Why are Stellar Systems Anisotropic?

Bettwieser, E.; Fricke, K. J.; Spurzem, R.

doi:10.1007/978-94-009-5335-2_31

Cited by 11 publications

(16 citation statements)

References 4 publications

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“…For a more detailed discussion of the energy diffusion process and its description in the context of the moment model, see Bettwieser & Spurzem (1986).…”

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

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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“…For a more detailed discussion of the energy diffusion process and its description in the context of the moment model, see Bettwieser & Spurzem (1986).…”

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

confidence: 99%

“…We shall consider this as a working hypothesis. For the anisotropic model we use a mean velocity dispersion σ 2 = (σ 2 r + 2σ 2 t )/3 for the temperature gradient and assume v r = v t (Bettwieser & Spurzem 1986). Thus, the equations we need to close our model are …”

Section: Gaseous Modelmentioning

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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“…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%

“…Moment models began with simple collisionless models and progressed to the anisotropic gaseous model (AGM) (Bettwieser & Spurzem 1986; Louis & Spurzem 1991; Spurzem 1992; Giersz & Spurzem 1994; Spurzem & Takahashi 1995). They have significantly contributed to the understanding of stellar dynamical systems by gradually adding new phenomena such as two‐body relaxation, three‐body encounters and energy transport processes in stellar systems with a mass spectrum.…”

Section: Introductionmentioning

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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“…by Larson (1970a) include anisotropy; however, it is less obvious how to generalize the closure equation of heat transport in an anisotropic case. So-called one-flux and two-flux closures have been examined, (Bettwieser & Spurzem 1986). In a more systematic study (Louis & Spurzem 1991) it could be shown, that at least the self-similar solutions in both cases were very similar, and even close to the solutions of a higher order moment model of Louis (1990).…”

Section: Introduction With Some Historical Remarksmentioning

confidence: 99%

Fluid Techniques and Evolution of Anisotropy

Spurzem¹

1996

Symp. - Int. Astron. Union

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Fluid dynamical techniques to model the dynamical evolution of star clusters, and their successors, gaseous models using an equation of heat conductivity to model relaxation effects, including anisotropy, are presented. The historical merits of such models are reviewed as well as the current status of their credibility, based on quantitative comparisons with other methods, like orbit-averaged Fokker-Planck solutions and direct N-body simulations.

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Why are Stellar Systems Anisotropic?

Cited by 11 publications

References 4 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

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

Fluid Techniques and Evolution of Anisotropy

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