Supernovae drive large-scale, incompressible turbulence through small-scale instabilities

TL;DR

This work identifies the unstable contact discontinuity in SNR cooling layers as the primary driver of incompressible turbulence in SN-driven galactic environments. By analyzing ~100 localized SNRs from high-resolution simulations, it derives a direct link between baroclinicity and the incompressible velocity field, establishing a predictive relation between baroclinic enstrophy and the velocity spectrum. The unstable layer exhibits a $k^{3/2}$ baroclinic spectrum and produces local incompressible modes with $\\\mathcal{P}_{\\bm{u}_s}(k) \\\propto k^{-3/2}$, while the shell's surface modes follow a 2D turbulence scaling $C(\\ell) \\\propto \\\ell^{-8/3}$. The study further shows that young SNRs can shed these surface modes into the surrounding ISM when a vortex-stretching timescale allows, linking small-scale instabilities to the large-scale turbulence cascade and providing a mechanism for SN-driven turbulence to influence kiloparsec-scale dynamics. The results offer a new phenomenology for turbulence in galaxies and highlight the role of Vishniac-like shell instabilities in seeding large-scale, incompressible turbulence through an inverse cascade.

Abstract

The sources of turbulence in our Galaxy may be diverse, but core-collapse supernovae (SNe) alone provide enough energy to sustain a steady-state galactic turbulence cascade at the observed velocity dispersion. By localizing and analyzing supernova remnants (SNRs) in high-resolution SN-driven galactic disk cut-out simulations from Beattie et al. (2025), I show that isolated SNRs source incompressible turbulence through baroclinic vorticity generation localized at the unstable contact discontinuity. Through the spherical harmonic power spectrum of the corrugations, I provide evidence that this process is seeded by surface instabilities and 2D turbulence on the shell, which corrugates and folds the interface, becoming the strongest source of baroclinicity in the simulations. I present an analytical relation for a baroclinicity-fed incompressible mode (co)spectrum, which matches that observed in the simulated SNRs, and reveals a $k^{-17/20}$ spectrum that drives the turbulence. I show that vortex stretching allows for modes to be shed from the contact discontinuity into the surrounding medium and derive a timescale criteria for this process, revealing that young SNR with radii close to the cooling radius are efficient at radiating turbulence. The unstable layer produces a spectrum of incompressible modes $\propto k^{-3/2}$ locally within the SNRs. Through the inverse cascade mechanism revealed in Beattie et al. (2025), this opens the possibility that the $k^{-3/2}$ spectrum, arising from corrugated folds in the unstable layer, imprints itself on kiloparsec scales, thereby connecting small-scale structure in the layer to the large-scale incompressible turbulence cascade.

Figures (12)

• Figure 1: The same as \ref{['fig:temperature_slices']}, but for the vorticity ($\omega = |\bm{\nabla} \times \bm{u}|$, left in each panel) and the baroclinicity ($\bm{\nabla}\rho \times \bm{\nabla} P/\rho^2$, right in each panel). The most intense $\omega$ regions, which are signatures of incompressible turbulence, correspond to the strongest $\bm{\nabla}\rho \times \bm{\nabla} P/\rho^2$ structures. The $\bm{\nabla}\rho \times \bm{\nabla} P/\rho^2$ structures closely trace the corrugated layer between the warm and hot plasma. Beattie2025_SLK41 finds that this layer generates $\bm{\omega}$ values three orders of magnitude larger than any other vorticity source in an SN-driven galactic disk environment. In this study, I show that these layers drive incompressible turbulence with a velocity spectrum $\propto k^{-3/2}$, the same spectrum as what is found in global SN-driven turbulence simulations of a galactic disk Connor2025_cascading_from_the_winds. An animation of this panel with a slider for the vertical bar between the vorticity and baroclinicity can be found https://astrojames.github.io/movies/.
• Figure 2: Left: The vorticity–baroclinic power (co)spectrum, $\mathcal{P}_{\omega \rm B}(k)$ (\ref{['eq:ps_ob']}), and the incompressible velocity-mode power spectrum, $\mathcal{P}_{\bm{u}_s}(k)$ (\ref{['eq:ps_sol']}), averaged over $\approx 100$ SNRs and normalized to test \ref{['eq:baro_sol_relation']}. Because the two transformed spectra scale with each other almost perfectly, the enstrophy sourced by baroclinicity, $\mathcal{P}_{\omega \rm B}$, fully accounts for the enstrophy flux entering the cascade, $d\Pi_{\bm{\omega}}/dk$. This demonstrates that the low-volume, fractal layer, which dominates the baroclinicity (see \ref{['app:baroclinic_source']} for a more detailed calculation showing that the unstable layer alone provides between all and 70% of the baroclinicity in the global simulations), drives the incompressible turbulence across a broad band of modes. Right: The two-dimensional volume-weighted probability density function (PDF) of vorticity and baroclinicity, showing a strong positive correlation, $\omega \sim |\bm{\nabla}\rho \times \bm{\nabla} P/\rho^2|$, that peaks and flattens at the $\bm{\nabla}\rho \times \bm{\nabla} P/\rho^2$ values concentrated within the fractal layer (see \ref{['fig:vort_baro_slices']}). This shows that volume-poor layers can dominate the baroclinic production.
• Figure 3: Top: The incompressible velocity-mode spectrum, $\mathcal{P}_{\bm{u}_s}(k)$, averaged (black) over the ensemble of localized SNRs and normalized by both the integral of the spectrum and a $k^{-3/2}$ compensation. The ensemble $1\sigma$ is shown in transparent blue. The wavenumber is normalized to $\ell_0 = 125\,\rm{pc}$, the domain size of the region extracted around each SNR. The plot shows the development of a self-similar range of modes that already exhibit a $\mathcal{P}_{\bm{u}_s}(k) \propto k^{-3/2}$ spectrum on the scales of individual SNRs. This is the same spectrum found in global disk cut-out simulations of SN-driven turbulence Padoan2016_supernova_drivingBeattie2025_SLK41Connor2025_cascading_from_the_winds. Bottom: The pure baroclinic power spectrum, $\mathcal{P}_{\rm B}(k)$ (\ref{['eq:ps_b']}), normalized in the same way as the top panel but with a $k^{3/2}$ compensation. This spectrum probes the organization of Fourier modes in the fractal layer between the warm and hot plasma in the SNR. It exhibits a $\mathcal{P}_{\rm B}(k) \propto k^{3/2}$ power law, peaking at high-$k$, reflecting the signature of a highly folded layer structure with strong gradients on very small scales Schekochihin2004_dynamo.
• Figure 4: Evolution of the unstable thin shell traced by $\bm{\nabla}\rho \times \bm{\nabla} P/\rho^2$ in the SNR. Each column from $(a)$ to $(d)$ shows the SNR at an increasing radius, $R_{\rm c}$ ($\sim$ age; indicated in red in the bottom row), all taken from the same early-time realization of the global simulation to ensure only internal instabilities impact the layer. As the shell expands, high-$k$ modes grow in the layer. By the time it reaches the full $125\,\rm pc$ domain size, the shell has become highly fractal, with deep, folded corrugations, without any background inhomogeneities to enhance or modify the unstable modes. Top row: the $\bm{\nabla}\rho \times \bm{\nabla} P/\rho^2$ "sky" for an observer at the center of the SNR, sliced at the radius, $R_{\rm c}$, highlighted in red in the bottom row, qualitatively showing that high-order spherical harmonics become increasingly excited as the SNR expands. Bottom row: two-dimensional slices of $\bm{\nabla}\rho \times \bm{\nabla} P/\rho^2$ (the same as in \ref{['fig:vort_baro_slices']}), showing the evolving, expanding corrugated layer.
• Figure 5: Main: the spherical harmonic power spectrum, $C(\ell)$, \ref{['eq:spherical_ps']}, for the fluctuations in the radial displacement vector, $\delta \xi_r$, \ref{['eq:displacement_vector']}. $\delta \xi_r$ directly probes the corrugations of the contact discontinuity. Each spectrum corresponds to a SNR from \ref{['fig:SNR_timeline']}, as indicated in the legend. Inset:$C(\ell)$ compensated by the $(a)$ spectrum, $C^{(a)}(\ell)$, to show which harmonics are growing with respect to the youngest SNR in \ref{['fig:SNR_timeline']}. The $C(\ell)$ admit to a power law $C(\ell) \propto \ell^{-8/3}$, which I show is consistent with 2D Kraichnan1967_two_dimensional_turbulence turbulence, \ref{['eq:2D_turbulence']}, that is self-generated on the thin shell, as discussed in \ref{['ssec:stuck_on_shell']}.