Dusty Clump Survival in Supernova Ejecta: Dust-Mediated Growth vs. Crushing by the Reverse Shock

Understanding the interaction of dense, cold ejecta clumps with a fast reverse shock, an instance of the "cloud-crushing" problem, is essential to assess whether core-collapse supernovae act as net dust factories or net dust destroyers. This work assesses whether dusty ejecta clumps are destroyed by the reverse shock or instead cool, condense, and grow in mass under realistic supernova-remnant conditions. Cloud-crushing timescales are computed and compared to radiative cooling timescales, including both gas-phase cooling and dust-induced cooling, for a large grid of clump densities, dust-to-gas mass ratios, and shock velocities. When the dust-to-gas mass ratio exceeds $10^{-3}$, gas-grain collisions become efficient enough that the cooling timescale $t_{\rm cool}$ falls below the cloud-crushing timescale $t_{\rm cc}$ over a broad span of clump densities and shock velocities, enabling dusty clumps to survive even fast reverse shocks. For example, at clump densities $\geq 2 \times 10^{4}$ cm$^{-3}$, dust-to-gas mass ratios $\sim 10^{-2}$, and shock velocities up to $2000$ km s$^{-1}$, enhanced gas-grain cooling drives the system into a regime where dusty clumps can gain additional cold mass and increase their dust masses. Strong radiative cooling can shield dust-rich clumps in supernova remnants, enabling a significant fraction of ejecta dust to be injected into the interstellar medium. These results mirror the "growth" regime found in studies of circumgalactic clouds and rapidly cooling shocked stellar winds, implying a larger dust survival in supernova remnants. Indeed, the dusty globules seen in the Crab Nebula occupy the predicted survival regime across a wide range of physical parameters.