Hardness Ratio Estimation in Low Counting X‐Ray Photometry

Hardness ratios are commonly used in X-ray photometry to indicate spectralproperties roughly. It is usually defined as the ratio of counts in twodifferent wavebands. This definition, however, is problematic when the countsare very limited. Here we instead define hardness ratio using the $\lambda$parameter of Poisson processes, and develop an estimation method via Bayesianstatistics. Our Monte Carlo simulations show the validity of our method. Basedon this new definition, we can estimate the hydrogen column density for thephotoelectric absorption of X-ray spectra in the case of low countingstatistics.Comment: 12 pages, 4 figures, 1 table. Originally submitted on 29-03-2006, and accepted on 24-08-2006 for publication in The Astrophysical Journa