Detection Template Family Research Articles

Search of S3 LIGO data for gravitational wave signals from spinning black hole and neutron star binary inspirals

We report on the methods and results of the first dedicated search for gravitational waves emitted during the inspiral of compact binaries with spinning component bodies. We analyze 788 hours of data collected during the third science run (S3) of the LIGO detectors. We searched for binary systems using a detection template family specially designed to capture the effects of the spin-induced precession of the orbital plane. We present details of the techniques developed to enable this search for spin-modulated gravitational waves, highlighting the differences between this and other recent searches for binaries with nonspinning components. The template bank we employed was found to yield high matches with our spin-modulated target waveform for binaries with masses in the asymmetric range 1.0M⊙<m1<3.0M⊙ and 12.0M⊙<m2<20.0M⊙ which is where we would expect the spin of the binary’s components to have a significant effect. We find that our search of S3 LIGO data has good sensitivity to binaries in the Milky Way and to a small fraction of binaries in M31 and M33 with masses in the range 1.0M⊙<m1, m2<20.0M⊙. No gravitational wave signals were identified during this search. Assuming a binary population with spinning components and Gaussian distribution of masses representing a prototypical neutron star–black hole system with m1≃1.35M⊙ and m2≃5M⊙, we calculate the 90%-confidence upper limit on the rate of coalescence of these systems to be 15.9 yr−1L−110, where L10 is 1010 times the blue light luminosity of the Sun.

A template bank to search for gravitational waves from inspiralling compact binaries: II. Phenomenological model

Matched filtering is used to search for gravitational waves emitted by inspiralling compact binaries in data from ground-based interferometers. One of the key aspects of the detection process is the deployment of a set of templates, also called a template bank, to cover the astrophysically interesting region of the parameter space. In a companion paper, we described the template bank algorithm used in the analysis of Laser Interferometer Gravitational-Wave Observatory (LIGO) data to search for signals from non-spinning binaries made of neutron star and/or stellar-mass black holes; this template bank is based upon physical template families. In this paper, we describe the phenomenological template bank that was used to search for gravitational waves from non-spinning black hole binaries (from stellar mass formation) in the second, third and fourth LIGO science runs. We briefly explain the design of the bank, whose templates are based on a phenomenological detection template family. We show that this template bank gives matches greater than 95% with the physical template families that are expected to be captured by the phenomenological templates.

Erratum: Detection template families for gravitational waves from the final stages of binary–black-hole inspirals: Nonspinning case [Phys. Rev. D67, 024016 (2003)

We investigate the problem of detecting gravitational waves from binaries of nonspinning black holes with masses m = 5--20 Msun, moving on quasicircular orbits, which are arguably the most promising sources for first-generation ground-based detectors. We analyze and compare all the currently available post--Newtonian approximations for the relativistic two-body dynamics; for these binaries, different approximations predict different waveforms. We then construct examples of detection template families that embed all the approximate models, and that could be used to detect the true gravitational-wave signal (but not to characterize accurately its physical parameters). We estimate that the fitting factor for our detection families is >~0.95 (corresponding to an event-rate loss <~15%) and we estimate that the discretization of the template family, for ~10^4 templates, increases the loss to <~20%.

Erratum: Detecting gravitational waves from precessing binaries of spinning compact objects: Adiabatic limit [Phys. Rev. D67, 104025 (2003)

Black-hole (BH) binaries with single-BH masses m=5--20 Msun, moving on quasicircular orbits, are among the most promising sources for first-generation ground-based gravitational-wave (GW) detectors. Until now, the development of data-analysis techniques to detect GWs from these sources has been focused mostly on nonspinning BHs. The data-analysis problem for the spinning case is complicated by the necessity to model the precession-induced modulations of the GW signal, and by the large number of parameters needed to characterize the system, including the initial directions of the spins, and the position and orientation of the binary with respect to the GW detector. In this paper we consider binaries of maximally spinning BHs, and we work in the adiabatic-inspiral regime to build families of modulated detection templates that (i) are functions of very few physical and phenomenological parameters, (ii) model remarkably well the dynamical and precessional effects on the GW signal, with fitting factors on average >~ 0.97, but (iii) might require increasing the detection thresholds, offsetting at least partially the gains in the fitting factors. Our detection-template families are quite promising also for the case of neutron-star--black-hole binaries, with fitting factors on average ~ 0.93. For these binaries we also suggest (but do not test) a further template family, which would produce essentially exact waveforms written directly in terms of the physical spin parameters.

Report on the search for binary black holes inspiral in S3 LIGO data

We report on the search for gravitational waves emitted by non-spinning binary black hole inspirals in the data taken during the third LIGO science run (S3). We give an overview of the data acquired during S3 and the target waveforms that we are searching for in this analysis. We briefly describe how the data was filtered using a BCV detection template family (using an hexagonal template bank placement in the mass parameter plane). Finally, we report on preliminary estimates of the sensitivity of the three LIGO detectors using software injections of effective one-body waveforms with component masses in the range 3-40 M⊙ and total mass M ⩽ 40 M⊙. We show that during S3, the three LIGO detectors have a detection efficiency of 50% up to several Mpc for L1 and H2, and up to 30 Mpc for H1.

Detecting gravitational waves from precessing binaries of spinning compact objects. II. Search implementation for low-mass binaries

Detection template families (DTFs) are built to capture the essential features of true gravitational waveforms using a small set of phenomenological waveform parameters. Buonanno, Chen, and Vallisneri [Phys. Rev. D 67, 104025 (2003)] proposed the BCV2 DTF to perform computationally efficient searches for signals from precessing binaries of compact stellar objects. Here we test the signal-matching performance of the BCV2 DTF for asymmetric-mass-ratio binaries, and specifically for double-black-hole binaries with component masses $({m}_{1},{m}_{2})\ensuremath{\in}[6,12]{M}_{\ensuremath{\bigodot}}\ifmmode\times\else\texttimes\fi{}[1,3]{M}_{\ensuremath{\bigodot}}$, and for black-hole--neutron-star binaries with component masses $({m}_{1},{m}_{2})=(10{M}_{\ensuremath{\bigodot}},1.4{M}_{\ensuremath{\bigodot}})$; we take all black holes to be maximally spinning. We find a satisfactory signal-matching performance, with fitting factors averaging between 0.94 and 0.98. We also scope out the region of BCV2 parameters needed for a template-based search, we evaluate the template match metric, we discuss a template-placement strategy, and we estimate the number of templates needed for searches at the LIGO design sensitivity. In addition, after gaining more insight in the dynamics of spin-orbit precession, we propose a modification of the BCV2 DTF that is parametrized by physical (rather than phenomenological) parameters. We test this modified ``BCV2P'' DTF for the ($10{M}_{\ensuremath{\bigodot}}$, $1.4{M}_{\ensuremath{\bigodot}}$) black-hole--neutron-star system, finding a signal-matching performance comparable to the BCV2 DTF, and a reliable parameter-estimation capability for target-binary quantities such as the chirp mass and the opening angle (the angle between the black-hole spin and the orbital angular momentum).

Detecting gravitational waves from test-mass bodies orbiting a Kerr black hole with P-approximant templates

In this study, we apply post-Newtonian (T-approximants) and resummed post-Newtonian (P-approximants) to the case of a test particle in equatorial orbit around a Kerr black hole. We compare the two approximants by measuring their effectualness (i.e., larger overlaps with the exact signal) and faithfulness (i.e., smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, T-approximant templates obtain an effectualness of ∼0.99 for spins q ⩽ 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of >0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q > 0. For q < 0, both T- and P-approximants perform equally well so that either of them could be used as a detection template family. However, for parameter estimation, the P-approximant templates still outperform the T-approximants.

Improved gravitational waveforms from spinning black hole binaries

The standard post-Newtonian approximation to gravitational waveforms, called T-approximants, from non-spinning black hole binaries are known not to be sufficiently accurate close to the last stable orbit of the system. A new approximation, called P-approximants, is believed to improve the accuracy of the waveforms rendering them applicable up to the last stable orbit. In this study we apply P-approximants to the case of a test-particle in equatorial orbit around a Kerr black hole parameterized by a spin parameter q that takes values between -1 and 1. In order to assess the performance of the two approximants we measure their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, that is orbits whose angular momentum is in the same sense as the spin angular momentum of the black hole, T-approximant templates obtain an effectualness of ~ 0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q>0. For q<0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family.

Detecting gravitational waves from precessing binaries of spinning compact objects: Adiabatic limit

Black-hole (BH) binaries with single-BH masses m=(5-20)M, moving on quasicircular orbits, are among the most promising sources for first-generation ground-based gravitational-wave (GW) detectors. Until now, the development of data-analysis techniques to detect GWs from these sources has been focused mostly on nonspinning BHs. The data-analysis problem for the spinning case is complicated by the necessity to model the precession-induced modulations of the GW signal, and by the large number of parameters needed to characterize the system, including the initial directions of the spins, and the position and orientation of the binary with respect to the GW detector. In this paper we consider binaries of maximally spinning BHs, and we work in the adiabatic-inspiral regime to build families of modulated detection templates that (i) are functions of very few physical and phenomenological parameters, (ii) model remarkably well the dynamical and precessional effects on the GW signal, with fitting factors on average greater than or similar to0.97, (iii) but, however, might require increasing the detection thresholds, offsetting at least partially the gains in the fitting factors. Our detection-template families are quite promising also for the case of neutron-star-black-hole binaries, with fitting factors on average approximate to0.93. For these binaries we also suggest (but do not test) a further template family, which would produce essentially exact waveforms written directly in terms of the physical spin parameters.

Detection template families for gravitational waves from the final stages of binary–black-hole inspirals: Nonspinning case

We investigate the problem of detecting gravitational waves from binaries of nonspinning black holes with masses m=5-20M., moving on quasicircular orbits, which are arguably the most promising sources for first-generation ground-based detectors. We analyze and compare all the currently available post-Newtonian approximations for the relativistic two-body dynamics; for these binaries, different approximations predict different waveforms. We then construct examples of detection template families that embed all the approximate models and that could be used to detect the true gravitational-wave signal (but not to characterize accurately its physical parameters). We estimate that the fitting factor for our detection families is greater than or similar to0.95 (corresponding to an event rate loss less than or similar to15%) and we estimate that the discretization of the template family, for similar to10(4) templates, increases the loss to less than or similar to20%.