Confidence regions for the direction of all-sky neutrino alerts in IceCube

The origin of cosmic rays is one of the principal questions at the center of multi-messenger astrophysics. Cosmic ray interactions at the site of acceleration are known to produce neutrinos and gamma-rays. Hence, a proper identification of the sources emitting these particles at high energies is instrumental in understanding where and how cosmic rays are accelerated. The field of multi-messenger astrophysics regroups information carried by different messengers (photons, neutrinos, cosmic rays, gravitational waves) and thus allows for a deeper understanding of the common source. In real-time correlation studies, simultaneous observations of several messengers, e.g. astrophysical neutrinos and gamma-rays, enhance the significance of each separate detection for a broader picture of the phenomena occurring in real-time. The IceCube Neutrino Observatory participates in the multi-messenger effort by working to identify sources of astrophysical neutrinos. The Gamma-ray Follow-Up (GFU) branch of IceCube monitors known gamma-ray emitters and warns in real-time partner telescopes when a cluster of neutrino events are detected coming from these sources. It also performs an all-sky unbiased search for flares of neutrinos. This work aims to investigate the creation of confidence regions around the estimated source positions for all-sky GFU cluster alerts. Showing that there is a simple, but robust way to locate the potential source of neutrino flares in the context of an unbiased search could later enable the sharing of these alerts. We do this by comparing the performances of the algorithm at the center of the alerting process with the predictions from Wilks’ theorem. This theorem would equate the distribution of the difference in log-likelihood between the algorithm estimation and the actual position of the source to a χ² distribution with two degrees of freedom. We will show that this expectation proves wrong in most cases, but by letting the number of degrees of freedom for the χ² distribution be a free parameter, we will be able to fit the data accurately for different hypotheses of signal strength, duration and location in the sky. Ultimately, the project leads to the creation of confidence bands to encase the 50 and 90% confidence regions. This method to estimate the source position for an all-sky alert will hopefully help determine how best to direct the attention of partner telescopes to coordinate observations