Optimal binning of X-ray spectra and response matrix design

¹ SRON Netherlands Institute for Space Research, Sorbonnelaan 2, 3584 CA Utrecht, The Netherlands
e-mail: J.S.Kaastra@sron.nl
² Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
³ Department of Physics and Astronomy, Universiteit Utrecht, PO Box 80000, 3508 TA Utrecht, The Netherlands

Received: 18 September 2015
Accepted: 8 January 2016

Abstract

Aims. A theoretical framework is developed to estimate the optimal binning of X-ray spectra.

Methods. We derived expressions for the optimal bin size for model spectra as well as for observed data using different levels of sophistication.

Results. 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.