Bayesian Estimation of Hardness Ratios: Modeling and Computations

By Taeyoung Park, V. Kashyap, Aneta Siemiginowska, D. V. van Dyk, A. Zezas, C. Heinke, B. Wargelin. 2006

276 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d7890ae2512195031b4aae998fe73fe1e4b20e48

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Citations in the corpus

1SXPS: A DEEP SWIFT X-RAY TELESCOPE POINT SOURCE CATALOG WITH LIGHT CURVES AND SPECTRA (2013, methodology): “For fainter sources we used the Bayesian method of Park et al. (2006), where we used the effective area option in their code to include the count-rate correction factors in the calculation.”
THE CHANDRA COSMOS SURVEY. I. OVERVIEW AND POINT SOURCE CATALOG (2009, methodology): “Upper and lower limits were calculated using the Bayesian Estimation of Hardness Ratio code (BEHR, Park et al. 2006).”
THE CHANDRA COSMOS LEGACY SURVEY: OPTICAL/IR IDENTIFICATIONS (2015, methodology): “Nevertheless, it is possible to use the Bayesian Estimation of Hardness Ratios (BEHR) method (Park et al. 2006) to derive a rough estimation of the X-ray spectral shape and therefore of the source nuclear obscuration.”
AEGIS-X: THE CHANDRA DEEP SURVEY OF THE EXTENDED GROTH STRIP (2008, methodology): “Hardness ratios HRs were calaculated using a Bayesian approach, following Park et al. (2006).”
THE CHANDRA COSMOS LEGACY SURVEY: OVERVIEW AND POINT SOURCE CATALOG (2016, methodology): “Given the low number of counts for most of the sources (see Figure 9), we used BEHR (Bayesian Estimation of Hardness Ratios, Park et al. 2006) which is particular effective in the low count regime, not needing a detection in both bands to work.”
THE CHANDRA SOURCE CATALOG (2009, methodology): “The hardness ratios included in the CSC are computed using a Bayesian approach developed by Park et al. (2006), which should be consulted for a detailed description of the algorithm.”
The outflow structure of GW170817 from late-time broad-band observations (2018, methodology): “In order to probe any possible spectral evolution we computed the hardness ratio (Park et al. 2006), defined as HR=H-S/H+S, where H are the net source counts in the hard band (2.0-7.0 keV) and S are the net source counts in the soft band (0.5-2.0 keV).”