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Several tentative associations between high-energy neutrinos and astrophysical sources have been recently reported, but a conclusive identification of these potential neutrino emitters remains challenging. We explore the use of Monte Carlo simulations of source populations to gain deeper insight into the physical implications of proposed individual source–neutrino associations. In particular, we focus on the IC170922A–TXS 0506+056 observation. Assuming a null model, we find a 7.6% chance of mistakenly identifying coincidences between γ -ray flares from blazars and neutrino alerts in 10-year surveys. We confirm that a blazar–neutrino connection based on the γ -ray flux is required to find a low chance coincidence probability and, therefore, a significant IC170922A–TXS 0506+056 association. We then assume this blazar–neutrino connection for the whole population and find that the ratio of neutrino to γ -ray fluxes must be ≲10 −2 in order not to overproduce the total number of neutrino alerts seen by IceCube. For the IC170922A–TXS 0506+056 association to make sense, we must either accept this low flux ratio or suppose that only some rare sub-population of blazars is capable of high-energy neutrino production. For example, if we consider neutrino production only in blazar flares, we expect the flux ratio of between 10 −3 and 10 −1 to be consistent with a single coincident observation of a neutrino alert and flaring γ -ray blazar. These constraints should be interpreted in the context of the likelihood models used to find the IC170922A–TXS 0506+056 association, which assumes a fixed power-law neutrino spectrum of E −2.13 for all blazars. 

ABSTRACT We present the results of a new, deeper, and complete search for high-redshift 6.5 < z < 9.3 quasars over 977 deg2 of the VISTA Kilo-Degree Infrared Galaxy (VIKING) survey. This exploits a new list-driven data set providing photometry in all bands Z, Y, J, H, Ks, for all sources detected by VIKING in J. We use the Bayesian model comparison (BMC) selection method of Mortlock et al., producing a ranked list of just 21 candidates. The sources ranked 1, 2, 3, and 5 are the four known z > 6.5 quasars in this field. Additional observations of the other 17 candidates, primarily DESI Legacy Survey photometry and ESO FORS2 spectroscopy, confirm that none is a quasar. This is the first complete sample from the VIKING survey, and we provide the computed selection function. We include a detailed comparison of the BMC method against two other selection methods: colour cuts and minimum-χ2 SED fitting. We find that: (i) BMC produces eight times fewer false positives than colour cuts, while also reaching 0.3 mag deeper, (ii) the minimum-χ2 SED-fitting method is extremely efficient but reaches 0.7 mag less deep than the BMC method, and selects only one of the four known quasars. We show that BMC candidates, rejected because their photometric SEDs have high χ2 values, include bright examples of galaxies with very strong [O iii] λλ4959,5007 emission in the Y band, identified in fainter surveys by Matsuoka et al. This is a potential contaminant population in Euclid searches for faint z > 7 quasars, not previously accounted for, and that requires better characterization.