Hardness Ratio Estimation in Low Counting X-ray Photometry

Hardness ratios are commonly used in X-ray photometry to indicate spectral properties roughly. It is usually defined as the ratio of counts in two different wavebands. This definition, however, is problematic when the counts are very limited. Here we instead define hardness ratio using the $\lambda$ parameter of Poisson processes, and develop an estimation method via Bayesian statistics. Our Monte Carlo simulations show the validity of our method. Based on this new definition, we can estimate the hydrogen column density for the photoelectric absorption of X-ray spectra in the case of low counting statistics.