TY - JOUR

T1 - Statistical Mechanics of Collisionless Orbits. V. The Approach to Equilibrium for Idealized Self-gravitating Systems

AU - Williams, Liliya L. R.

AU - Hjorth, Jens

PY - 2022/10/1

Y1 - 2022/10/1

N2 - Self-gravitating Newtonian systems consisting of a very large number of particles have generally defied attempts to describe them using statistical mechanics. This is paradoxical since many astronomical systems, or simulations thereof, appear to have universal, equilibrium structures for which no physical basis exists. A decade ago we showed that extremizing the number of microstates with a given energy per unit mass, under the constraints of conserved total energy and mass, leads to the maximum entropy state, n(E) proportional to exp (-beta (E - Phi(0))) - 1, known as DARKexp. This differential energy distribution, and the resulting density structures, closely approximate those of dark matter halos with central cusps, rho similar to r(-1), and outer parts, rho similar to r(-4). Here we define a nonequilibrium functional, S-D, which is maximized for DARKexp and increases monotonically during the evolution toward equilibrium of idealized collisionless systems of the extended spherical infall model. Systems that undergo more mixing more closely approach DARKexp.

AB - Self-gravitating Newtonian systems consisting of a very large number of particles have generally defied attempts to describe them using statistical mechanics. This is paradoxical since many astronomical systems, or simulations thereof, appear to have universal, equilibrium structures for which no physical basis exists. A decade ago we showed that extremizing the number of microstates with a given energy per unit mass, under the constraints of conserved total energy and mass, leads to the maximum entropy state, n(E) proportional to exp (-beta (E - Phi(0))) - 1, known as DARKexp. This differential energy distribution, and the resulting density structures, closely approximate those of dark matter halos with central cusps, rho similar to r(-1), and outer parts, rho similar to r(-4). Here we define a nonequilibrium functional, S-D, which is maximized for DARKexp and increases monotonically during the evolution toward equilibrium of idealized collisionless systems of the extended spherical infall model. Systems that undergo more mixing more closely approach DARKexp.

KW - VIOLENT RELAXATION

KW - DENSITY PROFILES

KW - MAXIMUM-ENTROPY

KW - KINETIC-THEORY

KW - H-FUNCTIONS

KW - EVOLUTION

KW - UNIVERSAL

KW - ORIGIN

KW - CLUSTERS

KW - HALOS

U2 - 10.3847/1538-4357/ac8d06

DO - 10.3847/1538-4357/ac8d06

M3 - Journal article

VL - 937

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 2

M1 - 67

ER -