We present results of an archival coincidence analysis between Fermi Large Area Telescope (LAT) gamma-ray data and public neutrino data from the IceCube neutrino observatory's 40-string (IC 40) and 59-string (IC 59) observing runs. Our analysis has the potential to detect either a statistical excess of neutrino + gamma-ray (ν?+?γ) emitting transients or, alternatively, individual high gamma-multiplicity events, as might be produced by a neutrino observed by IceCube coinciding with a LAT-detected gamma-ray burst. Dividing the neutrino data into three data sets by hemisphere (IC 40, IC 59-North, and IC 59-South), we construct uncorrelated null distributions by Monte Carlo scrambling of the neutrino data sets. We carry out signal-injection studies against these null distributions, demonstrating sensitivity to individual ν?+?γ events of sufficient gamma-ray multiplicity, and to ν?+?γ transient populations responsible for >13% (IC 40), >9% (IC 59-North), or >8% (IC 59-South) of the gamma-coincident neutrinos observed in these data sets, respectively. Analyzing the unscrambled neutrino data, we identify no individual high-significance neutrino + high gamma-multiplicity events and no significant deviations from the test statistic null distributions. However, we observe a similar and unexpected pattern in the IC 59-North and IC 59-South residual distributions that we conclude reflects a possible correlation (p?=?7.0%) between IC 59 neutrino positions and persistently bright portions of the Fermi gamma-ray sky. This possible correlation should be readily testable using eight years of further data already collected by IceCube. We are currently working with Astrophysical Multimessenger Observatory Network (AMON) partner facilities to generate low-latency ν?+?γ alerts from Fermi-LAT gamma-ray and IceCube and ANTARES neutrino data and distribute these in real time to AMON follow-up partners.
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