Localization Method for the Pointing Observation with the Collimated Telescopes of Insight-HXMT

An accurate target source position is sometimes useful for the pointing observation with the collimated telescopes of the Hard X-ray Modulation Telescope (Insight-HXMT), which is determined by the reliability of the instrumental response. Insight-HXMT has the unique design that all three main payloads (LE, ME and HE) consist of detector groups with three fields of views (FOVs) whose orientations differ by 60 degrees. As the point-spread functions are different at different positions in the FOV coordinates, the count rate ratios between the detector groups depend on the position of an X-ray source in the FOVs. Based on the multi-FOV design, we develop a localization method for an X-ray source in the pointing observation of Insight-HXMT. The accuracy of the method is investigated with the pointing observations of the Crab with different exposures. We find that the statistical error decreases with the exposure, and the systematic error is dominant for the exposure >128 s. With the exposure of 1024 s, the total error is 0.degrees 015 for the Crab. This method can effectively distinguish the Rapid Burster H 1730-333 and Slow Burster GX 354-0, which are only 0.degrees 5 apart and can both contribute to bursts in the light curve obtained by Insight-HXMT. We also apply the pointing observation localization method to locate the X-ray counterpart of FRB 200428 with high precision. The located position is consistent with SGR J1935+2154 within 1 sigma uncertainty of 10 ', which provides important evidence that fast radio bursts can originate from magnetars.