Flare Duty Cycle of Gamma-Ray Blazars and Implications for High-Energy Neutrino Emission

Gamma-ray flares of blazars may be accompanied by high-energy neutrinos due to interactions of high-energy cosmic rays in the jet with photons, as suggested by the detection of the high-energy neutrino IceCube-170922A during a major gamma-ray flare from blazar TXS 0506+056 at the $\sim3\sigma$ significance level. In this work, we present a statistical study of gamma-ray emission from blazars to constrain the contribution of gamma-ray flares to their neutrino output. We construct weekly binned light curves for 145 gamma-ray bright blazars in the {\it Fermi} Large Area Telescope (LAT) Monitored Source List. We derive the fraction of time spent in the flaring state (flare duty cycle) and the fraction of energy released during each flare from the light curves with a Bayesian blocks algorithm. We find that blazars with lower flare duty cycles and energy fractions are more numerous among our sample. We identify no significant differences between blazar sub-classes in terms of flaring activity. Then using a general scaling relation for the neutrino and gamma-ray luminosities, $L_{\nu} \propto (L_{\gamma})^{\gamma}$ with a weighting exponent of ${\gamma} = 1.0 - 2.0$, normalized to the quiescent gamma-ray or X-ray flux of each blazar, we evaluate the neutrino energy flux of each gamma-ray flare. The gamma-ray flare distribution indicates that blazar neutrino emission may be dominated by flares for $\gamma\gtrsim1.5$. The neutrino energy fluxes for one-week and 10-year bins are compared with the declination-dependent IceCube sensitivity to constrain the standard neutrino emission models for gamma-ray flares. Finally, we present the upper-limit contribution of blazar gamma-ray flares to the isotropic diffuse neutrino flux.