Simulation-based spectral analysis of X-ray CCD data affected by photon pile-up

We have developed a simulation-based method of spectral analysis for pile-up-affected data of X-ray CCDs without any loss of photon statistics. As effects of the photon pile-up appear as complicated nonlinear detector responses, we employ a detailed simulation to calculate the important processes in an X-ray observation including physical interactions, detector signal generation, detector readout, and a series of data reduction processes. This simulation naturally reproduces X-ray-like and background-like events as results of X-ray photon merging in a single pixel or in a chunk of adjacent pixels, allowing us to construct a nonlinear spectral analysis framework that can treat pile-up-affected observation data. For validation, we have performed data analysis of Suzaku X-ray Imaging Spectrometer (XIS) observations using this framework with various parameters of the detector simulation, all of which are optimized for that instrument. We present three cases of different pile-up degrees: PKS 2155-304 (negligible pile-up), Aquila X-1 (moderate pile-up), and the Crab Nebula (strong pile-up); we show that the nonlinear analysis method produces results consistent with a conventional linear analysis for the negligible pile-up condition, and accurately corrects well-known pile-up effects such as spectral hardening and flux decrease for the pile-up cases. These corrected results are consistent with those obtained by a widely used core-exclusion method or by other observatories with much higher timing resolutions (without pile-up). Our framework is applicable to any types of CCDs used for X-ray astronomy, including future missions such as X-ray Imaging and Spectroscopy Mission (XRISM), by appropriate optimization of the simulation parameters.