Abstract
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.
Highlights
A major obstacle to understanding the nature of the faintest X-ray sources is poor statistics, which prevents the usual practices of spectral analysis, such as fitting with known models
We present a new technique, quantile analysis, to classify the spectral properties of X-ray sources with limited statistics
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
Summary
A major obstacle to understanding the nature of the faintest X-ray sources is poor statistics, which prevents the usual practices of spectral analysis, such as fitting with known models. The common practice of extracting spectral properties of X-ray sources with poor statistics is to calculate the X-ray hardness or color of the sources (e.g., Schulz et al 1989; Kim et al 1992; Netzer et al 1994; Prestwich et al 2003) In this conventional method, the full energy range is divided into two or three subbands and the detected source photons are counted separately in each band. The spectral model dependence of error bars in this kind of color-color diagram is inevitable, and the dependence is determined by the choice of the sub–energy bands for a full energy range In this example, the subbands are chosen so that the diagram is mostly sensitive near À 1⁄4 2 and NH < 1022 cmÀ2. One might have to repeat the analysis with different choices of subbands to explore all the interesting possibilities of spectral shapes
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