Statistical Mechanics of Violent Relaxation in Stellar Systems

Chavanis, Pierre‐Henri

doi:10.1007/978-3-642-56200-6_2

Cited by 30 publications

(85 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have introduced a numerical algorithm in the form of a relaxation equation (Chavanis 1996(Chavanis , 2001aChavanis et al 1996) constructed so as to increase monotonically entropy at fixed energy in the microcanonical ensemble and free energy at fixed temperature in the canonical ensemble. With this numerical algorithm, we can cover the whole bifurcation diagram in parameter space and check, by an independant method, the stability limits of Katz (1978).…”

Section: Resultsmentioning

confidence: 99%

“…In the case of dense clusters of compact stars (neutron stars or stellar mass black holes), the gravothermal catastrophe can lead to the formation of supermassive black holes of the right size to explain quasars and AGNs (Shapiro & Teukolsky 1995). Statistical mechanics is also relevant for collisionless self-gravitating systems (e.g., elliptical galaxies, dark matter, ...) undergoing a violent relaxation (Lynden-Bell 1967;Chavanis et al 1996;Chavanis & Sommeria 1998;Chavanis 1998aChavanis , 2001a. In particular, the inner regions of elliptical galaxies are close to isothermal and this is an important ingredient to understand de Vaucouleurs' R 1/4 law (Hjorth & Madsen 1993).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Gravitational instability of finite isothermal spheres

Chavanis

2002

A&A

155

343

View full text Add to dashboard Cite

Abstract. We investigate the stability of bounded self-gravitating systems in the canonical ensemble by using a thermodynamical approach. Our study extends the earlier work of Padmanabhan (1989) in the microcanonical ensemble. By studying the second variations of the free energy, we find that instability sets in precisely at the point of minimum temperature in agreement with the theorem of Katz (1978). The perturbation that induces instability at this point is calculated explicitly; it has not a "core-halo" structure contrary to what happens in the microcanonical ensemble. We also study Jeans type gravitational instability of isothermal gaseous spheres described by Navier-Stokes equations. The introduction of a container and the consideration of an inhomogeneous distribution of matter avoids the Jeans swindle. We show analytically the equivalence between dynamical stability and thermodynamical stability and the fact that the stability of isothermal gas spheres does not depend on the viscosity. This confirms the findings of Semelin et al. (2001) who used numerical methods or approximations. We also give a simpler derivation of the geometric hierarchy of scales inducing instability discovered by these authors. The density profiles that trigger these instabilities are calculated explicitly; high order modes of instability present numerous oscillations whose nodes also follow a geometric progression. This suggests that the system will fragment in a series of "clumps" and that these "clumps" will themselves fragment in substructures. The fact that both the domain sizes leading to instability and the "clumps" sizes within a domain follow a geometric progression with the same ratio suggests a fractal-like behavior. This gives further support to the interpretation of de Vega et al. (1996) concerning the fractal structure of the interstellar medium.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gravitational instability of finite isothermal spheres

Chavanis

2002

A&A

155

343

View full text Add to dashboard Cite

show abstract

“…Another kinetic theory of violent relaxation was developed by Kadomtsev & Pogutse (1970), Severne & Luwel (1980) and Chavanis (2002aChavanis ( , 2004 by using a quasilinear theory of the Vlasov-Poisson system. Subtracting Eqs.…”

Section: The Quasilinear Theorymentioning

confidence: 99%

“…This dynamical effect can physically solve the infinite mass problem associated with the maximization of the Boltzmann entropy (in the sense of Lynden-Bell) in an unlimited domain. Another approach consists of developing a quasilinear theory of the Vlasov-Poisson system (Kadomtsev & Pogutse 1970;Severne & Luwel 1980;Chavanis 2002aChavanis , 2004). This approach is expected to describe a "gentle relaxation" valid close to the equilibrium state when the fluctuations have weakened.…”

Section: Introductionmentioning

confidence: 99%

On the coarse-grained evolution of collisionless stellar systems

Chavanis¹,

Bouchet²

2005

A&A

View full text Add to dashboard Cite

Abstract.We describe the dynamical evolution of collisionless stellar systems on a coarse-grained scale. We first discuss the statistical theory of violent relaxation, following the seminal paper of Lynden-Bell (1967). Consistently with this statistical approach, we present kinetic equations for the coarse-grained distribution function f (r, u, t) based on a Maximum Entropy Production Principle or on a quasi-linear theory of the Vlasov-Poisson system. Then, we develop a deterministic approach where the coarse-grained distribution function is defined as a convolution of the fine-grained distribution function f (r, u, t) by a Gaussian window. We derive the dynamical equation satisfied by f (r, u, t) and show that its stationary states are different from those predicted by the statistical theory of violent relaxation. This implies that the notion of coarse-graining must be defined with care. We apply these results to the HMF (Hamiltonian Mean Field) model and find that the spatial density is similar to a Tsallis q-distribution where the q parameter is related to the resolution length.

show abstract

“…For about fifty years, many authors have attempted statistical-mechanical approaches to investigate the properties of self-gravitating systems (to name a few, Antonov 1962;Lynden-Bell 1967;Shu 1978;Tremaine et al 1986;Sridhar 1987;Stiavelli & Bertin 1987;White & Narayan 1987;Tsallis 1988;Spergel & Hernquist 1992;Soker 1996;Kull et al 1997;Nakamura 2000;Chavanis 2002;Hjorth & Williams 2010). However, these attempts have encountered many formal difficulties, and little progress has been made (Mo et al 2010).…”

Section: Introductionmentioning

confidence: 99%

A statistical-mechanical explanation of dark matter halo properties

Kang

2011

A&A

View full text Add to dashboard Cite

Context. Cosmological N-body simulations have revealed many empirical relationships of dark matter halos, yet the physical origin of these halo properties still remains unclear. On the other hand, the attempts to establish the statistical mechanics for self-gravitating systems have encountered many formal difficulties, and little progress has been made for about fifty years. Aims. The aim of this work is to strengthen the validity of the statistical-mechanical approach we have proposed previously to explain the dark matter halo properties. Methods. By introducing an effective pressure instead of the radial pressure to construct the specific entropy, we use the entropy principle and proceed in a similar way as previously to obtain an entropy stationary equation.Results. An equation of state for equilibrated dark halos is derived from this entropy stationary equation, by which the dark halo density profiles with finite mass can be obtained. We also derive the anisotropy parameter and pseudo-phase-space density profile. All these predictions agree well with numerical simulations in the outer regions of dark halos. Conclusions. Our work provides further support to the idea that statistical mechanics for self-gravitating systems is a viable tool for investigation.

show abstract

Statistical Mechanics of Violent Relaxation in Stellar Systems

Cited by 30 publications

References 56 publications

Gravitational instability of finite isothermal spheres

Gravitational instability of finite isothermal spheres

On the coarse-grained evolution of collisionless stellar systems

A statistical-mechanical explanation of dark matter halo properties

Contact Info

Product

Resources

About