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Register a new userDetection of gravitational waves from inspiraling compact binaries using a network of interferometric detectors
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We formulate the data analysis problem for the detection of the Newtonian waveform from an inspiraling compact-binary by a network of arbitrarily oriented and arbitrarily distributed laser interferometric gravitational wave detectors. We obtain for the first time the relation between the optimal statistic and the magnitude of the network correlation vector, which is constructed from the matched network-filter. This generalizes the calculation reported in an earlier work (gr-qc/9906064), where the detectors are taken to be coincident.
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We calculate the gravitational waveform for spinning, precessing compact binary inspirals through second post-Newtonian order in the amplitude. When spins are collinear with the orbital angular momentum and the orbits are quasi-circular, we further provide explicit expressions for the gravitational-wave polarizations and the decomposition into spin-weighted spherical-harmonic modes. Knowledge of the second post-Newtonian spin terms in the waveform could be used to improve the physical content of analytical templates for data analysis of compact binary inspirals and for more accurate comparisons with numerical-relativity simulations.
We rigorously analyze the frequency response functions and antenna sensitivity patterns of three types of interferometric detectors to scalar mode of gravitational waves which is predicted to exist in the scalar-tensor theory of gravity. By a straightforward treatment, we show that the antenna sensitivity pattern of the simple Michelson interferometric detector depends strongly on the wave length $lambda_{rm SGW}$ of the scalar mode of gravitational waves if $lambda_{rm SGW}$ is comparable to the arm length of the interferometric detector. For the Delay-Line and Fabry-Perot interferometric detectors with arm length much shorter than $lambda_{rm SGW}$, however, the antenna sensitivity patterns depend weakly on $lambda_{rm SGW}$ even though $lambda_{rm SGW}$ is comparable to the effective path length of those interferometers. This agrees with the result obtained by Maggiore and Nicolis.
Inspiralling compact binaries are expected to circularize before their gravitational-wave signals reach the sensitive frequency band of ground-based detectors. Current searches for gravitational waves from compact binaries using the LIGO and Virgo detectors therefore use circular templates to construct matched filters. Binary formation models have been proposed which suggest that some systems detectable by the LIGO--Virgo network may have non-negligible eccentricity. We investigate the ability of the restricted 3.5 post-Newtonian order TaylorF2 template bank, used by LIGO and Virgo to search for gravitational waves from compact binaries with masses $M le 35 M_odot$, to detect binaries with non-zero eccentricity. We model the gravitational waves from eccentric binaries using the $x$-model post-Newtonian formalism proposed by Hinder emph{et. al.} [I. Hinder, F. Hermann, P. Laguna, and D. Shoemaker, arXiv:0806.1037v1]. We find that small residual eccentricities ($e_0 lesssim 0.05$ at 40 Hz) do not significantly affect the ability of current LIGO searches to detect gravitational waves from coalescing compact binaries with total mass $2 M_odot < M < 15 M_odot$. For eccentricities $e_0 gtrsim 0.1$, the loss in matched filter signal-to-noise ratio due to eccentricity can be significant and so templates which include eccentric effects will be required to perform optimal searches for such systems.
We report the construction of a three-dimensional template bank for the search for gravitational waves from inspiralling binaries consisting of spinning compact objects. The parameter space consists of two dimensions describing the mass parameters and one reduced-spin parameter, which describes the secular (non-precessing) spin effects in the waveform. The template placement is based on an efficient stochastic algorithm and makes use of the semi-analytical computation of a metric in the parameter space. We demonstrate that for low-mass ($m_1 + m_2 lesssim 12,M_odot$) binaries, this template bank achieves effective fitting factors $sim0.92$--$0.99$ towards signals from generic spinning binaries in the advanced detector era over the entire parameter space of interest (including binary neutron stars, binary black holes, and black hole-neutron star binaries). This provides a powerful and viable method for searching for gravitational waves from generic spinning low-mass compact binaries. Under the assumption that spin magnitudes of black-holes [neutron-stars] are uniformly distributed between 0--0.98 [0 -- 0.4] and spin angles are isotropically distributed, the expected improvement in the average detection volume (at a fixed signal-to-noise-ratio threshold) of a search using this reduced-spin bank is $sim20-52%$, as compared to a search using a non-spinning bank.
Inferring astrophysical information from gravitational waves emitted by compact binaries is one of the key science goals of gravitational-wave astronomy. In order to reach the full scientific potential of gravitational-wave experiments we require techniques to mitigate the cost of Bayesian inference, especially as gravitational-wave signal models and analyses become increasingly sophisticated and detailed. Reduced order models (ROMs) of gravitational waveforms can significantly reduce the computational cost of inference by removing redundant computations. In this paper we construct the first reduced order models of gravitational-wave signals that include the effects of spin-precession, inspiral, merger, and ringdown in compact object binaries, and which are valid for component masses describing binary neutron star, binary black hole and mixed binary systems. This work utilizes the waveform model known as IMRPhenomPv2. Our ROM enables the use of a fast reduced order quadrature (ROQ) integration rule which allows us to approximate Bayesian probability density functions at a greatly reduced computational cost. We find that the ROQ rule can be used to speed up inference by factors as high as 300 without introducing systematic bias. This corresponds to a reduction in computational time from around half a year to a half a day, for the longest duration/lowest mass signals. The ROM and ROQ rule are available with the main inference library of the LIGO Scientific Collaboration, LALInference.
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