The momentum budget of clustered supernova feedback in a 3D, magnetised medium

While the evolution of superbubbles driven by clustered supernovae has been studied by numerous authors, the resulting radial momentum yield is uncertain by as much as an order of magnitude depending on the computational methods and assumed properties of the surrounding interstellar medium (ISM). In this work, we study the origin of these discrepancies, and seek to determine the correct momentum budget for a homogeneous ISM. We carry out 3D hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations of clustered supernova explosions, using a Lagrangian method and checking for convergence with respect to resolution. We find that the terminal momentum of a shell driven by clustered supernovae is dictated primarily by the mixing rate across the contact discontinuity between the hot and cold phases, and that this energy mixing rate is dominated by numerical diffusion even at the highest resolution we can complete, 0.03 $M_\odot$. Magnetic fields also reduce the mixing rate, so that MHD simulations produce higher momentum yields than HD ones at equal resolution. As a result, we obtain only a lower limit on the momentum yield from clustered supernovae. Combining this with our previous 1D results, which provide an upper limit because they allow almost no mixing across the contact discontinuity, we conclude that the momentum yield per supernova from clustered supernovae in a homogeneous ISM is bounded between $2\times 10^5$ and $3\times 10^6$ $M_\odot$ km s$^{-1}$. A converged value for the simple homogeneous ISM remains elusive.