A Novel Parameterization for Rapid Cooling in Supernova Remnants, with applications to the Pa 30 nebula

Abstract: We systematically study how cooling creates structural changes in supernova remnants as they evolve. Inspired by the peculiar morphology of the Pa 30 nebula, we adopt a framework in which to characterize supernova remnants under different degrees of cooling. Our cooling framework characterizes remnants with a singular parameter called $β$ that sets how rapidly the system's thermal energy is radiated or emitted away. A continuum of morphologies is created by the implementation of different cooling timescales. For $β\gtrsim 400$, or when the cooling timescale is shorter than $\approx \frac{1}{400}$ of the Sedov time, the ejecta is shaped into a filamentary structure similar to Pa 30. We explain the filament creation by the formation of Rayleigh-Taylor Instability fingers where cooling has prevented the Kelvin-Helmholtz Instability from overturning and mixing out the tips. The ejecta in these filaments have not decelerated and are moving almost completely ballistically at $\approx 95-100\%$ their free expansion speed. In this rapid cooling regime, an explosion energy $\approx 3.5 \times 10^{47}$ erg is inferred. We also propose the cooling mechanism required to create these structures necessitates removing energy at a rate of $2\%$ of $E_{\rm ej}/t$, which implies a cooling luminosity of $\approx 10^{36}$ erg/s.