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 XIS observations by 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 a future mission such as XRISM by appropriate optimization of the simulation parameters.