Statistical Mechanics of Collisionless Orbits. V. The Approach to Equilibrium for Idealized Self-gravitating Systems
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Statistical Mechanics of Collisionless Orbits. V. The Approach to Equilibrium for Idealized Self-gravitating Systems. / Williams, Liliya L. R.; Hjorth, Jens.
In: Astrophysical Journal, Vol. 937, No. 2, 67, 01.10.2022.Research output: Contribution to journal › Journal article › Research › peer-review
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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 -
ID: 321957238