Signatures of secondary acceleration in neutrino flares

High-energy neutrino flares are interesting prospective counterparts to photon flares, as their detection would guarantee the presence of accelerated hadrons within a source, provide precious information about cosmic-ray acceleration and interactions, and thus impact the subsequent modeling of non-thermal emissions in explosive transients. In these sources, photomeson production can be efficient, producing a large amount of secondary particles, such as charged pions and muons, that decay and produce high-energy neutrinos. Before their decay, secondary particles can experience energy losses and acceleration, which can impact high-energy neutrino spectra and thus affect their detectability. In this work, we focus on the impact of secondary acceleration. We consider a one zone model, characterized mainly by a variability timescale $t_{\rm var}$, a luminosity $L_{\rm bol}$, a bulk Lorentz factor $\Gamma$. The mean magnetic field $B$ is deduced from these parameters. The photon field is modeled by a broken power-law. This generic model allows to evaluate systematically the maximum energy of high-energy neutrinos in the parameter space of explosive transients, and shows that it could be strongly affected by secondary acceleration for a large number of source categories. In order to determine the impact of secondary acceleration on the high-energy neutrino spectrum and in particular on its peak energy and flux, we complement these estimates by several case studies. We show that secondary acceleration can increase the maximum neutrino flux, and produce a secondary peak at the maximum energy in the case of efficient acceleration. Secondary acceleration could therefore enhance the detectability of very-high-energy neutrinos, that will be the target of next generation neutrino detectors such as KM3NeT, IceCube-Gen2, POEMMA or GRAND.