Investigation of bias for neutrino flare reconstruction with the IceCube Neutrino Telescope

The origin of cosmic rays remains a central question in multi-messenger astrophysics. Hadronic interactions at acceleration sites produce both neutrinos and gamma rays, so identifying the sources of these high-energy messengers is key to locating and characterizing cosmic-ray accelerators. By integrating information from photons, neutrinos, cosmic rays, and gravitational waves, multi-messenger studies enhance the significance of contemporaneous detections and enable a more complete view of transient phenomena. Within this framework, the IceCube Neutrino Observatory contributes through the Gamma-ray Follow-Up (GFU) program, which monitors known gamma-ray emitters and issues real-time alerts to partner facilities when clusters of neutrino events are observed. This work investigates biases in the time-dependent likelihood analysis currently used in the GFU branch and tests the performance of an alternative formulation that accounts for Poissonian fluctuations in the low-event regime expected for transient neutrino sources. Performance is evaluated through simulations scanning the number of events, spectral index, flare duration, and source declination. The current likelihood shows systematic overestimations in the low-count regime for short flares. To mitigate these effects, a Poissonian term is introduced to better describe event counting statistics. The modified method is compared with the standard implementation, yielding improved reconstruction of key parameters. It also estimates the flux required to reveal transient sources and to establish their statistical significance, showing that the Poissonian likelihood provides better performance than the current one. These results highlight both strengths and limitations of the present framework and point to concrete upgrades for next-generation IceCube analyses and future detector extensions.