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Complementarity of stacking and multiplet constraints on blazar neutrinos

The full paper

Overview

We investigate the blazar contribution to the cumulative neutrino intensity assuming a generic relationship between neutrino and gamma-ray luminosities, Lν ∝ (L_ph)^γ. 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 blazars resolved by Fermi-LAT as well as the unresolved counterpart. The figure below shows the fraction of Fermi-LAT-resolved blazars in the cumulative neutrino flux as a function of the index γ. Combining this ratio with the existing limits of stacking analyses, we obtain the constraints on the blazar overall contributions (detected blazars + undetected blazars).

In addition, we present another type of constraints on the origins of IceCube diffuse neutrinos, using the negative results from the clustering test of neutrino-induced muon track events. These high-energy track events are generally detected by IceCube with the angular resolution ∼ 0.5 deg, which enables us to determine the incoming directions and perform clustering analysis on their time and spatial distributions. So far, all the clustering tests based on high-energy muon neutrinos have found no statistically significant evidence of clustering in the arrival distribution of neutrinos.

The bottom figure illustrates the upper limits for the all-blazar neutrino flux from Fermi-LAT 2LAC and Fermi-LAT 3LAC analysis. We show all-flavor neutrino fluxes for all curves and data points in this figure. The left panel shows the stacking constraints on the contributions of all blazars to the cumulative neutrino flux and high-energy neutrino multiplet constraints on the blazar contributions in the neutrino sky for an ε^-2 neutrino spectrum. The magenta and green areas correspond to the all-blazar upper limit from Fermi-LAT-2LAC and Fermi−3LAC equal weighting analysis, respectively. The cyan horizontal area shows the cumulative neutrino flux detected by IceCube. The blue dashed, red dash-dotted and thick black lines illustrate the m ≥ 2 multiplet constraints for FSRQs, BL Lacs and all blazars whereas the corresponding areas show the uncertainties. The thin black line is the m ≥ 3 multiplet constraint for all blazars. Right panel: the energy-dependent upper limits from the stacking analysis for the all-blazar contributions, assuming a neutrino spectral index s = 2.5.

In conclusion, we found that the multiplet constraints are the most important at lower values of γ, e.g. γ ∼ < 1.0, whereas all-blazar constraints derived from the existing stacking upper limits are more stringent for a stronger luminosity correlation, e.g., γ ∼> 1.5. The joint consideration of these two kinds of limits supports the extended argument that all blazars, including Fermi−unresolved ones, are unlikely to dominate the cumulative neutrino background for a generic correlation between the neutrino and gamma-ray luminosities, Lν ∝ (Lph)^γ , with the index 0 ∼< γ ∼< 2.5.