Anomalously slow phase transitions in self-gravitating systems

The kinetics of collapse and explosion transitions in microcanonical self-gravitating ensembles is analyzed. A system of point particles interacting via an attractive soft Coulomb potential and confined to a spherical container is considered. We observed that for 100–200 particles collapse takes ${10}^3–{10}^4$ particle crossing times to complete; i.e., it is by two to three orders of magnitude slower than the velocity relaxation. In addition, it is found that the collapse time decreases rapidly with an increase of the soft-core radius. We found that such an anomalously long collapse time is caused by the slow energy exchange between a higher-temperature compact core and relatively cold diluted halo. The rate of energy exchange between the faster modes of the core particles and slower-moving particles of the halo is exponentially small in the ratio of the frequencies of these modes. As the soft-core radius increases and the typical core modes become slower, the ratio of core and halo frequencies decreases and the collapse accelerates. Implications for astrophysical systems and phase transition kinetics are discussed.

Figure 1

Plots of entropy $s\left(ϵ\right)$ (solid line) and temperature $\tau \left(ϵ\right)=dϵ∕ds$ (dashed line) vs energy $ϵ$ for a system with a gravitational phase transition and a soft-core radius $x_0=0.005$.

Figure 2

Plots of the relative values of (from top to the bottom) the number of core particles, $N_c^{\prime }\left(\tau \right)$ (blue), and total temperature ${\Theta }^{\prime }\left(\tau \right)$ (red) vs $\tau$ for a collapse in system with $ϵ=-0.5$, $N=125$, and $x_0=0.005$. The time evolution of the core temperature ${\Theta }_c^{\prime }\left(\tau \right)$ is practically indistinguishable from $N_c^{\prime }\left(\tau \right)$ and cannot be seen in the plot.

Figure 3

Same as in Fig. 2 but for $x_0=0.01$.

Figure 4

Sketch of a core-halo particle scattering event.

Figure 5

Plots of the relative values of the (from top to the bottom) number of core particles, $N_c^{\prime }\left(\tau \right)$ (blue), total temperature ${\Theta }^{\prime }\left(\tau \right)$ (red), and core temperature ${\Theta }_c^{\prime }\left(\tau \right)$ (black) vs $\tau$ for the explosion in system with $ϵ=0.5$, $N=125$, and $x_0=\mathrm{0.005.}$