Enhanced Momentum Feedback from Clustered Supernovae

Young stars typically form in star clusters, so the supernovae (SNe) they produce are clustered in space and time. This clustering of SNe may alter the momentum per SN deposited in the interstellar medium (ISM) by affecting the local ISM density, which in turn affects the cooling rate. We study the effect of multiple SNe using idealized 1D hydrodynamic simulations which explore a large parameter space of the number of SNe, and the background gas density and metallicity. The results are provided as a table and an analytic fitting formula. We find that for clusters with up to ~100 SNe the asymptotic momentum scales super-linearly with the number of SNe, resulting in a momentum per SN that can be an order of magnitude larger than for a single SN, with a maximum efficiency for clusters with 10-100 SNe. We argue that additional physical processes not included in our simulations -- self-gravity, breakout from a galactic disk, and galactic shear -- can slightly reduce the momentum enhancement from clustering, but the average momentum per SN still remains a factor of 4 larger than the isolated SN value when averaged over a realistic cluster mass function for a star-forming galaxy. We conclude with a discussion of the possible role of mixing between hot and cold gas, induced by multi-dimensional instabilities or preexisting density variations, as a limiting factor in the buildup of momentum by clustered SNe, and suggest future numerical experiments to explore these effects.