Optimal binning of X-ray spectra and response matrix design

Abstract

A theoretical framework is developed to estimate the optimal binning of X-ray spectra. We derived expressions for the optimal bin size for model spectra as well as for observed data using different levels of sophistication. It is shown that by taking into account both the number of photons in a given spectral model bin and their average energy over the bin size, the number of model energy bins and the size of the response matrix can be reduced by a factor of $10-100$. The response matrix should then contain the response at the bin centre as well as its derivative with respect to the incoming photon energy. We provide practical guidelines for how to construct optimal energy grids as well as how to structure the response matrix. A few examples are presented to illustrate the present methods.

16 pages, 7 figures, accepted for publication in Astronomy and Astrophysics

References in corpus (3)

• A fast and long-lived outflow from the supermassive black hole in NGC 5548
• Abundance and temperature distributions in the hot intra-cluster gas of Abell 4059
• Multiwavelength campaign on Mrk 509 XIV. Chandra HETGS spectra

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