GECAM Localization of High-energy Transients and the Systematic Error

The Gravitational Wave High-energy Electromagnetic Counterpart All-sky Monitor (GECAM) is a pair of microsatellites (i.e., GECAM-A and GECAM-B) dedicated to monitoring gamma-ray transients including the high-energy electromagnetic counterparts of gravitational waves, such as gamma-ray bursts, soft gamma-ray repeaters, solar flares, and terrestrial gamma-ray flashes. Since launch in 2020 December, GECAM-B has detected hundreds of astronomical and terrestrial events. For these bursts, localization is the key for burst identification and classification as well as follow-up observations in multiple wavelengths. Here, we propose a Bayesian localization method with Poisson data with Gaussian background profile likelihood to localize GECAM bursts based on the distribution of burst counts in detectors with different orientations. We demonstrate that this method can work well for all kinds of bursts, especially extremely short ones. In addition, we propose a new method to estimate the systematic error of localization based on a confidence level test, which can overcome some problems of the existing method in the literature. We validate this method by Monte Carlo simulations, and then apply it to a burst sample with accurate location and find that the mean value of the systematic error of GECAM-B localization is similar to 2.degrees 5. By considering this systematic error, we can obtain a reliable localization probability map for GECAM bursts. Our methods can be applied to other gamma-ray monitors.