Particle Acceleration and Transport at Collisionless Shocks: Effects of Superdiffusion Deduced from Data Analysis and Numerical Simulations*

Collisionless shocks in space and astrophysical plasmas are among the main candidates to explain the acceleration of particles to very high energies. Direct evidence of shock acceleration is given by spacecraft in the heliosphere, but how the properties of accelerated particles, like the energy spectrum, intensity, and maximum energy, depend on the shock parameters (i.e., Mach numbers, compression ratio, plasma beta, and shock normal angle) defies a satisfactory understanding. In recent years, we have extended the standard scenario of diffusive shock acceleration (DSA) to the case of superdiffusive transport, formulating what we call superdiffusive shock acceleration (SSA). The latter allows us to better interpret spacecraft observations, since it predicts an upstream energetic particle profile that decays as a power-law rather than as an exponential. Further, SSA also accounts for (i) a downstream particle flux which is not constant but decays, (ii) energy spectral indices harder than the ones predicted DSA, and (iii) shorter acceleration times. We show how the predictions of SSA are tested with a number of heliospheric shock crossings, and how a numerical implementation of superdiffusive transport can lead to a very good fit of the observed energetic particle time profiles, both upstream and downstream. We also show how SSA may lead to a simple interpretation of the extended precursor of relativistic electrons at supernova remnant shocks, and how it may provide a solution to the apparent discrepancy in shock Mach numbers, as deduced from radio and from X-rays observations, for galaxy cluster merger shocks. These results imply that superdiffusive transport should be consistently taken into account when considering energetic particle transport and acceleration at shocks. 

This research was carried out in collaboration with Silvia Perri and Giuseppe Prete. Funding from Regione Calabria of Italy is acknowledged.