in the gravothermal oscillation phase is smaller than previous estimates because of the following two reasons. First, the time-averaged core size is about a half of the maximum size. Second, the core size depends on $N$ as $N^{-1/\alpha}$, with index alpha $2\sim 3$.

For NGC6624 and M15, core sizes seem to be too small for a stably expanding cluster, no matter what is the heat source. So it is highly likely that they are undergoing the gravothermal oscillation.

Discussion
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We performed direct $N$-body simulation of the post-collapse evolution of globular clusters. We confirmed that the gravothermal oscillation actually takes place in a point-mass $N$-body system.

Whether real globular clusters undergo gravothermal oscillation or not is a question which requires further research. If clusters contain many primordial binaries, even after the core collapse they might still be burning the primordial binaries. In addition, the effect of two-body binaries to the evolution of the cluster is still unclear. In fact, the cross section for the binary formation by tidal capture is not fully understood yet (Mardling 1995a, 1995b).

The most straightforward way to study the effect of primordial binaries or two-body capture is the direct $N$-body simulation. In principle, we can 