isothermal expansion is driven by the heat supplied from outside the core. In other words, the expansion is gravothermal.

The core size — result and interpretation
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Figure 5 shows the evolution of the number of particles in the core. For all runs, the number of particles at the maximum contraction is of the order of 10, while that at the maximum expansion is $\sim 1\%$ of the total number of particles. This result is again in good agreement with gas models and FP calculations ($e.g.$, [@Heggie1989] [@Breeden1994]).

Figure 6 shows the fraction of time for which the number of particles in the core is smaller than the value $N_c$ as a function of $N_c/N$, for the post-collapse phase. In other words, this figure shows the cumulative distribution of the core mass. For $N > 8192$, the median core mass is around 0.5-0.6 %. This corresponds to $r_c/r_h \sim
0.01$. For $N=32,768$, the core mass is somewhat smaller than that for 16k or 8k runs.

Whether the core size in the gravothermal oscillation phase depends on the total number of particles or not is not well understood. Bettwieser and Sugimoto (1984) argued that clusters spend most of the time in 