nazgul: A statistical approach to gamma-ray burst localization. Triangulation via non-stationary time-series models

Abstract

Context. Gamma-ray bursts can be located via arrival time signal triangulation using gamma-ray detectors in orbit throughout the solar system. The classical approach based on cross-correlations of binned light curves ignores the Poisson nature of the time-series data, and is unable to model the full complexity of the problem. Aims. To present a statistically proper and robust GRB timing/triangulation algorithm as a modern update to the original procedures used for the Interplanetary Network (IPN). Methods. A hierarchical Bayesian forward model for the unknown temporal signal evolution is learned via random Fourier features (RFF) and fitted to each detector's time-series data with time-differences that correspond to GRB's position on the sky via the appropriate Poisson likelihood. Results. Our novel method can robustly estimate the position of a GRB as verified via simulations. The uncertainties generated by the method are robust and in many cases more precise compared to the classical method. Thus, we have a method that can become a valuable tool for gravitational wave follow-up. All software and analysis scripts are made publicly available here (https://github.com/grburgess/nazgul) for the purpose of replication.

18 pages, 30 figures. Submitted to A&A. Criticism gladly welcome

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• Discovery of the linear energy-dependence of the spectral lag of X-ray bursts from SGR J1935+2154
• Localisation of gamma-ray bursts from the combined SpIRIT+HERMES-TP/SP nano-satellite constellation
• The Second Catalog of Interplanetary Network Localizations of Konus Short Duration Gamma-Ray Bursts
• A proposed network of Gamma-ray Burst detectors on the Global Navigation Satellite System Galileo G2
• Telescope Concepts in Gamma-Ray Astronomy
• Misidentification of Short GRBs as Magnetars in Nearby Galaxies