Momentum and energy injection by a supernova remnant into an inhomogeneous medium

We investigate the effect of mass-loading from embedded clouds on the evolution of supernova remnants and on the energy and momentum that they inject into an inhomogeneous interstellar medium. We use 1D hydrodynamical calculations and assume that the clouds are numerous enough that they can be treated in the continuous limit. The destruction of embedded clouds adds mass into the remnant, increasing its density and pressure, and decreasing its temperature. The remnant cools more quickly, is less able to do PdV work on the swept-up gas, and ultimately attains a lower final momentum (by up to a factor of two or more). We thus find that the injection of momentum is more sensitive to an inhomogeneous environment than previous work has suggested, and we provide fits to our results for the situation where the cloud mass is not limited. The behaviour of the remnant is more complex in situations where the cloud mass is finite and locally runs out. In the case of multiple supernovae in a clustered environment, later supernova explosions may encounter higher densities than previous explosions due to the prior liberation of mass from engulfed clouds. If the cloud mass is finite, later explosions may be able to create a sustained hot phase when earlier explosions have not been able to.