Coherent Bayesian Inference on Compact Binary Inspirals Using a Network of Interferometric Gravitational Wave Detectors

              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
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