is rather vaguely defined due to larger fluctuations in a core-halo than in a uniform state.

Similarly to a collapse, the system remains thermalized in the velocity space during an explosion. The velocity distribution remains Maxwellian throughout the evolution with the temperature corresponding to the current value of kinetic energy. As an illustration, Fig. \[fig\_velm\] shows the ratio of the moments of velocity distribution, $19 \langle v^2 \rangle ^2 /
5 \langle v^4 \rangle$, which should be 1 for a Gaussian distribution.

![\[fig\_velm\] Plot of he ratio of the moments of velocity distribution, $19 \langle v^2 \rangle ^2 /
5 \langle v^4 \rangle$, vs.time $\t$ for a system with $\e=0.5$ and $N=250$.](fig14.eps){width=".45\textwidth"}

However, as it is evident from a comparison between the Figs. \[fig\_expl\] and \[fig\_expla\], as $\e$ gets closer to $\e_{expl}$ the explosion takes longer to initiate. We have observed, that even for $\e=0.3$, which is noticeably larger than $\e_{expl} \approx 0.267$, the explosion does not happen during the first $\t=30000$ of evolution. This suggests that either the MF value for $\e_{expl}$ is incorrect, or during the incitation of the system we somehow prepare the system not exactly in the equilibrium (metastable) core-halo state. If the latter is the 