If the expansion were driven only by binary heating, it could not continue without energy input for the timescale more than 100 times longer than the core relaxation time.

Figure 3 shows temperature profiles for the contracting and expanding phases. Near the end of the expanding phase the temperature inversion of the order of 5% is clearly visible. Since these profiles are time-averaged over 10 time units (80 snapshots), the actual inversion might be somewhat stronger. Note that the temperature inversion is visible only near the end of long expansion phases also in gas model and FP calculations ([@Bettwieser1984], [@Cohn1989]).

Figure 4 shows the relation between the central density and the central velocity dispersion. The trajectory shows striking resemblance to what obtained by gas model calculation (Goodman 1987). The fact that the trajectory shows clockwise rotations means that this is a refrigeration cycle, in which the central region absorbs heat when the temperature is low, and release heat when the temperature is high (Bettwieser and Sugimoto 1984, Bettwieser 1985). In particular, the later phase of the large expansions (indicated by the arrow marked “B”) is nearly isothermal. Since the binding energy of binaries is unchanged during this phase, this nearly 