Dynamical Simulation of Gravothermal Catastrophe

Abstract

We investigate the dynamical evolution of gravothermal catastrophe in a model of a spherical cluster where, besides the energy and angular momentum, an additional integral of motion is also taken into account. Using dynamical simulation, we study a system of concentric, rotating, spherical shells employing a precise, event-driven, algorithm that permits the controlled exchange of internal angular momentum. Initially the system starts to relax to a locally stable state that is in good agreement with mean field predictions. This is followed by core collapse with the development of a core-halo structure and gravothermal oscillation.

Gravitational instabilities of isothermal spheres in the presence of a cosmological constant

“…Thus, point B is simultaneously the turning point of stability (from stable branch AB to the unstable branch BS) and the marginal point of the strong instability. This strong instability leads to a core-halo structure as verified by monte-carlo simulations [6,15,16,17,18] and is associated with a collapse phase transition [6,7,8,29], while the weak instability leads to a fractal structure and is associated with a fragmented collapse, called a clumping phase transition [5,6,7,8,29]. This fractal structure is due to the secondary instabilities that set in at points S 1 , S 2 , etc.…”

“…Lynden-Bell and Wood [2] conjectured that at the region of no equilibrium, that is for ER < −0.335GM 2 , the system would overheat and collapse. This gravothermal catastrophe picture was later confirmed by numerical simulations [15,16,17,6,18] and has been known as 'core collapse' [19], which plays a crucial role in the evolution of globular clusters. As indicated by de Vega and Sanchez [6] the collapse is a zeroth order phase transition, since the temperature and pressure increase discontinuously at the transition (the Gibbs free energy becomes discontinuous).…”

Dynamics of finite and infinite self-gravitating systems with cold quasi-uniform initial conditions

“…Such states are known variously as "quasi-equilbria", or "meta-equilibria" or "quasi-stationary" states, because they are understood not to be true equilibria, but rather stable only on a time scale which diverges as some power of N -in proportion to N/ log N for the case of gravity, according to simple arguments [12]. Indeed on these much longer timescales -which we do not explore here -the system is believed to be intrinsically unstable to so-called "gravothermal catastrophe" [13] (see, e.g., [14] for a recent exploration of this regime, and further references). We will use here the term "quasi-stationary states", shortened to QSS, in line with the predominant usage in the statistical physics literature in the last few years.…”

“…We can thus define an infinite volume limit for the system, as that in which the equations of motion are given by Eqs. (14) with the sum in the "force" taken over an appropriate infinite system (i.e. in the class in which it is defined).…”

“…When the regulated force term on the right-hand side of Eqs. (14) is well defined in an infinite distribution, they can be conveniently rewritten as…”