Postshock turbulence and diffusive shock acceleration in young supernova remnants

¹ Laboratoire de Physique Théorique et d'Astroparticules (LPTA), UMR 5207 CNRS, Université Montpellier II, 13 place E. Bataillon, 34095 Montpellier Cedex 5, France e-mail: Alexandre.Marcowith@LPTA.in2p3.fr
² Laboratoire AstroParticule & Cosmologie (APC), UMR 7164 CNRS, Université Paris Diderot, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France e-mail: fcasse@apc.univ-paris7.fr

Received: 30 July 2009
Accepted: 24 December 2009

Abstract

Context. Thin X-ray filaments are observed in the vicinity of young supernova remnants (SNR) blast waves. Identifying the process that creates these filaments would provide direct insight into the particle acceleration occurring within SNR and in particular the cosmic ray yield.

Aims. We investigate magnetic amplification in the upstream medium of a SNR blast wave through both resonant and non-resonant regimes of the streaming instability. We attempt to understand more clearly of the diffusive shock acceleration (DSA) efficiency by considering various relaxation processes of the magnetic fluctuations in the downstream medium. Multiwavelength radiative signatures originating in the SNR shock wave are used to test various downstream turbulence relaxation models.

Methods. Analytical and numerical calculations that couple stochastic differential equation schemes with 1D spherical magnetohydrodynamics simulations are used to investigate, in the context of test particles, turbulence evolution in both the forshock and post-shock regions. Stochastic second-order Fermi acceleration induced by resonant modes, magnetic field relaxation and amplification, and turbulence compression at the shock front are considered to model the multiwavelength filaments produced in SNRs. The γ-ray emission is also considered in terms of inverse Compton mechanism.

Results. We confirm the result of Parizot and collaborators that the maximum CR energies should not go well beyond PeV energies in young SNRs where X-ray filaments are observed. To reproduce observational data, we derive an upper limit to the magnetic field amplitude and so ensure that stochastic particle reacceleration remains inefficient. Considering various magnetic relaxation processes, we then infer two necessary conditions to achieve efficient acceleration and X-ray filaments in SNRs: (1) the turbulence must fulfil the inequality 2 - β - ≥ 0; where β is the turbulence spectral index and  is the relaxation length energy power-law index; (2) the typical relaxation length must be of the order the X-ray rim size. We find that Alvénic/fast magnetosonic mode damping fulfils all conditions; while non-linear Kolmogorov damping does not. By confronting previous relaxation processes with observational data, we deducte that among our SNR sample, data for the older ones (SN1006 and G347.3-0.5) does not comply with all conditions, which means that their X-ray filaments are probably controlled by radiative losses. The younger SNRs, Cassiopeia A, Tycho, and Kepler pass all tests and we infer that the downstream magnetic field amplitude is in the range of 200–300 μGauss.