Limits on diffusive shock acceleration in supernova remnants in the presence of cosmic-ray streaming instability and wave dissipation

Abstract

Abstract. The instability in the cosmic-ray precursor of a supernova shock moving in interstellar medium is studied. The level of magnetohydrodynamic turbulence in this region determines the maximum energy of particles accelerated by the diffusive shock acceleration mechanism. A high efficiency of cosmic ray acceleration is accepted, and the consideration is not limited by the case of weak turbulence. It is assumed that Kolmogorov-type nonlinear wave interactions together with the ion-neutral collisions restrict the amplitude of the random magnetic field. As a result, the maximum energy of accelerated particles strongly depends on the age of the supernova remnant. The maximum energy can be as high as ∼1017 Z eV in young supernova remnants and falls to about ∼1010 Z eV at the end of the Sedov stage. Thus the standard estimate of maximum particle energy based on the Bohm limit calculated for the interstellar magnetic field strength is not justified in this case. This finding may explain why supernova remnants with age of more than a few thousand years are not prominent sources of very high energy gamma-rays.

Nonlinear shock acceleration in the presence of seed particles

“…The maximum energy of the particles accelerated in supernova remnants in the presence of large acceleration efficiencies was also studied in [24,25].…”

Prospects for Cherenkov Telescope Array Observations of the Young Supernova Remnant RX J1713.7−3946

“…This motivates us to measure any possible time variation of the gammaray spectrum over long timescales. It has been shown that the maximum energy of CRs confined in SNRs depends on the SNR age during the Sedov phase (e.g., Ptuskin & Zirakashvili 2003;Ohira et al 2012). Since the downstream magnetic field strength around the shock decays with the shock velocity, as the SNR ages it becomes harder to confine high-energy CRs through pitch-angle scatterings near the shock.…”

“…The value of α is important for understanding the average source spectrum of Galactic CRs, which should be steeper than E −2 ). Although there are theoretical studies on α (e.g., Ptuskin & Zirakashvili 2003;Yan et al 2012), its precise value has not yet been determined observationally or theoretically. To reproduce the spectrum of Galactic CRs, we can phenomenologically assume that E max,p ≈10 15.5 eV at the beginning of the Sedov phase (t Sedov ), and that E max,p ≈1 GeV at the end of the Sedov phase (≈10 2.5 t Sedov ), from which we can obtain α≈2.6 ).…”

Radio polarization maps of shell-type SNRs – II. Sedov models with evolution of turbulent magnetic field

“…Ptuskin & Zirakashvili 2003): Γw = ΓL + ΓNL. The first one is due to collisions of protons with neutral hydrogen of the density nH (e.g.…”

“…There is no commonly accepted approach to the description of the non-linear damping (see e.g. Ptuskin & Zirakashvili 2003, and references therein). We take the expression for the rate of non-linear Landau damping from Ptuskin & Zirakashvili (2003), namely from their Eq.…”