A Proton Synchrotron Blazar Model for Flaring in Markarian~501

The spectral energy distribution (SED) of blazars typically has a double-humped appearance usually interpreted in terms of synchrotron self-Compton models. In proton blazar models, the SED is instead explained in terms of acceleration of protons and subsequent cascading. We discuss a variation of the Synchrotron Proton Blazar model, first proposed by M\"ucke & Protheroe (1999), in which the low energy part of the SED is mainly synchrotron radiation by electrons co-accelerated with protons which produce the high energy part of the SED mainly asproton synchrotron radiation. We assume shock acceleration, and consider the case where the maximum energy of the accelerated protons is above the threshold for pion photoproduction interactions on the synchrotron photons of the low energy part of the SED. Using a Monte Carlo/numerical technique to simulate the interactions and subsequent cascading of the accelerated protons, we are able to fit the observed SED of Markarian 501 during the April 1997 flare. We find that the emerging cascade spectra initiated by gamma-rays from $\pi^0$ decay and by $e^\pm$ from $\mu^\pm$ decay turn out to be relatively featureless. Synchrotron radiation produced by $\mu^\pm$ from $\pi^\pm$ decay, and even more importantly by protons, and subsequent synchrotron-pair cascading, is able to reproduce well the high energy part of the SED. For this fit we find that synchrotron radiation by protons dominates the TeV emission, pion photoproduction being less important with the consequence that we predict a lower neutrino flux than in other proton blazar models