Theory of Cosmic Ray and High-Energy Gamma-Ray Production in Supernova Remnants

Abstract

A kinetic model of particle acceleration in supernova remnants (SNRs) is extended to study the cosmic ray (CR) and associated high-energy γ-ray production during SN shock propagation through the inhomogeneous circumstellar medium of a progenitor star that emits a wind. The wind forms a low-density bubble surrounded by a swept-up shell of interstellar matter. γ-rays are produced as a result of decay of pions which in turn are the result of collisions of CRs with nuclei of the thermal plasma. The time evolution of the SNRs is followed numerically, taking into account the nonlinear backreaction of the accelerated CRs. The model for SNRs includes injection of suprathermal particles at the shock front and heating of the thermal plasma due to dissipation of Alfvén waves in the precursor region. Examples typical for SN type Ib and SN type II explosions are considered. Apart from the confirmation of the known fact that acceleration is extremely rapid and that the upper momentum cutoff is reached almost immediately after the explosion due to the high wind magnetic field, it is also shown that the CRs are accelerated with a high efficiency. Depending on the circumstellar parameters, 20% to 40% of the SN explosion energy is absorbed by CRs during the SNR evolution for a moderate injection rate, when a fraction η = 10 −3 of the gas particles, swept up by the supernova shock, is accelerated. The CR momentum spectrum, ultimately produced in the SNRs, has a power law form N ∝ p −γ with an index γ = 2.0 to 2.1 in a wide energy range up to a maximum energy, which is about 10 14 eV, if the CR diffusion coefficient is as small as the Bohm limiting value. It is to be expected that the resulting CR chemical composition at high energies reflects more the stellar wind composition, whereas at lower energies it corresponds more to that of the average interstellar medium. The expected π 0 -decay γ-ray flux is however considerably lower than in the case of a uniform interstellar medium; a relatively high γ-ray luminosity in the band ǫ γ > ∼ 1 TeV, detectable at distances of several kpc, is only expected in the case of a relatively dense ISM with Send offprint requests to: H.J. Völk a number density above 10 cm −3 . Extremely high γ-ray emission may be produced when the SN shock propagates through the slow dense wind of a red supergiant, the progenitor of a SN type II. In this case SNRs might be visible in γ-rays for several hundred years out to distances of tens of kpc. For the case of a SN type Ib the expected π 0 -decay γ-ray TeV-energy flux during the whole SNR evolution remains lower than 10 −11 cm −2 s −1 if the interstellar number density is less than 0.3 cm −3 .