Thermal Relaxation in One-Dimensional Self-Gravitating Systems

In this paper, we study the thermal relaxation in the one-dimensional self-gravitating system, or the so-called sheet model. According to the standard argument, the thermal relaxation time of the system is around $Nt_c$, where $N$ is the number of sheets and $t_c$ is the crossing time. It has been claimed that the system does not reach the thermal equilibrium in this thermal relaxation timescale, and that it takes much longer time for the system to reach true thermal equilibrium. We demonstrate that this behavior is explained simply by the fact that the relaxation time is long. The relaxation time of sheets with average binding energy is $\sim 20 Nt_c$, and that of sheets with high energy can exceed $1000 Nt_c$. Thus, one needs to take the average over the relaxation timescale of high-energy sheets, if one wants to look at the thermal characteristic of these high energy sheets.