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

TL;DR

The paper develops a unified cooling framework for supernova remnants by introducing a singular parameter $β$ that dictates the cooling efficiency, and uses 3D moving-mesh hydrodynamics to map how increasing cooling reshapes RTI fingers into long, radial filaments resembling Pa 30. The authors demonstrate that $β\gtrsim400$ yields highly filamentary, nearly ballistic ejecta and a heavily corrugated forward shock, with cooling contributing at most ~2% of the ejecta energy by the Pa 30 epoch and a luminosity around $L_{\text{cool}}\sim10^{35}$ erg s$^{-1}$ for plausible efficiencies. They dynamically match Pa 30 with $β\approx800$, inferring an ejecta energy of $E_{\text{ej}}\approx3.5\times10^{47}$ erg and a surrounding density $n_{\text{CSM}}\approx0.088$ cm$^{-3}$, consistent with a WD merger–driven Type Iax progenitor. The work additionally predicts observational signatures—such as faint radio emission and a characteristic filament separation around $Δ\theta\approx4^\circ$—to test the cooling scenario and offers a framework that could generalize to other young SNRs.

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.

Figures (9)

• Figure 1: Three-dimensional visualization of the remnant structure for no cooling implemented and for our most rapid cooling with $\beta = 800$. Both models are at $t=0.1 \, t_{\text{Sedov}}$. The yellow-colored iso-surface is a choice of density intended to target the shape of the ejecta, in units of $\rho_{\text{CSM}}$. Furthermore, the transparent blue-colored iso-surface represents the pressure near the forward shock displayed in units of $P_0$. See \ref{['table: runtime params']} for physical scalings. With a rapid cooling timescale, the ejecta has been shaped into long and thin spikes that jut out and almost pierce through the forward shock. This causes the contour of the forward shock to be corrugated and sculpted around the filaments.
• Figure 2: Integrated shocked ejecta density along the $z$ axis for our model suite at $t=0.1 \, t_{\text{Sedov}}$. The forward shock (white-dashed line) and the reverse shock (black-dashed line) are overlaid for clarity and are determined using the conditions in \ref{['methods subsec: tracking rRS and rFS']}. The integrated shocked column density is computed by an integration along the line of sight only in the ejecta at radii greater than the reverse shock radius. The color bar is in units of $\unit{g\per \cm\cubed}$. The projection of the shocked ejecta density demonstrates the extent of radial symmetry the RTI fingers are spatially. For highly radial configurations, the filaments will stack onto each other as opposed to smearing out in a less symmetric case. As $\beta$ increases from the $0$ to $800$, the extent in which the RTI fingers turn over and mix out lessens, resulting in thin and narrow radial filaments.
• Figure 3: Cross-section slices of pressure ($\unit{erg \per \cubic\cm}$) for four different $\beta$ values. The side lengths are scaled arbitrary to easily compare between different $\beta$ values at $t=0.1 \, t_{\text{Sedov}}$. The forward shock (outer white-dashed line) and the reverse shock (inner white-dashed line) are overlaid for clarity and are determined using the conditions in \ref{['methods subsec: tracking rRS and rFS']}. We suggest that these pressure slices demonstrate the contour of the forward shock, which becomes grooved with increasing $\beta$. In other words, for $\beta=0$, the pressure is distributed uniformly in a smooth spherical shell while the higher $\beta$ runs have a spiked structure that molds around the filamentary structure shown in \ref{['fig:3d isosurface']} and \ref{['fig: shock ej col density']}. We note that for the more strongly cooled off remnants, the pressure is orders of magnitude less than the standard no-cooling case seen in $\beta = 0$. This could suggest observing SNRs in a regime displayed by $\beta \approx 200-800$ would be difficult as the signals would be much fainter.
• Figure 4: Cross-section slices of the homologous expansion fraction $k = v/(r/t)$ for the velocity in the domain at $t=0.1 \, t_{\text{Sedov}}$. The distribution of $k$ demonstrates that as $\beta$ increases, or when a more rapid cooling timescale is implemented, the velocity of the material in the filaments gets more ballistic ($k\approx 0.9-1.0$). Stronger cooling prevents the shocked ejecta from decelerating and the Rayleigh-Taylor instability sculpts it into long filaments that have not slowed down from free expansion speeds. The forward and reverse shock positions determined using the conditions specified in \ref{['methods subsec: tracking rRS and rFS']} are plotted as dashed blue and black lines respectively.
• Figure 5: Radially averaged ejecta velocities $v_{\text{ej}}(r)$ and homologous expansion fraction $k_{\text{ej}}(r) = v_{\text{ej}}(r)/t$ for our model suite. Each column denotes a different time. The average is constrained to regions where the ejecta is at least $90 \%$ abundant and weighted by the ejecta density in that region. Each column denotes a different time and the color scheme denotes a different $\beta$. We remark that as $\beta$ is increased, the ejecta velocity becomes more ballistic within the shocked region, with $k \approx 1$ in the most extreme cases. We remark on the continuum achieved in the velocity profiles when comparing between $\beta$s. The forward and reverse shock are denoted as black vertical lines for clarity (see \ref{['methods subsec: tracking rRS and rFS']}). We note that the locations of the shocks identified in the radially averaged velocity profiles themselves are different, but we explain this by our averaging process that was weighted by ejecta-dominant zones.