Supernovae under microscope: how 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. We scan the parameter space of ISM density ($n_{g0}$), number of SNe ($N_{rm OB}$), and star cluster radius ($r_{rm cl}$) to study the conditions for the formation of an overpressured (super)bubble. 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.