Momentum injection by clustered supernovae: Testing subgrid feedback prescriptions

Using a 1D Lagrangian code specifically designed to assess the impact of multiple, timeresolved supernovae (SNe) from a single-star cluster on the surrounding medium, we test three commonly used feedback recipes: delayed cooling (e.g. used in the GASOLINE-2 code), momentum-energy injection (a resolution-dependent transition between momentumdominated feedback and energy-dominated feedback used, e.g. in the FIRE-2 code), and simultaneous energy injection (e.g. used in the EAGLE simulations). Our work provides an intermediary test for these recipes: we analyse a setting that is more complex than the simplified scenarios for which many were designed, but one more controlled than a full galactic simulation. In particular, we test how well these models reproduce the enhanced momentum efficiency seen for an 11 SN cluster simulated at high resolution (0.6 pc; a factor of 12 enhancement relative to the isolated SNcase) when these subgrid recipes are implemented in low resolution (20 pc) runs. We find that: (1) the delayed cooling model performs well - resulting in 9 times the momentum efficiency of the fiducial isolated SN value - when SNe are clustered and 1051 erg are injected per SN, while clearly overpredicting the momentum efficiency in the single SN test case; (2) the momentum-energy model always achieves good results, with a factor of 5 boost in momentum efficiency; and (3) injecting the energy from all SNe simultaneously does little to prevent overcooling and greatly underproduces the momentum deposited by clustered SNe, resulting in a factor of 3 decrease in momentum efficiency on the average.