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We model the diffusive shock acceleration of particles in a system of two colliding shock waves and present a method to solve the time-dependent problem analytically in the test-particle approximation and high energy limit. In particular, we show that in this limit the problem can be analysed with the help of a self-similar solution. While a number of recent works predict hard ($E^{-1}$) spectra for the accelerated particles in the stationary limit, or the appearance of spectral breaks, we found instead that the spectrum of accelerated particles in a time-dependent collision follows quite closely the canonical $E^{-2}$ prediction of diffusive shock acceleration at a single shock, except at the highest energy, where a hardening appears, originating a bumpy feature just before the exponential cutoff. We also investigated the effect of the reacceleration of pre-existing cosmic rays by a system of two shocks, and found that under certain conditions spectral features can appear in the cutoff region. Finally, the mathematical methods presented here are very general and could be easily applied to a variety of astrophysical situations, including for instance standing shocks in accretion flows, diverging shocks, backward collisions of a slow shock by a faster shock, and wind-wind or shock-wind collisions.
Powerful stellar winds and supernova explosions with intense energy release in the form of strong shock waves can convert a sizeable part of the kinetic energy release into energetic particles. The starforming regions are argued as a favorable site o
We present a model for the non-thermal emission from a colliding-wind binary. Relativistic protons and electrons are assumed to be accelerated through diffusive shock acceleration (DSA) at the global shocks bounding the wind-wind collision region. Th
We present a model for the creation of non-thermal particles via diffusive shock acceleration in a colliding-wind binary. Our model accounts for the oblique nature of the global shocks bounding the wind-wind collision region and the finite velocity o
The supernova remnant SN 1006 is a powerful source of high-energy particles and evolves in a relatively tenuous and uniform environment, though interacting with an atomic cloud in its northwestern limb. The X-ray image of SN 1006 reveals an indentati
Cosmic-ray acceleration has been a long-standing mystery and despite more than a century of study, we still do not have a complete census of acceleration mechanisms. The collision of strong stellar winds in massive binary systems creates powerful sho