the value of N is small by today’s standards there was still fair agreement during the pre‐collapse phase.…”

Section: Direct N‐bodymentioning

confidence: 99%

Gravothermal oscillations in two-component models of star clusters

Breen

Heggie

2011

Monthly Notices of the Royal Astronomical Society

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In this paper, gravothermal oscillations are investigated in two-component clusters with a range of different stellar mass ratios and total component mass ratios. The critical number of stars at which gravothermal oscillations first appeared is found using a gas code. The nature of the oscillations is investigated and it is shown that the oscillations can be understood by focusing on the behaviour of the heavier component, because of mass segregation. It is argued that, during each oscillation, the re-collapse of the cluster begins at larger radii while the core is still expanding. This re-collapse can halt and reverse a gravothermally driven expansion. This material outside the core contracts because it is losing energy both to the cool expanding core and to the material at larger radii. The core collapse times for each model are also found and discussed. For an appropriately chosen case, direct N -body runs were carried out, in order to check the results obtained from the gas model, including evidence of the gravothermal nature of the oscillations and the temperature inversion that drives the expansion.Comment: 13 pages, 18 figures and 8 tables. Accepted for publication in MNRA

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“…Where the loss‐cone effects can be neglected, a Schwarzschild–Boltzmann‐type distribution function can be assumed: Third‐order moments of the velocity distribution that represent the stellar‐dynamical energy flux do not alter such a distribution function significantly (Bettwieser & Sugimoto 1985).…”

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

confidence: 99%

“…Third-order moments of the velocity distribution that represent the stellar-dynamical energy flux do not alter such a distribution function significantly (Bettwieser & Sugimoto 1985). An important quantity is the critical radius, r crit .…”

Section: Loss-cone Physicsmentioning

confidence: 99%

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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Gravitational N-body problem and the validity of concepts of the gas model

Cited by 13 publications

References 0 publications

A new Monte Carlo code for star cluster simulations

A new Monte Carlo code for star cluster simulations

Gravothermal oscillations in two-component models of star clusters

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

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