Bayesian estimation of hardness ratios: Modeling and computations

Taeyouno Park, Vinay L. Kashyap, Aneta Siemiginowska, David A. Van Dyk, Andreas Zezas, Craig Heinke, Bradford J. Wargelin

Research output: Contribution to journalArticlepeer-review

236 Citations (Scopus)


A commonly used measure to summarize the nature of a photon spectrum is the so-called hardness ratio, which compares the numbers of counts observed in different passbands. The hardness ratio is especially useful to distinguish between and categorize weak sources as a proxy for detailed spectral fitting. However, in this regime classical methods of error propagation fail, and the estimates of spectral hardness become unreliable. Here we develop a rigorous statistical treatment of hardness ratios that properly deals with detected photons as independent Poisson random variables and correctly deals with the non-Gaussian nature of the error propagation. The method is Bayesian in nature and thus can be generalized to carry out a multitude of source-population-based analyses. We verify our method with simulation studies and compare it with the classical method. We apply this method to real-world examples, such as the identification of candidate quiescent low-mass X-ray binaries in globular clusters and tracking the time evolution of a flare on a low-mass star.

Original languageEnglish
Pages (from-to)610-628
Number of pages19
JournalAstrophysical Journal
Issue number1 I
Publication statusPublished - 2006 Nov 20

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science


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