Special Features of Galactic Dynamics

Efthymiopoulos, Christos; Voglis, N.; Kalapotharakos, Constantinos

doi:10.1007/978-3-540-72984-6_11

Cited by 26 publications

(25 citation statements)

References 290 publications

(369 reference statements)

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“…Even globular clusters, classically viewed as being characterized by collisional processes, seem to present evidences of collisionless dynamics [14], which are yet to be clearly understood. See [5,[15][16][17] for some important papers on the subject, [18,19] for reviews and [20,21] for recent models.…”

Section: Introductionmentioning

confidence: 99%

Statistical mechanics of self-gravitating systems: Mixing as a criterion for indistinguishability

et al. 2014

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We propose an association between the phase-space mixing level of a self-gravitating system and the indistinguishability of its constituents (stars or dark matter particles). This represents a refinement in the study of systems exhibiting incomplete violent relaxation. Within a combinatorial analysis similar to that of Lynden-Bell, we make use of this association to obtain a distribution function that deviates from the Maxwell-Boltzmann distribution, increasing its slope for high energies. Considering the smallness of the occupation numbers for large distances from the center of the system, we apply a correction to Stirling's approximation which increases the distribution slope also for low energies. The distribution function thus obtained presents some resemblance to the "S" shape of distributions associated with cuspy density profiles (as compared to the distribution function obtained from the Einasto profile), although it is not quite able to produce sharp cusps. We also argue how the association between mixing level and indistinguishability can provide a physical meaning to the assumption of particle-permutation symmetry in the N-particle distribution function, when it is used to derive the one-particle Vlasov equation, which raises doubts about the validity of this equation during violent relaxation.

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Section: Introductionmentioning

confidence: 99%

Statistical mechanics of self-gravitating systems: Mixing as a criterion for indistinguishability

et al. 2014

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“…The timescale for that relaxation process, according to some theoretical arguments (Lynden-Bell 1967;Kandrup 1990) and to results from N -body simulations, is the dynamical time scale, which is orders of magnitude smaller than the age of any self-gravitating system. This process is called violent relaxation (Lynden-Bell 1967;Shu 1978;Madsen 1987;Shu 1987;Efthymiopoulos et al 2007;Bindoni & Secco 2008;Levin et al 2014). Considering the N-body problem itself, Gurzadian & Savvidy (1986) have derived, based on the Ergodic theory, another relaxation time-scale associated to collective effects, namely τ ∝ N 1/3 τ cr , which is still orders of magnitude smaller than Eq.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, Nbody simulations of galaxy formation have shown evidence of very complex motions in phase space and the fast achievement (in a dynamical time-scale) of a quasi-stationary state -see Merritt (1999) and references therein (see also on the role of chaotic mixing in violent relaxation). This seems to indicate that violent relaxation is a real relaxation process, in the sense that it drives the system irreversibly towards the equilibrium state (see also Kandrup 1990), even though violent relaxation is known to be incomplete, ending before the achievement of thermodynamical equilibrium, which would be described by a Maxwell-Boltzmann distribution (Merritt 1999;Kandrup et al 1993;Efthymiopoulos et al 2007). Consequently, the system keeps some correlation with the initial conditions.…”

Section: Introductionmentioning

confidence: 99%

The Arrow of Time in the Collapse of Collisionless Self-gravitating Systems: Non-validity of the Vlasov–Poisson Equation during Violent Relaxation

Silva

Pedra

Sodré

et al. 2017

ApJ

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The collapse of a collisionless self-gravitating system, with the fast achievement of a quasi-stationary state, is driven by violent relaxation, with a typical particle interacting with the time-changing collective potential. It is traditionally assumed that this evolution is governed by the Vlasov-Poisson equation, in which case entropy must be conserved. We run N-body simulations of isolated self-gravitating systems, using three simulation codes: NBODY-6 (direct summation without softening), NBODY-2 (direct summation with softening) and GADGET-2 (tree code with softening), for different numbers of particles and initial conditions. At each snapshot, we estimate the Shannon entropy of the distribution function with three different techniques: Kernel, Nearest Neighbor and EnBiD. For all simulation codes and estimators, the entropy evolution converges to the same limit as N increases. During violent relaxation, the entropy has a fast increase followed by damping oscillations, indicating that violent relaxation must be described by a kinetic equation other than the Vlasov-Poisson, even for N as large as that of astronomical structures. This indicates that violent relaxation cannot be described by a time-reversible equation, shedding some light on the so-called "fundamental paradox of stellar dynamics". The long-term evolution is well described by the orbit-averaged Fokker-Planck model, with Coulomb logarithm values in the expected range 10 − 12. By means of NBODY-2, we also study the dependence of the 2-body relaxation time-scale on the softening length. The approach presented in the current work can potentially provide a general method for testing any kinetic equation intended to describe the macroscopic evolution of N-body systems.

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“…A more complete description of all these subjects can be found in Contopoulos (2002). Introductory lectures on these questions of galactic dynamics and celestial mechanics may be found in Hénon (1983) or Efthymiopoulos et al (2007).…”

Section: Introductionmentioning

confidence: 99%