High-energy cosmic neutrinos from spine-sheath BL Lac jets

We recently proposed that structured (spine-sheath) jets associated to BL Lac objects offer a suitable environment for the production of the extragalactic high-energy ($E>100$ TeV) neutrino recently revealed by IceCube. Our previous analysis was limited to low-power BL Lac objects. We extend our preliminary study to the entire BL Lac population. We assume that the power of cosmic rays as well as the radiative luminosity of the sheath depend linearly on the the jet power. In turn, we assume that the latter is well traced by the $\gamma$-ray luminosity. We exploit the BL Lac $\gamma$-ray luminosity function and its cosmic evolution as recently inferred from Fermi-LAT data to derive the expected neutrino cumulative intensity from the entire BL Lac population. When considering only the low-power BL Lacs, a large cosmic ray power for each source is required to account for the neutrino flux. Instead, if BL Lacs of all powers produce neutrinos, the power demand decreases, and the required cosmic ray power becomes of the same order of the radiative jet power. We also discuss the prospects for the direct association of IceCube events with BL Lacs, providing an estimate of the expected counts for the most promising sources.