Taeyoung Park et al. 2006 ApJ 652 610 doi:10.1086/507406
Taeyoung Park1, Vinay L. Kashyap2, Aneta Siemiginowska2, David A. van Dyk3, Andreas Zezas2, Craig Heinke4 and Bradford J. Wargelin2
Show affiliationsA 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.
Issue 1 (2006 November 20)
Received 2005 December 24, accepted for publication 2006 June 14
Taeyoung Park et al. 2006 ApJ 652 610
Taeyoung Park et al. 2008 ApJ 688 807
Thomas A. Fleming et al. 2000 ApJ 533 372
Eusebius J Doedel et al 2006 Nonlinearity 19 2947
Chas A. Egan and Charles H. Lineweaver 2010 ApJ 710 1825
A Yanase and A Hasegawa 1980 J. Phys. C: Solid State Phys. 13 1989
Wei Lu and Charles M Lieber 2006 J. Phys. D: Appl. Phys. 39 R387
Lyndon Evans and Philip Bryant 2008 JINST 3 S08001
Qurrat-ul-Ain Gulfam and Jörg Evers 2010 J. Phys. B: At. Mol. Opt. Phys. 43 045501
A. A. Abdo et al. 2009 ApJ 700 1059