Characterizing X-ray line complexes using cumulative distribution functions

As part of the Spanish contribution to the Athena mission, an important effort has been invested in the detailed study of the impact of different algorithms devoted to the proper characterization of the energy of each photon that will be detected by X-IFU (see e.g., Ceballos et al. 2019a, 2019b, Cobo et al. 2020, Vega-Ferrero et al. 2022).

The spectral resolutions achieved with the different strategies are evaluated by fitting X-ray line complexes corresponding to laboratory data generated with calibrated X-ray sources. Traditionally the data are binned in order to generate histograms which are subsequently fitted using the familiar chi-squared statistic or a maximum likelihood approach (Fowler 2014).

In this work, we show how the use of cumulative distribution functions (CDF) can be employed to determine the fit of X-ray line complexes constituted by several lines without the need to perform an a priori data rebinning. The method has been checked using simulated data, and the results indicate that it can recover photons beyond the fitting range. The procedure has been programmed in Python and the source code is publicly available.