Bayesian Estimation of Hardness Ratios: Modeling and Computations
Abstract
A commonly used measure to summarize the nature of a photon spectrum is the socalled 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 nonGaussian nature of the error propagation. The method is Bayesian in nature and thus can be generalized to carry out a multitude of sourcepopulationbased analyses. We verify our method with simulation studies and compare it with the classical method. We apply this method to realworld examples, such as the identification of candidate quiescent lowmass Xray binaries in globular clusters and tracking the time evolution of a flare on a lowmass star.
 Publication:

The Astrophysical Journal
 Pub Date:
 November 2006
 DOI:
 10.1086/507406
 arXiv:
 arXiv:astroph/0606247
 Bibcode:
 2006ApJ...652..610P
 Keywords:

 Methods: Statistical;
 Stars: Flare;
 XRays: Binaries;
 Astrophysics
 EPrint:
 43 pages, 10 figures, 3 tables