Most Probable Phase Distribution in Spherical Star Systems and Conditions for Its Existence

Abstract

The initial stages of the evolution of a spherical star system can be pictured in the following way. The stars have their beginning in a comparatively small region; the mechanism of the origin of initial velocities is not known exactly. From the point of view of the contemporary state of stellar astronomy, it is an acceptable view that the initial velocities have their origin in the attraction of each individual star towards the center of gravity of the system. The second possible assumption is to attribute the origin of initial velocities to forces of an explosive character. But in either case, initially, all orbits have to be almost exactly radial.

Remarks about the thermodynamics of astrophysical systems in mutual interaction and related notions

“…It explains, as example, how interior of stars become hotter while shrink under its own gravitational field, a process that enables the occurrence of nuclear fusion reactions among more heavy atomic nuclei along the stellar evolution. The ubiquitous character of negative heat capacities in astrophysics can be justified through simple arguments as the virial theorem [14], or even more elaborated astrophysical models such as Antonov isothermal model [15] and King models of star clusters [16]. Nowadays, the existence of negative heat capacities has been reported in many other physical scenarios [17,18,19,20,21,22] and its physical relevance is now widely accepted.…”

“…His arguments were based on virial theorem of classical mechanics [23]. Decades later [24], Lynden-Bell and Wood considered the concept of negative specific heat to explain gravothermal catastrophe of isothermal model of Antonov [15]. While astronomers enjoyed Eddington incongruous conclusions, the notion of negative specific heat (or negative heat capacity) was received that time with skepticism by the statistical mechanics community [19,25].…”

Do-it-yourself computational astronomy

“…Thus, the central high-density region can evolve much faster than the rest of the system does. To give a clear understanding of the system, it will be helpful to consider the system in a spherical adiabatic wall [4,26,12].…”

“…Antonov [4] found that the system has neutral stability at D = 709. Hachisu and Sugimoto [12] performed a stability analysis of the system by means of the perturbation equation, and found that the system is unstable against the redistribution of the heat if D > 709.…”

From Quasars to ExtraordinaryN‐body Problems

“…Here Aarseth's name stands out as a persistent pioneer exploring this problem [1], although many others have contributed, especially Heggie [18] through his work on triple interactions. Both in globular cluster theory and in dynamical systems Henon's work stands out for its beauty [19]- [21], while Antonov [2] was responsible for a fundamental advance in the understanding of gravitational ,…”