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arXiv:grqc/0609131v2 26 Jul 2007 Coherent Bayesian inference on compact binary inspirals using a network of interferometric gravitational wave detectors Christian R¨over and Renate Meyer Department of Statistics, The University of Auckland, Auckland, New Zealand Nelson Christensen Physics and Astronomy, Carleton College, Northfield, MN, USA (Dated: February 7, 2008) Presented in this paper is the description of a Markov chain Monte Carlo (MCMC) routine for conducting coherent parameter estimation for interferometric gravitational wave observations of an inspiral of binary compact objects using multiple detectors. Data from several interferometers are processed, and all nine parameters (ignoring spin) associated with the binary system are inferred, including the distance to the source, the masses, and the location on the sky. The data is matched with timedomain inspiral templates that are 2.5 postNewtonian (PN) in phase and 2.0 PN in amplitude. We designed and tuned an MCMC sampler so that it is able to efficiently find the posterior mode(s) in the parameter space and perform the stochastic integration necessary for inference within a Bayesian framework. Our routine could be implemented as part of an inspiral detection pipeline for a world wide network of detectors. Examples are given for simulated signals and data as seen by the LIGO and Virgo detectors operating at their design sensitivity. PACS numbers: 02.70.Uu, 04.80.Nn, 05.45.Tp, 07.05.Kf, 97.80.d. Keywords: gravitational waves, compact binary inspirals, coherent parameter estimation I. INTRODUCTION The era of gravitational wave astronomy is now close upon us as numerous interferometric detectors are operating. The Laser Interferometer Gravitational Wave Observatory (LIGO) [1, 2, 3] has now reached its target sensitivity, and there is the hope that a detection could come at any time [4]. Around the globe a worldwide network of detectors is coming online; Virgo in Italy [5, 6, 7], GEO in Germany [8, 9], and TAMA in Japan [10, 11] are operating alongside LIGO in the quest for gravity wave detection. These ground based laser interferometers are sensitive to gravitational radiation in the frequency band from 40 Hz up to 8 kHz. Coalescing binaries containing neutron stars or black holes promise to be one of the cleanest and most probable sources of detectable radiation [12]. Observation of inspiral events could provide important information on the structure of neutron stars [13, 14]. Even cosmological information can be extracted from the observation of inspiral events [15, 16, 17, 18, 19]. The characteristics of radiation in the postNewtonian regime will provide insight into highly nonlinear general relativistic effects, such as the observation of the formation of a Kerr black hole as the binary system decays [18, 20, 21]. The LIGO Scientific Collaboration (LSC) has been actively searching for binary inspiral events [22, 23], as well as conducting searches in coincidence with TAMA [24]. Using the data from LIGO’s S2 run, it was possible to set an upper limit on the neutron star coalescence rate of less than 50 per year per Milky Way equivalent galaxy [23]. The LSC has also conducted searches for binary inspiral signals from primordial black holes (0.2–1.0 M⊙) in the halo of our galaxy [25], plus more massive black hole systems where component masses are in the 3–20 M⊙ range [26]. Bayesian inferential methods provide a means to use data from interferometric gravitational wave detectors in order to extract the parameters of a binary inspiral event. Markov chain Monte Carlo (MCMC) methods are a powerful computation technique for parameter estimation within this framework; they are especially useful in applications where the number of parameters is large [27]. Nice descriptions of the positive aspects of a Bayesian analysis of scientific and astrophysical data are provided in [28, 29, 30]. In previous work we have developed MCMC routines for extracting five parameters associated with a binary inspiral event from data generated by a single interferometric detector [31, 32, 33]. Our MCMC code took data from a single interferometer, Fourier transformed it into the frequency domain, and then compared the result with 2.0 postNewtonian (PN) stationary phase templates [34]. One of the new methods that we implement in this current study, presented in this paper, is an MCMC routine that takes time domain interferometric data, and compares it to time domain templates that are 2.5 PN in phase, and 2.0 PN in amplitude; a trivial modification of the code (though not implemented in the study presented here) is to extend the accuracy of the signal waveforms to 3.5 PN in phase and 2.5 PN in amplitude [35, 36, 37, 38, 39]. A critical task for a worldwide gravity wave detection network will be to not only detect a binary inspiral signal, but to say where it came from. For this purpose the LSC has developed a coherent binary inspiral search pipeline [40, 41, 42]. Coherent binary search pipelines and methods are also being developed within the Virgo collaboration [43] and TAMA [44]. Along similar lines, we have developed a coherent MCMC parameter estimation routine, and in this Typeset by REVTEX
Object Description
Collection Title  Scholarly Publications by Carleton Faculty and Staff 
Journal Title  Physical Review D 
Article Title  Coherent Bayesian Inference on Compact Binary Inspirals Using a Network of Interferometric Gravitational Wave Detectors 
Article Author 
Christensen, Nelson Rover, Christian Meyer, Renate 
Carleton Author 
Christensen, Nelson 
Department  Physics 
Field  Science and Mathematics 
Year  2007 
Volume  75 
Publisher  American Institute of Physics 
File Name  032_ChristensenNelson_CoherentBayesianInferenceOnCompactBinaryInspirals.pdf; 032_ChristensenNelson_CoherentBayesianInferenceOnCompactBinaryInspirals.pdf 
Rights Management  This document is authorized for selfarchiving and distribution online by the author(s) and is free for use by researchers. 
RoMEO Color  RoMEO_Color_Green 
Preprint Archiving  Yes 
Postprint Archiving  Yes 
Publisher PDF Archiving  Yes 
Paid OA Option  Yes 
Contributing Organization  Carleton College 
Type  Text 
Format  application/pdf 
Language  English 
Description
Article Title  Page 1 
FullText  arXiv:grqc/0609131v2 26 Jul 2007 Coherent Bayesian inference on compact binary inspirals using a network of interferometric gravitational wave detectors Christian R¨over and Renate Meyer Department of Statistics, The University of Auckland, Auckland, New Zealand Nelson Christensen Physics and Astronomy, Carleton College, Northfield, MN, USA (Dated: February 7, 2008) Presented in this paper is the description of a Markov chain Monte Carlo (MCMC) routine for conducting coherent parameter estimation for interferometric gravitational wave observations of an inspiral of binary compact objects using multiple detectors. Data from several interferometers are processed, and all nine parameters (ignoring spin) associated with the binary system are inferred, including the distance to the source, the masses, and the location on the sky. The data is matched with timedomain inspiral templates that are 2.5 postNewtonian (PN) in phase and 2.0 PN in amplitude. We designed and tuned an MCMC sampler so that it is able to efficiently find the posterior mode(s) in the parameter space and perform the stochastic integration necessary for inference within a Bayesian framework. Our routine could be implemented as part of an inspiral detection pipeline for a world wide network of detectors. Examples are given for simulated signals and data as seen by the LIGO and Virgo detectors operating at their design sensitivity. PACS numbers: 02.70.Uu, 04.80.Nn, 05.45.Tp, 07.05.Kf, 97.80.d. Keywords: gravitational waves, compact binary inspirals, coherent parameter estimation I. INTRODUCTION The era of gravitational wave astronomy is now close upon us as numerous interferometric detectors are operating. The Laser Interferometer Gravitational Wave Observatory (LIGO) [1, 2, 3] has now reached its target sensitivity, and there is the hope that a detection could come at any time [4]. Around the globe a worldwide network of detectors is coming online; Virgo in Italy [5, 6, 7], GEO in Germany [8, 9], and TAMA in Japan [10, 11] are operating alongside LIGO in the quest for gravity wave detection. These ground based laser interferometers are sensitive to gravitational radiation in the frequency band from 40 Hz up to 8 kHz. Coalescing binaries containing neutron stars or black holes promise to be one of the cleanest and most probable sources of detectable radiation [12]. Observation of inspiral events could provide important information on the structure of neutron stars [13, 14]. Even cosmological information can be extracted from the observation of inspiral events [15, 16, 17, 18, 19]. The characteristics of radiation in the postNewtonian regime will provide insight into highly nonlinear general relativistic effects, such as the observation of the formation of a Kerr black hole as the binary system decays [18, 20, 21]. The LIGO Scientific Collaboration (LSC) has been actively searching for binary inspiral events [22, 23], as well as conducting searches in coincidence with TAMA [24]. Using the data from LIGO’s S2 run, it was possible to set an upper limit on the neutron star coalescence rate of less than 50 per year per Milky Way equivalent galaxy [23]. The LSC has also conducted searches for binary inspiral signals from primordial black holes (0.2–1.0 M⊙) in the halo of our galaxy [25], plus more massive black hole systems where component masses are in the 3–20 M⊙ range [26]. Bayesian inferential methods provide a means to use data from interferometric gravitational wave detectors in order to extract the parameters of a binary inspiral event. Markov chain Monte Carlo (MCMC) methods are a powerful computation technique for parameter estimation within this framework; they are especially useful in applications where the number of parameters is large [27]. Nice descriptions of the positive aspects of a Bayesian analysis of scientific and astrophysical data are provided in [28, 29, 30]. In previous work we have developed MCMC routines for extracting five parameters associated with a binary inspiral event from data generated by a single interferometric detector [31, 32, 33]. Our MCMC code took data from a single interferometer, Fourier transformed it into the frequency domain, and then compared the result with 2.0 postNewtonian (PN) stationary phase templates [34]. One of the new methods that we implement in this current study, presented in this paper, is an MCMC routine that takes time domain interferometric data, and compares it to time domain templates that are 2.5 PN in phase, and 2.0 PN in amplitude; a trivial modification of the code (though not implemented in the study presented here) is to extend the accuracy of the signal waveforms to 3.5 PN in phase and 2.5 PN in amplitude [35, 36, 37, 38, 39]. A critical task for a worldwide gravity wave detection network will be to not only detect a binary inspiral signal, but to say where it came from. For this purpose the LSC has developed a coherent binary inspiral search pipeline [40, 41, 42]. Coherent binary search pipelines and methods are also being developed within the Virgo collaboration [43] and TAMA [44]. Along similar lines, we have developed a coherent MCMC parameter estimation routine, and in this Typeset by REVTEX 