The effect of cosmic ray acceleration on supernova blast wave dynamics

Abstract

Non-relativistic shocks accelerate ions to highly relativistic energies provided that the orientation of the magnetic field is closely aligned with the shock normal (quasiparallel shock configuration). In contrast, quasi-perpendicular shocks do not efficiently accelerate ions. We model this obliquity-dependent acceleration process in a spherically expanding blast wave setup with the moving-mesh code arepo for different magnetic field morphologies, ranging from homogeneous to turbulent configurations. A Sedov-Taylor explosion in a homogeneous magnetic field generates an oblate ellipsoidal shock surface due to the slower propagating blast wave in the direction of the magnetic field. This is because of the efficient cosmic ray (CR) production in the quasi-parallel polar cap regions, which softens the equation of state and increases the compressibility of the post-shock gas. We find that the solution remains self-similar because the ellipticity of the propagating blast wave stays constant in time. This enables us to derive an effective ratio of specific heats for a composite of thermal gas and CRs as a function of the maximum acceleration efficiency. We finally discuss the behavior of supernova remnants expanding into a turbulent magnetic field with varying coherence lengths. For a maximum CR acceleration efficiency of about 15 per cent at quasi-parallel shocks (as suggested by kinetic plasma simulations), we find an average efficiency of about 5 per cent, independent of the assumed magnetic coherence length.

Shock-accelerated cosmic rays and streaming instability in the adaptive mesh refinement code Ramses

“…Obliquity-dependency of the acceleration leads to a significant modification of the CR distribution in the shell of the Sedov explosion with either a polar or patchy distribution when the coherence length of the background magnetic field is respectively larger or smaller than the bubble size. This also has consequences on the final shape of the bubble, with a significant elongation of the bubble when the magnetic field has a large field coherence with respect to the bubble size (Pais et al 2018). Finally, the effect of CR streaming and CR acceleration has been tested in an turbulent box mimicking the motions within the interstellar medium on tens of pc scales (Commerçon et al 2019).…”

“…Finally, the new CR energy is updated with ∆e CR = φ CR ∆t/∆x According to detailed simulations of accelerated CRs at shocks (Caprioli & Spitkovsky 2014), their acceleration efficiency depends on both the Mach number of the shock and the upstream magnetic field orientation with respect to the normal to the shock θ B = arccos(b 1 .n s ). The dependency of the efficiency of CR acceleration with this so-called "magnetic obliquity" can be factorized out η(M, X CR , θ B ) = η 0 ξ(M, X CR )ζ(θ B ) and approximated by the following functional form (Pais et al 2018)…”

“…Note that the exact shape of the ellipsoid is a function of the obliquity-independent part of the acceleration efficiency, i.e. the larger ξ is, the more stretched is the explosion (see Pais et al 2018, for a thorough analysis of this effect). As expected, the density is also larger along the x-direction than along the y-direction (z-direction) as a result of the dependency of the density jump to the adiabatic index of the gas (for strong shocks, R ρ = 4 for γ e = 5/3 and R ρ = 6 for γ e = 7/5).…”

Simulating the interstellar medium and stellar feedback on a moving mesh: implementation and isolated galaxies

“…Examples include the impact of cosmic rays (e.g. Recchia et al 2016;Pais et al 2018;Jacob et al 2018), stellar jets (Frank et al 2014), high-energy photons from X-ray binaries (Kannan et al 2016b), runaway stars (Kimm & Cen 2014), among others. As such, caution should be exercised when interpreting the results of the models or the meaning of parameters currently used in numerical simulations since they are, by construction, only approximations to the real physics driving the structure and evolution of galaxies.…”

Lighting Up Dark Matter Haloes

“…The degree of sophistication reached by current hydrodynamical simulations is impressive and the level of agreement with observational data encouraging. Recent work has also focused on the inclusion of "non-standard" galaxy formation physics like magnetic fields and cosmic rays (see, e.g., [92,93]). However, different (plausible and often equally successful) physical models for stellar feedback have been proposed (see the discussion in [94]), and it remains difficult to discriminate between them (we will come back to this issue below).…”