New spectral classification technique for X-ray sources: Quantile analysis

We present a new technique, quantile analysis, to classify the spectral properties of X-ray sources with limited statistics. Quantile analysis is superior to conventional approaches, such as X-ray hardness ratio or X-ray color analysis, for studying relatively faint sources or investigating a certain phase or state of a source in detail, where poor statistics do not allow spectral fitting using a model. Instead of working with predetermined energy bands, we determine the energy values that divide the detected photons into predetermined fractions of the total counts, such as the median (50%), terciles (33% and 67%), and quartiles (25% and 75%). We use these quantiles as an indicator of the X-ray hardness or color of the source. We show that the median is an improved substitute for the conventional X-ray hardness ratio. The median and other quantiles form a phase space, similar to the conventional X-ray color-color diagrams. The quantile-based phase space is more evenly sensitive over various spectral shapes than the conventional color-color diagrams, and it is naturally arranged to properly represent the statistical similarity of various spectral shapes. We demonstrate the new technique in the 0.3-8 keV energy range using the Chandra ACIS-S detector response function and a typical aperture photometry involving background subtraction. The technique can be applied in any energy band, provided the energy distribution of photons can be obtained.