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

Sergio Martínez-González

TL;DR

This paper addresses whether dense, dusty clumps in core‑collapse supernova remnants can survive the reverse shock or instead grow via dust‑mediated cooling. It extends the cloud‑crushing framework to include both gas‑phase and dust‑induced radiative cooling, exploring a broad grid of clump densities, dust–to–gas ratios, and shock speeds. The key finding is that when the dust content satisfies $\mathcal{D} \gtrsim 10^{-3}$, gas–grain collisions boost cooling enough for $t_{ m cool}$ to fall below the cloud‑crushing time $t_{ m cc}$ across wide conditions, enabling survival or even growth of dusty clumps; examples include $n_{ m cl} \gtrsim 2\times10^{4}$ cm$^{-3}$, $\mathcal{D} \sim 10^{-2}$, and $v_{ m sh} \lesssim 2000$ km s$^{-1}$. Observed dusty globules in the Crab Nebula fall within the predicted survival regime, supporting higher dust survival fractions in SNRs. The work suggests core‑collapse SNe can inject more dust into the ISM than previously thought, though it remains to be validated with magnetohydrodynamic simulations that fully include dust microphysics.

Abstract

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.

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

TL;DR

This paper addresses whether dense, dusty clumps in core‑collapse supernova remnants can survive the reverse shock or instead grow via dust‑mediated cooling. It extends the cloud‑crushing framework to include both gas‑phase and dust‑induced radiative cooling, exploring a broad grid of clump densities, dust–to–gas ratios, and shock speeds. The key finding is that when the dust content satisfies , gas–grain collisions boost cooling enough for to fall below the cloud‑crushing time across wide conditions, enabling survival or even growth of dusty clumps; examples include cm, , and km s. Observed dusty globules in the Crab Nebula fall within the predicted survival regime, supporting higher dust survival fractions in SNRs. The work suggests core‑collapse SNe can inject more dust into the ISM than previously thought, though it remains to be validated with magnetohydrodynamic simulations that fully include dust microphysics.

Abstract

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 , gas-grain collisions become efficient enough that the cooling timescale falls below the cloud-crushing timescale over a broad span of clump densities and shock velocities, enabling dusty clumps to survive even fast reverse shocks. For example, at clump densities cm, dust-to-gas mass ratios , and shock velocities up to km s, 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.

Paper Structure

This paper contains 7 sections, 11 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Analytic model and methods
  3. Cloud‐crushing timescale
  4. Radiative cooling times
  5. Grain processing
  6. Parameter-space analysis
  7. Conclusions

Figures (2)

  • Figure 1: Cooling rate per unit volume vs. temperature. Solid curve: gas-phase cooling Schureetal2009. Dashed, dash-dotted, dotted: dust-induced cooling for $\mathcal{D}=10^{-4}, 10^{-3}, 10^{-2}$, respectively, assuming a log-normal grain-size distribution (5 nm $<a<$ 0.5 $\mu$m).
  • Figure 2: Regimes of clump survival versus crushing for clumps with $R_{\rm cl}=500$ AU. The maps show $t_{\rm cool}/t_{\rm cc}$ as a function of shock velocity and clump density. The panels correspond to cases with metal-line cooling only (top left), and different dust-to-gas mass ratios: $\mathcal{D}=10^{-4}$ (top right), $\mathcal{D}=10^{-3}$ (bottom left), and $\mathcal{D}=10^{-2}$ (bottom right). The red solid lines mark $t_{\rm cool}=t_{\rm cc}$. Clumps above the line (lower $v_{\rm sh}$ or higher $n_{\rm cl}$) can cool/grow, while below the line they are crushed. Higher dust-to-gas mass ratios expand the survival region. Blue dashed: isobaric $\mathcal{R}=1$; purple dotted: isochoric $\mathcal{R}=1$. Isochoric crossings occur only at $v_{\rm sh}\!\lesssim$ a few $10^2$ km s$^{-1}$; realistic clumps fall between these limits. In both cases, regions above the $\mathcal{R}=1$ lines correspond to grain growth exceeding thermal sputtering. The hatched area indicates the range of observed dusty globules in the Crab Nebula.