Beaming patterns of neutrino emission from photo-pion production in relativistic jets

In the light of growing evidence that blazars are responsible for part of the astrophysical very-high-energy neutrino flux detected by IceCube, models for neutrino production through photo-pion interactions in blazar jets have been developed. Evidence is also mounting that photon fields originating external to the jet are strongly favored over the co-moving primary electron synchrotron photon field as target for photo-pion interactions. Even though those external photon fields appear highly anisotropic in the co-moving frame of the emission region, current models usually consider neutrino production to occur isotropically in the co-moving frame, resulting in a beaming pattern that is identical to intrinsically isotropic synchrotron and synchrotron self-Compton emission. In this paper, we derive the resulting beaming patterns of neutrinos produced by interactions wich external photon fields, taking into account all relevant anisotropy effects. It is shown that neutrino emission resulting from photo-pion production on a stationary and isotropic (in the AGN rest frame) external photon field is significantly more strongly beamed along the jet direction than intrinsically isotropic emission. For the most highly beamed sources, this implies that expected neutrino fluxes are grossly under-estimated or jet-power requirements for the production of a given neutrino flux grossly over-estimated when not accounting for the proper Doppler boosting and beaming characteristics.