How multiple supernovae overlap to form superbubbles

Abstract

We explore the formation of superbubbles through energy deposition by\nmultiple supernovae (SNe) in a uniform medium. We use total energy conserving,\n3-D hydrodynamic simulations to study how SNe correlated in space and time\ncreate superbubbles. While isolated SNe fizzle out completely by $\\sim 1$ Myr\ndue to radiative losses, for a realistic cluster size it is likely that\nsubsequent SNe go off within the hot/dilute bubble and sustain the shock till\nthe cluster lifetime. For realistic cluster sizes, we find that the bubble\nremains overpressured only if, for a given $n_{g0}$, $N_{\\rm OB}$ is\nsufficiently large. While most of the input energy is still lost radiatively,\nsuperbubbles can retain up to $\\sim 5-10\\%$ of the input energy in form of\nkinetic+thermal energy till 10 Myr for ISM density $n_{g0} \\approx 1$\ncm$^{-3}$. We find that the mechanical efficiency decreases for higher\ndensities ($\\eta_{\\rm mech} \\propto n_{g0}^{-2/3}$). We compare the radii and\nvelocities of simulated supershells with observations and the classical\nadiabatic model. Our simulations show that the superbubbles retain only\n$\\lesssim 10\\%$ of the injected energy, thereby explaining the observed smaller\nsize and slower expansion of supershells. We also confirm that a sufficiently\nlarge ($\\gtrsim 10^4$) number of SNe is required to go off in order to create a\nsteady wind with a stable termination shock within the superbubble. We show\nthat the mechanical efficiency increases with increasing resolution, and that\nexplicit diffusion is required to obtain converged results.\n