Journal Article

On the escape of particles from cosmic ray modified shocks

D. Caprioli, P. Blasi and E. Amato

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 396, issue 4, pages 2065-2073
Published in print July 2009 | ISSN: 0035-8711
Published online July 2009 | e-ISSN: 1365-2966 | DOI:
On the escape of particles from cosmic ray modified shocks

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Stationary solutions to the problem of particle acceleration at shock waves in the non-linear regime, when the dynamical reaction of the accelerated particles on the shock cannot be neglected, are known to show a prominent energy flux escaping from the shock towards upstream infinity. On physical grounds, the escape of particles from the upstream region of a shock has to be expected in all those situations in which the maximum momentum of accelerated particles, pmax, decreases with time, as is the case for the Sedov–Taylor phase of expansion of a shell supernova remnant, when both the shock velocity and the cosmic ray induced magnetization decrease. In this situation, at each time t, particles with momenta larger than pmax(t) leave the system from upstream, carrying away a large fraction of the energy if the shock is strongly modified by the presence of cosmic rays. This phenomenon is of crucial importance for explaining the cosmic ray spectrum detected at the Earth. In this paper, we discuss how this escape flux appears in the different approaches to non-linear diffusive shock acceleration, and especially in the quasi-stationary semi-analytical kinetic ones. We apply our calculations to the Sedov–Taylor phase of a typical supernova remnant, including in a self-consistent way particle acceleration, magnetic field amplification and the dynamical reaction on the shock structure of both particles and fields. Within this framework, we calculate the temporal evolution of the maximum energy reached by the accelerated particles and of the escape flux towards upstream infinity. The latter quantity is directly related to the cosmic ray spectrum detected at the Earth.

Keywords: acceleration of particles; shock waves

Journal Article.  6808 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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