double peaks. For $N > 50,000$, oscillation becomes apparently chaotic ([@Heggie1989], [@Breeden1994]).

Both the contraction and the expansion are driven by the gravothermal instability, and the energy production by binaries acts as the trigger to start the expansion. During the expansion, the thermal energy flows in from the halo to the core, and this heat flux is supported by so-called “temperature inversion”. This temperature inversion itself is formed through the expansion of the core driven by the binary heating in the following way.

Binaries deposit the energy to the core through “indirect heating” ([@Hut1985]). When a binary hardens through interaction with a third star, that star is likely to be kicked out of the core, because the recoil velocity is much larger than the velocity dispersion of the core. As a result, the binding energy of the core becomes smaller. The core expands to reestablish the dynamical equilibrium. This expansion causes the velocity dispersion of the core to decrease. Thus the central temperature becomes lower than the temperature of the region just outside the core.

Once the central temperature becomes lower than the temperature around the core, the heat starts to flow inward. This inward heat flux let the core 