Complementarity of Stacking and Multiplet Constraints on the Blazar Contribution to the Cumulative High-Energy Neutrino Intensity

We investigate the blazar contribution to the cumulative neutrino intensity assuming a generic relationship between neutrino and gamma-ray luminosities, $\log (L_{\nu})\propto \log(L_{\rm ph})$. Using the gamma-ray luminosity functions for blazars including flat spectrum radio quasars (FSRQs) and BL Lac objects, as well as the Fermi-LAT detection efficiency, we estimate contributions from resolved blazars and all blazars. Combining the existing upper limits from stacking analyses, the cumulative neutrino flux from all blazars are constrained. We also evaluate effects of the redshift evolution and the effective local number densities for each class of FSRQs, BL Lacs, and all blazars, by which we place another type of constraints on the blazar contribution using the non-detection of high-energy neutrino multiplets. We demonstrate that these two upper limits are complementary, and the joint consideration of stacking and multiplet analyses support arguments that blazars are disfavored as the dominant sources in the 100 TeV neutrino sky.