their $N$-body results can be extrapolated to larger values of $N$, cores with primordial binaries and cores in gravothermal oscillation would be clearly distinguishable. On the other hand, FP result by Gao (1991) indicates that the typical core size at the “primordial binary burning” phase and that at the gravothermal oscillation phase would not be much different. To obtain a definitive answer, we need to perform simulations of clusters with primordial binaries using the number of particles larger than that employed by McMillan (1990).

The core size — comparison with observations
--------------------------------------------

Djorgovski and King (1986) showed that 15% of galactic globular clusters have unresolved density cusp. They classified these clusters as “post core collapse” (PCC). Recent ground-based observations ([@Lugger1995]) and HST results ([@Sosin1995], [@Guhathakurta1994], [@Yanny1994]) demonstrated that some of the PCC clusters have the cusps unresolved even with HST (NGC6624, M15). For these clusters, the surface density profile shows the power law down to 0.3 arcsec. Other clusters (M30), though the slope seems to levels off toward the center, turned out to be difficult to determine the slope accurately because there are too few stars. In the case of M30, the core radius can be anywhere smaller than 1.5 