How multiple supernovae overlap to form superbubbles

We explore the formation of superbubbles through energy deposition by multiple supernovae (SNe) in a uniform medium. We use total energy conserving, 3-D hydrodynamic simulations to study how SNe correlated in space and time create superbubbles. While isolated SNe fizzle out completely by $\sim 1$ Myr due to radiative losses, for a realistic cluster size it is likely that subsequent SNe go off within the hot/dilute bubble and sustain the shock till the cluster lifetime. For realistic cluster sizes, we find that the bubble remains overpressured only if, for a given $n_{g0}$, $N_{\rm OB}$ is sufficiently large. While most of the input energy is still lost radiatively, superbubbles can retain up to $\sim 5-10\%$ of the input energy in form of kinetic+thermal energy till 10 Myr for ISM density $n_{g0} \approx 1$ cm$^{-3}$. We find that the mechanical efficiency decreases for higher densities ($\eta_{\rm mech} \propto n_{g0}^{-2/3}$). We compare the radii and velocities of simulated supershells with observations and the classical adiabatic model. Our simulations show that the superbubbles retain only $\lesssim 10\%$ of the injected energy, thereby explaining the observed smaller size and slower expansion of supershells. We also confirm that a sufficiently large ($\gtrsim 10^4$) number of SNe is required to go off in order to create a steady wind with a stable termination shock within the superbubble. We show that the mechanical efficiency increases with increasing resolution, and that explicit diffusion is required to obtain converged results.