Evolution of clustered supernovae
  We study the merging and evolution of isolated supernovae (SNe) remnants in a
stellar cluster into a collective superbubble, with the help of 3-D
hydrodynamic simulations. We particularly focus on the transition stage when
the isolated SNe remnants gradually combine to form a superbubble. We find that
when the SN rate is high ($\nu_{\rm sn}\sim 10^{-9}$ pc$^{-3}$ yr$^{-1}$), the
merging phase lasts for $\sim 10^4$ yr, for $n=1\hbox{--}10$ cm$^{-3}$, and the
merging phase lasts for a longer time ($\sim 0.1$ Myr or more) for lower SN
rates ($\nu_{\rm sn}\le 10^{-10}$ pc$^{-3}$ yr$^{-1}$). During this transition
phase, the growing superbubble is filled with dense and cool fragments of
shells and most of the energy is radiated away during this merging process.
After passing through the intermediate phase, the superbubble eventually
settles on to a new power-law wind asymptote that is smaller than estimated in
a continuous wind model. This results in a significant (more than {\it several
times}) underestimation of the mechanical luminosity needed to feed the bubble.
We determine the X-ray and H$\alpha$ surface brightnesses as functions of time
for such merging SNe in a stellar cluster and find that clusters with high SN
rate shine predominantly in soft X-rays and H$\alpha$. In particular, a low
value of the volume averaged H$\alpha$ to H$\beta$ ratio and its large spread
can be a good indicator of the transition phase of merging SNe.
