On the shape of the spectrum of cosmic rays accelerated inside superbubbles

¹ Laboratoire Astrophysique Interactions Multi-échelles (AIM), CEA/Irfu, CNRS/INSU, Université Paris VII, L'Orme des Merisiers, Bât. 709, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France e-mail: g.ferrand@cea.fr
² Laboratoire de Physique Théorique et Astroparticules (LPTA), CNRS/IN2P3, Université Montpellier II, Place Eugène Bataillon, 34095 Montpellier Cedex, France e-mail: alexandre.marcowith@lpta.in2p3.fr

Received: 21 October 2009
Accepted: 16 November 2009

Abstract

Context. Supernova remnants are believed to be a major source of energetic particles (cosmic rays) on the Galactic scale. Since their progenitors, namely the most massive stars, are commonly found clustered in OB associations, one has to consider the possibility of collective effects in the acceleration process.

Aims. We investigate the shape of the spectrum of high-energy protons produced inside the superbubbles blown around clusters of massive stars.

Methods. We embed simple semi-analytical models of particle acceleration and transport inside Monte Carlo simulations of OB associations timelines. We consider regular acceleration (Fermi 1 process) at the shock front of supernova remnants, as well as stochastic reacceleration (Fermi 2 process) and escape (controlled by magnetic turbulence) occurring between the shocks. In this first attempt, we limit ourselves to linear acceleration by strong shocks and neglect proton energy losses.

Results. We observe that particle spectra, although highly variable, have a distinctive shape because of the competition between acceleration and escape: they are harder at the lowest energies (index s<4) and softer at the highest energies (s>4). The momentum at which this spectral break occurs depends on the various bubble parameters, but all their effects can be summarized by a single dimensionless parameter, which we evaluate for a selection of massive star regions in the Galaxy and the LMC.

Conclusions. The behaviour of a superbubble in terms of particle acceleration critically depends on the magnetic turbulence: if B is low then the superbubble is simply the host of a collection of individual supernovae shocks, but if B is high enough (and the turbulence index is not too high), then the superbubble acts as a global accelerator, producing distinctive spectra, that are potentially very hard over a wide range of energies, which has important implications on the high-energy emission from these objects.