present, however, actual cost is difficult to estimate because the calculation cost depends strongly on the core size, of which we have rather little knowledge (see section 4). It should be noted that the number of floating point operations used to follow the life of a binary depends only weakly on the total number of particles in the system ([@Makino1990]). Therefore, while the CPU time for the orbit integration of single stars would increase as $N^{2.3}$, the cost of binaries would increases only as $N$. It is likely that for large $N$ the cost of binaries is relatively small, even for simulations with primordial binaries.

Result
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The core oscillation
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Figure 1 shows the time evolution of the central density for all runs. The time is scaled so that thermal timescale is the same for all runs. The scaling factor is $t_r(1000)/t_r(N) = 212.75\log(0.11N)/N$ (Giersz and Heggie 1994). The core density shows oscillations with a large amplitude in calculations with large $N$ ($>$16k). No matter what is the real nature of this oscillation, it is at least clear that the core density of the $N$-body system shows oscillation with the amplitude comparable to that observed in gas models or 