Thermodynamic properties of an evaporation process in self-gravitatingN-body systems

Abstract

By means of N-body simulations, we consider self-gravitating open systems enclosed in a spherical container with semipermeable reflecting walls, in order to investigate the thermodynamics of the evaporation process in self-gravitating N-body systems ͑such as the escape of stars from globular clusters͒. To simulate the evaporation process, when the energy of a particle exceeds a certain threshold value, the particle passes through the semipermeable reflecting wall freely. We show that the thermodynamic properties of the evaporation process, such as the dependence of the temperature on energy, agree well with those of stellar polytropes, if the system is in an approximate virial equilibrium state. However, in a lower-energy region or for a rapid evaporation process, the thermodynamic properties deviate from those for the stellar polytrope. Nevertheless, we found that a negative specific heat occurs even in the lower-energy region or for a rapid evaporation process.

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

“…G, v i , and r ij represent the gravitational constant, the speed of the ith particle, and the distance between the ith and j th particles, respectively. The mass m i of each particle is set to be m. The superscript notation w represents a value of the whole system, since a high-energy particle passes through the semipermeable reflecting wall in our evaporation-collapse process [30]. That is, in the evaporation-collapse process, the number N s (r i ,r j < R) of particles in the sphere decreases from the number N of particles in the whole system.…”

“…We define the total energy E in the sphere, substituting N s into N in Eq. (2) [30]. (In the cold collapse process, E is equal to E w , since N s is equal to N .…”

“…where E w KE , E w PE , and m i represent kinetic energy, potential energy, and mass of the ith point particle, respectively [30]. G, v i , and r ij represent the gravitational constant, the speed of the ith particle, and the distance between the ith and j th particles, respectively.…”

“…For the cold collapse process, an adiabatic wall is employed and the initial temperature is set to be sufficiently low. For the evaporation-collapse process, the particle passes through a semipermeable reflecting wall freely when the total energy ε i of the ith particle exceeds an energy threshold ε esc [30]. In this study, ε esc is set to be 0.…”

“…Self-gravitating or long-range attractive interacting systems exhibit several peculiar features [1][2][3][4], such as gravothermal catastrophe [5,6], negative specific heat [7][8][9], violent relaxation [10], nonequilibrium thermodynamics, and nonextensive statistical mechanics [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. In these systems, the velocity distributions are non-Gaussian [31][32][33], especially in quasiequilibrium states and metastable states.…”