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arXiv:gr-qc/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 time-domain inspiral templates that are 2.5 post-Newtonian (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 poste-rior 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 op-erating. 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 world-wide network of detectors is coming on-line; 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 inter-ferometers 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 prob-able sources of detectable radiation [12]. Observation of inspiral events could provide important information on the structure of neutron stars [13, 14]. Even cosmologi-cal information can be extracted from the observation of inspiral events [15, 16, 17, 18, 19]. The characteristics of radiation in the post-Newtonian regime will provide insight into highly non-linear 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 search-ing for binary inspiral events [22, 23], as well as conduct-ing 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 sig-nals 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 es-timation within this framework; they are especially use-ful 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 de-veloped MCMC routines for extracting five parameters associated with a binary inspiral event from data gen-erated 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 post-Newtonian (PN) stationary phase templates [34]. One of the new meth-ods that we implement in this current study, presented in this paper, is an MCMC routine that takes time do-main interferometric data, and compares it to time do-main 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 world-wide 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 co-herent 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_Christensen-Nelson_CoherentBayesianInferenceOnCompactBinaryInspirals.pdf; 032_Christensen-Nelson_CoherentBayesianInferenceOnCompactBinaryInspirals.pdf |
Rights Management | This document is authorized for self-archiving 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:gr-qc/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 time-domain inspiral templates that are 2.5 post-Newtonian (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 poste-rior 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 op-erating. 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 world-wide network of detectors is coming on-line; 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 inter-ferometers 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 prob-able sources of detectable radiation [12]. Observation of inspiral events could provide important information on the structure of neutron stars [13, 14]. Even cosmologi-cal information can be extracted from the observation of inspiral events [15, 16, 17, 18, 19]. The characteristics of radiation in the post-Newtonian regime will provide insight into highly non-linear 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 search-ing for binary inspiral events [22, 23], as well as conduct-ing 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 sig-nals 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 es-timation within this framework; they are especially use-ful 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 de-veloped MCMC routines for extracting five parameters associated with a binary inspiral event from data gen-erated 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 post-Newtonian (PN) stationary phase templates [34]. One of the new meth-ods that we implement in this current study, presented in this paper, is an MCMC routine that takes time do-main interferometric data, and compares it to time do-main 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 world-wide 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 co-herent MCMC parameter estimation routine, and in this Typeset by REVTEX |