Deconvolution in high-energy astrophysics: science, instrumentation, and methods

In recent years, there has been an avalanche of new data in observational high-energy astrophysics. Recently launched or soon-to-be launched space-based telescopes that are designed to detect and map ultra-violet, X-ray, and $\gamma$-ray electromagnetic emission are opening a whole new window to study the cosmos. Because the production of high-energy electromagnetic emission requires temperatures of millions of degrees and is an indication of the release of vast quantities of stored energy, these instruments give a completely new perspective on the hot and turbulent regions of the universe. The new instrumentation allows for very high resolution imaging, spectral analysis, and time series analysis; the Chandra X-ray Observatory, for example, produces images at least thirty times sharper than any previous X-ray telescope. The complexity of the instruments, of the astronomical sources, and of the scientific questions leads to a subtle inference problem that requires sophisticated statistical tools. For example, data are subject to non-uniform stochastic censoring, heteroscedastic errors in measurement, and background contamination. Astronomical sources exhibit complex and irregular spatial structure. Scientists wish to draw conclusions as to the physical environment and structure of the source, the processes and laws which govern the birth and death of planets, stars, and galaxies, and ultimately the structure and evolution of the universe. ¶ The California-Harvard Astrostatistics Collaboration is a group of astrophysicists and statisticians working together to develop statistical methods, computational techniques, and freely available software to address outstanding inferential problems in high-energy astrophysics. We emphasize fully model-based statistical inference; we explicitly model the complexities of both astronomical sources and the data generation mechanisms inherent in new high-tech instruments, and fully utilize the resulting highly structured models in learning about the underlying astronomical and physical processes. Using these models requires sophisticated scientific computation, advanced methods for statistical inference, and careful model checking procedures. ¶ Here we discuss the broad scientific goals of observation high-energy astrophysics, the specifics of the data collection mechanism involved with the Chandra X-ray Observatory, current statistical methods, and the Bayesian models and methods that we propose. We illustrate our statistical strategy in the context of several applied examples, including the estimation of hardness ratios, spectral analysis, multiscale image analysis, and reconstruction of the distribution of the temperature of hot plasma in a stellar corona. This paper was presented at the Case Studies in Bayesian Statistics Workshop 7 held at Carnegie Mellon University in September 2003.