Photohadronic neutrinos from transients in astrophysical sources

Abstract

We investigate the spectrum of photohadronically produced neutrinos at very high energies (VHE, $\ensuremath{\gtrsim}{10}^{14}\mathrm{eV}$) in astrophysical sources whose physical properties are constrained by their variability, in particular jets in active galactic nuclei (blazars) and gamma-ray bursts (GRBs). We discuss in detail the various competing cooling processes for energetic protons, as well as the cooling of pions and muons in the hadronic cascade, which impose limits on both the efficiency of neutrino production and the maximum neutrino energy. If the proton acceleration process is of the Fermi type, we can derive a model independent upper limit on the neutrino energy from the observed properties of any cosmic transient, which depends only on the assumed total energy of the transient. For standard energetic constraints, we can rule out major contributions above ${10}^{19}\mathrm{eV}$ from current models of both blazars and GRBs; and in most models much stronger limits apply in order to produce measurable neutrino fluxes. For GRBs, we show that the cooling of pions and muons in the hadronic cascade imposes the strongest limit on the neutrino energy, leading to cutoff energies of the electron and muon neutrino spectrum at the source differing by about one order of magnitude. We also discuss the relation of maximum cosmic ray energies to maximum neutrino energies and fluxes in GRBs, and find that the production of both the highest energy cosmic rays and observable neutrino fluxes at the same site can only be realized under extreme conditions; a test implication of this joint scenario would be the existence of strong fluxes of GRB correlated muon neutrinos up to ultrahigh energies, $g{10}^{17}\mathrm{eV}.$ Secondary particle cooling also leads to slightly revised estimates for the neutrino fluxes from (nontransient) active galactic nuclei cores, which are commonly used in estimates for VHE detector event rates. Since our approach is quite general we conclude that the detection or nondetection of neutrinos above $\ensuremath{\sim}{10}^{19}\mathrm{eV}$ correlated with blazar flares or GRBs (e.g., with the Pierre Auger Observatory) would provide strong evidence against or in favor of current models for cosmic ray acceleration and neutrino production in these sources.