expand further, and the temperature of the core continues to decrease. This self-supported expansion can continue as far as the temperature gradient outside the core is small. In practice, however, temperature gradient becomes larger as the core size becomes larger, and the temperature inversion vanishes at a certain core size. After that, the core starts to recollapse.

The critical number of particles for multi-component systems is larger than that for single-component systems, and for a “realistic” mass function, the critical number of particle can be as large as $3 \times
10^5$ ([@Murphy1990]).

The question whether such gravothermal oscillation would takes place in real globular clusters or in $N$-body systems has not been settled yet. Both gaseous models and FP models have many simplifying assumptions that might make the evolution completely different from that of a real cluster. For example, both assume spherical symmetry, while in $N$-body simulations cores are known to wander around ([@Makino1987], [@Heggie1994]). Both assume that the energy production by binaries is smooth, while in $N$-body system binaries are formed stochastically and emit energy intermittently.

An $N$-body simulation with a sufficiently large number of particles has been impossible, simply because the requirement for computer power has been excessive. 