Transition of velocity distributions in collapsing self-gravitatingN-body systems

Abstract

By means of N -body simulations, we study the evolution of gravity-dominated systems from an early relaxation to a collapse, focusing on the velocity distributions and thermodynamic properties. To simulate the dynamical evolution, we consider self-gravitating small N -body systems enclosed in a spherical container with adiabatic or semipermeable walls. It is demonstrated that in the early relaxation process, the velocity distribution is non-Gaussian and q-Gaussian, since the system is in quasiequilibrium states (here q is the Tsallis entropic parameter). Thereafter, the velocity distribution undergoes higher non-Gaussian distributions, especially when the core forms rapidly in the collapse process; i.e., q tends to be larger than that for the quasiequilibrium state, since the velocity distribution further deviates from Gaussian. However, after the core forms sufficiently, the velocity distribution gradually relaxes toward a Gaussian-like distribution. Accordingly, the velocity distribution evolves from a non-Gaussian distribution through a higher non-Gaussian distribution to a Gaussian-like distribution; i.e., the velocity distribution does not monotonically relax toward a Gaussian-like distribution in our collapse simulations. We clearly show such a transition of the velocity distribution, based not only on the Tsallis entropic parameter but also on the ratio of velocity moments. We also find that a negative specific heat occurs in a collapse process with mass and energy loss (such as the escape of stars from globular clusters), even if the velocity distribution is Gaussian-like.

Self-similar orbit-averaged Fokker-Planck equation for isotropic spherical dense clusters (ii) physical properties and negative heat capacity of pre-collapse core

“…The results of (Komatsu et al, 2010(Komatsu et al, , 2012 well reflect the core-collapsing core-inner halo structure. In (Komatsu et al, 2012) they obtained a Maxwellian-like velocity distribution function, and showed not only negative specific but also 9 As R M >> 1, the halo density ρ(r, t) is independent of the dynamics in the core or relaxation evolution in self-similar analysis, which provides dρ(r, t)/dt = 0, hence D(R) ∝ R −α and ρ t ∝ r −α t . 10 One may recall the failure of the Bohr model in which electron releases electromagnetic radiation due to the acceleration and deeply penetrates into the potential well around the ion.…”

“…Lastly, the rest compares the core of the ss-OAFP model to the N-body simulations (Komatsu et al, 2010(Komatsu et al, , 2012 executed under the physical condition similar to the core. Strictly speaking, systems similar to the ss-OAFP model does not only exist in nature but also as a result of numerical N-body simulation 11 since complete core-collapse itself is a mathematical concept.…”

“…Also, the system must be large enough to form core-halo structure to make the fluxes occur. (Komatsu et al, 2010(Komatsu et al, , 2012 embodies such conditions by using a N-body simulation for N = 125 ∼ 250. To achieve the condition, they used a partially permeable wall through which the evaporation (escape) rate of particles from the system can change by controlling the escape energy, that is, the degree of permeability.…”

Tachyonic $δ$-Tsallis entropy of a thermal tachyonic BIon

“…In another research, the evolution of the Tsallis entropy during non-adiabatic processes like the accelerated expansion of the late uni-verse has been considered [9]. In addition, the application of this entropy in other aspects of cosmology and physics has been investigated [10,11]. And nally, employing the modied entropy-area relation suggested by Tsallis and Cirto and the holographic hypothesis, a new holo-graphic dark energy (HDE) model was proposed [12].…”

Tsallis $$\delta $$ δ -entropy in an accelerating BIon

“…In another research, the evolutions of Tsallis entropy during Non-adiabatic-like the accelerated expansion of the late universe has been considered [9]. In addition, the application of this entropy in other aspects of cosmology and physics has been investigated [10,11] in other studies. And finally, employing the modified entropy-area relation suggested by Tsallis and Cirto and the holographic hypothesis, a new holographic dark energy (HDE) model was proposed [12].…”