Search for Continuous and Transient Neutrino Emission Associated with IceCube's Highest-Energy Tracks: An 11-Year Analysis

IceCube alert events are neutrinos with a moderate-to-high probability of having astrophysical origin. In this study, we analyze 11 years of IceCube data and investigate 122 alert events and a selection of high-energy tracks detected between 2009 and the end of 2021. This high-energy event selection (alert events + high-energy tracks) has an average probability of $\geq 0.5$ to be of astrophysical origin. We search for additional continuous and transient neutrino emission within the high-energy events' error regions. We find no evidence for significant continuous neutrino emission from any of the alert event directions. The only locally significant neutrino emission is the transient emission associated with the blazar TXS~0506+056, with a local significance of $ 3 \sigma$, which confirms previous IceCube studies. When correcting for 122 test positions, the global p-value is $0.156$ and is compatible with the background hypothesis. We constrain the total continuous flux emitted from all 122 test positions at 100~TeV to be below $1.2 \times 10^{-15}$~(TeV cm$^2$ s)$^{-1}$ at 90% confidence assuming an $E^{-2}$ spectrum. This corresponds to 4.5% of IceCube's astrophysical diffuse flux. Overall, we find no indication that alert events, in general, are linked to lower-energetic continuous or transient neutrino emission.