Impact of Secondary Acceleration in Gamma-Ray Bursts
Context. It is clear from the observation of charged cosmic rays up to energies of 1020 eV that particle acceleration must occur in astrophysical sources. Acceleration of secondary particles like muons and pions, produced in cosmic ray interactions, are usually neglected, however, when calculating the flux of neutrinos from cosmic ray interactions. Aims. Here, we discuss the acceleration of secondary muons, pions, and kaons in gamma-ray bursts within the internal shock scenario, and their impact on the neutrino fluxes. Methods. We introduce a two-zone model consisting of an acceleration zone (the shocks) and a radiation zone (the plasma downstream the shocks). The acceleration in the shocks, which is an unavoidable consequence of the efficient proton acceleration, requires efficient transport from the radiation back to the acceleration zone. On the other hand, stochastic acceleration in the radiation zone can enhance the secondary spectra of muons and kaons significantly if there is a sufficiently large turbulent region. Results. Overall, it is plausible that neutrino spectra can be enhanced by up to a factor of two at the peak by stochastic acceleration, that an additional spectral peaks appears from shock acceleration of the secondary muons and pions, and that the neutrino production from kaon decays is enhanced. Conclusions. Depending on the GRB parameters, the general conclusions concerning the limits to the internal shock scenario obtained by recent IceCube and ANTARES analyses may be affected by up to a factor of two by secondary acceleration. Most of the changes occur at energies above 107 GeV, so the effects for next-generation radio-detection experiments will be more pronounced. In the future, however, if GRBs are detected as high-energy neutrino sources, the detection of one or several pronounced peaks around 106 GeV or higher energies could help to derive the basic properties of the magnetic field strength in the GRB.