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 journalArticle

161 Citations (Scopus)

Abstract

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
Volume652
Issue number1 I
DOIs
Publication statusPublished - 2006 Nov 20

Fingerprint

hardness
modeling
propagation
random variables
photons
globular clusters
flares
stars
method
estimates
x rays
simulation

All Science Journal Classification (ASJC) codes

  • Astronomy and Astrophysics
  • Space and Planetary Science

Cite this

Park, T., Kashyap, V. L., Siemiginowska, A., Van Dyk, D. A., Zezas, A., Heinke, C., & Wargelin, B. J. (2006). Bayesian estimation of hardness ratios: Modeling and computations. Astrophysical Journal, 652(1 I), 610-628. https://doi.org/10.1086/507406
Park, Taeyouno ; Kashyap, Vinay L. ; Siemiginowska, Aneta ; Van Dyk, David A. ; Zezas, Andreas ; Heinke, Craig ; Wargelin, Bradford J. / Bayesian estimation of hardness ratios : Modeling and computations. In: Astrophysical Journal. 2006 ; Vol. 652, No. 1 I. pp. 610-628.
@article{13cf25a983094d89970443b0ba89be68,
title = "Bayesian estimation of hardness ratios: Modeling and computations",
abstract = "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.",
author = "Taeyouno Park and Kashyap, {Vinay L.} and Aneta Siemiginowska and {Van Dyk}, {David A.} and Andreas Zezas and Craig Heinke and Wargelin, {Bradford J.}",
year = "2006",
month = "11",
day = "20",
doi = "10.1086/507406",
language = "English",
volume = "652",
pages = "610--628",
journal = "Astrophysical Journal",
issn = "0004-637X",
publisher = "IOP Publishing Ltd.",
number = "1 I",

}

Park, T, Kashyap, VL, Siemiginowska, A, Van Dyk, DA, Zezas, A, Heinke, C & Wargelin, BJ 2006, 'Bayesian estimation of hardness ratios: Modeling and computations', Astrophysical Journal, vol. 652, no. 1 I, pp. 610-628. https://doi.org/10.1086/507406

Bayesian estimation of hardness ratios : Modeling and computations. / Park, Taeyouno; Kashyap, Vinay L.; Siemiginowska, Aneta; Van Dyk, David A.; Zezas, Andreas; Heinke, Craig; Wargelin, Bradford J.

In: Astrophysical Journal, Vol. 652, No. 1 I, 20.11.2006, p. 610-628.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Bayesian estimation of hardness ratios

T2 - Modeling and computations

AU - Park, Taeyouno

AU - Kashyap, Vinay L.

AU - Siemiginowska, Aneta

AU - Van Dyk, David A.

AU - Zezas, Andreas

AU - Heinke, Craig

AU - Wargelin, Bradford J.

PY - 2006/11/20

Y1 - 2006/11/20

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=33845300804&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33845300804&partnerID=8YFLogxK

U2 - 10.1086/507406

DO - 10.1086/507406

M3 - Article

AN - SCOPUS:33845300804

VL - 652

SP - 610

EP - 628

JO - Astrophysical Journal

JF - Astrophysical Journal

SN - 0004-637X

IS - 1 I

ER -

Park T, Kashyap VL, Siemiginowska A, Van Dyk DA, Zezas A, Heinke C et al. Bayesian estimation of hardness ratios: Modeling and computations. Astrophysical Journal. 2006 Nov 20;652(1 I):610-628. https://doi.org/10.1086/507406