Phase resolved deadtime of the Crab pulsar using IXPE data

Abstract

After receiving an X-ray photon, an X-ray detector is not operational for a duration known as deadtime. It is detector specific and its effect on the data depends upon the luminosity of the source. It reduces the observed photon count rate in comparison to the expected one. In periodic sources such as the Crab pulsar, it can distort the folded light curve (FLC). An undistorted FLC of the Crab pulsar is required in combination with its polarization properties for studying its X-ray emission mechanism. This work derives a simple formula for the distortion of the FLC of a pulsar caused by the detector deadtime, and validates it using Crab pulsar data from the X-ray observatories {{\it NICER}} and {{\it NUSTAR}}, which have very small and relatively large detector deadtimes respectively. Then it derives a method for correcting the distorted FLC of the Crab pulsar in {{\it IXPE}} data, which has intermediate detector deadtime. The formula is verified after addressing several technical issues. This work ends with a discussion of why an undistorted FLC is important for studying the formation of cusps in the FLC of the Crab pulsar.