2006/06/10 by Taeyoung Park, Vinay L. Kashyap, Aneta Siemiginowska +4 · 17 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Bayesian inference #Bayesian probability #Computation #Gamma-ray bursts and supernovae #Measure (data warehouse) #Observational error #Poisson distribution #Scientific Research and Discoveries #Uniqueness #astro-ph
paper · pdf · doi:10.1086/507406
published as Astrophys.J. 652:610-628, 2006 · 43 pages, 10 figures, 3 tables; submitted to ApJ
arxiv created 2006/06/10 · openalex publication_date 2006/11/16 · arxiv updated 2016/04/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06
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.