On the acceleration of cosmic rays at the post-adiabatic shocks of supernova remnants

TL;DR

This work analyzes how radiative cooling in the post-adiabatic phase of SNRs reshapes the downstream flow, creating sharp velocity gradients and regions where $u_2<0$ that can enhance diffusive shock acceleration (DSA). By combining 1D MHD simulations with analytic and numerical treatments of time-dependent CR transport, the authors show that the resulting CR spectra harden and $p_ ext{max}$ can exceed classical predictions, with the acceleration efficiency amplified by the augmented compression and flow nonuniformity. A key finding is that the radio spectral index is expected to decrease as post-adiabatic evolution proceeds, consistent with observations such as Kes 73, and that magnetic-field geometry modulates these effects. The study highlights the need for multidimensional MHD-CR coupling to fully capture the feedback between CRs, radiative losses, and plasma dynamics in aging SNRs.

Abstract

When a supernova remnant (SNR) interacts with the dense material of an interstellar cloud, its shock wave decelerates rapidly, and the post-shock temperature drops to levels that permit efficient cooling of the shocked plasma. At this stage, the shock enters the post-adiabatic phase of its evolution. During this phase, the internal structure of the SNR undergoes significant changes, particularly in the immediate post-shock region, at spatial scales relevant to cosmic ray acceleration. Once the shock enters the post-adiabatic regime, the efficiency of diffusive shock acceleration increases due to a higher plasma compression, to a change in the direction of the advection velocity, and to an increased rate of momentum gain. As a result, the momentum spectrum of relativistic particles hardens, deviating from a pure power law at high energies. Particles could reach higher maximum values compared to classical predictions. We highlight the dynamics of post-adiabatic flows in SNRs, study their impact on particle acceleration, and present supporting observational evidence in the radio band.

Figures (13)

• Figure 1: Top. The evolution of the radius $R$ (dashed lines) and speed $V$ (solid lines) of the forward shock. Bottom. The time dependence of the expansion parameter $m$. Three vertical lines mark the times $t_\mathrm{tr}$ (left), $1.49t_\mathrm{tr}$ (middle) and $t_\mathrm{sf}$ (right).
• Figure 2: Spatial distributions of the flow speed $u_2$, magnetic field strength $B_2$, and number density $n_2$ downstream of the shock at several moments of time. The left column is for the model 1 and the right column for the model 2.
• Figure 3: Distances $x_\mathrm{A}$ and $x_\mathrm{B}$ from the shock for the two models. The flow speed $u_2<0$ between the two solid lines. The vertical lines mark the times $1.49t_\mathrm{tr}$ and $t_\mathrm{sf}$. The flow speed $u_2>0$ in the whole domain before $1.49t_\mathrm{tr}$.
• Figure 4: The electron spectral index versus the age for a sample of SNRs with the radio and GeV $\gamma$-ray emission detected 2019ApJ...874...50Z. The size of the circles is proportional to $\lg(n)$. The red line represents a linear fit with $k = -0.363$.
• Figure 5: The distribution of the radio spectral index over Kes 73 measured between 1.4 and 5.0 GHz (left) and the ${}^{12}$CO ($J=3\rightarrow2$) intensity map 2013ApJS..209....8D integrated over the velocity range between 94 and 95 ${\,\rm km/s}$, in units ${\,\rm K\ km/s}$ (right). Contours correspond to the values of the radio index $0.8$, $0.6$, and $0.4$. Also 2017ApJ...851...37L present ${}^{12}$CO ($J=1\rightarrow 0$) intensity maps around Kes 73 at various velocities. Those in the range 86-97 km/s correlate with the radio index map as well.