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Y. Yu, D. van Dyk (Dept. of Statistics, Harvard University), A. Connors (Eureka Scientific), V. L. Kashyap, A. Siemiginowska (Harvard-Smithsonian Center for Astrophysics)
Pile-up occurs in X-ray detectors when two or more photons arrive in an event detection island during the same frame. Such coincident events are counted as a single higher energy event or lost altogether if the total energy goes above the on-board discriminators. Thus, for bright sources pile-up can seriously distort both the count rate and the energy spectrum. Accounting for pile-up is perhaps the most important outstanding data-analytic challenge for Chandra. In this paper, we describe how Bayesian hierarchical models can be designed to account for such physical processes in X-ray detectors. For example, we can design spectral models with components accounting for instrument response, background, absorption, and pile-up. A Markov Chain Monte Carlo algorithm dramatically simplifies computational complexity by fitting one component at a time. For pile-up, we need to stochastically separate a subset of the observed counts into multiple counts of lower energy based on the current iteration of the particular spectral/spatial model being fit. Because the Bayesian framework allows for the inclusion of other sources of information, event grades (i.e, a description of the likelihood of the degree of pile-up based on the spatial distribution of the charge) can be used to improve the fit. Our method is illustrated with the spectral analysis of 3c273 observed with ACIS-S on board of Chandra X-ray Observatory.
The authors gratefully acknowledge funding for this project partially provided by NSF grant DMS-97-05157, the Chandra X-ray Observatory, and by NASA grant NAS8-39073.