E. Ochsner

Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.

Systematic and statistical errors in a Bayesian approach to the estimation of the neutron-star equation of state using advanced gravitational wave detectors

Advanced ground-based gravitational-wave detectors are capable of measuring tidal influences in binary neutron-star systems. In this work, we report on the statistical uncertainties in measuring tidal deformability with a full Bayesian parameter estimation implementation. We show how simultaneous measurements of chirp mass and tidal deformability can be used to constrain the neutron-star equation of state. We also study the effects of waveform modeling bias and individual instances of detector noise on these measurements. We notably find that systematic error between post-Newtonian waveform families can significantly bias the estimation of tidal parameters, thus motivating the continued development of waveform models that are more reliable at high frequencies.

Status of NINJA: the Numerical INJection Analysis project

The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new collaborative effort between the numerical relativity community and the data analysis community. NINJA focuses on modeling and searching for gravitational wave signatures from the coalescence of binary system of compact objects. We review the scope of this collaboration and the components of the first NINJA project, where numerical relativity groups, shared waveforms and data analysis teams applied various techniques to detect them when embedded in colored Gaussian noise.

Reduced Basis Catalogs for Gravitational Wave Templates

We introduce a reduced basis approach as a new paradigm for modeling, representing and searching for gravitational waves. We construct waveform catalogs for nonspinning compact binary coalescences, and we find that for accuracies of 99% and 99.999% the method generates a factor of about 10-10(5) fewer templates than standard placement methods. The continuum of gravitational waves can be represented by a finite and comparatively compact basis. The method is robust under variations in the noise of detectors, implying that only a single catalog needs to be generated.

Investigating the effect of precession on searches for neutron-star-black-hole binaries with Advanced LIGO

The first direct detection of neutron-star– black-hole binaries will likely be made with gravitational-wave observatories. Advanced LIGO and Advanced Virgo will be able to observe neutron-star– black-hole mergers at a maximum distance of 900 Mpc. To achieve this sensitivity, gravitational-wave searches will rely on using a bank of filter waveforms that accurately model the expected gravitational-wave signal. The emitted signal will depend on the masses of the black hole and the neutron star and also the angular momentum of both components. The angular momentum of the black hole is expected to be comparable to the orbital angular momentum when the system is emitting gravitational waves in Advanced LIGO’s and Advanced Virgo’s sensitive band. This angular momentum will affect the dynamics of the inspiralling system and alter the phase evolution of the emitted gravitational-wave signal. In addition, if the black hole’s angular momentum is not aligned with the orbital angular momentum, it will cause the orbital plane of the system to precess. In this work we demonstrate that if the effect of the black hole’s angular momentum is neglected in the waveform models used in gravitational-wave searches, the detection rate of (10+1.4)M_⊙ neutron-star– black-hole systems with isotropic spin distributions would be reduced by 33%–37% in comparison to a hypothetical perfect search at a fixed signal-to-noise ratio threshold. The error in this measurement is due to uncertainty in the post-Newtonian approximations that are used to model the gravitational-wave signal of neutron-star– black-hole inspiralling binaries. We describe a new method for creating a bank of filter waveforms where the black hole has nonzero angular momentum that is aligned with the orbital angular momentum. With this bank we find that the detection rate of (10+1.4)M_⊙ neutron-star– black-hole systems would be reduced by 26%–33%. Systems that will not be detected are ones where the precession of the orbital plane causes the gravitational-wave signal to match poorly with nonprecessing filter waveforms. We identify the regions of parameter space where such systems occur and suggest methods for searching for highly precessing neutron-star– black-hole binaries.

Gravitational waves from black hole-neutron star binaries: Effective Fisher matrices and parameter estimation using higher harmonics

Inspiralling black hole-neutron star (BH-NS) binaries emit a complicated gravitational wave signature, produced by multiple harmonics sourced by their strong local gravitational field and further modulated by the orbital planes precession. Some features of this complex signal are easily accessible to ground-based interferometers (e.g., the rate of change of frequency); others less so (e.g., the polarization content); and others unavailable (e.g., features of the signal out of band). For this reason, an ambiguity function (a diagnostic of dissimilarity) between two such signals varies on many parameter scales and ranges. In this paper, we present a method for computing an approximate, effective Fisher matrix from variations in the ambiguity function on physically pertinent scales which depend on the relevant signal to noise ratio. As a concrete example, we explore how higher harmonics improve parameter measurement accuracy. As previous studies suggest, for our fiducial BH-NS binaries and for plausible signal amplitudes, we see that higher harmonics at best marginally improve our ability to measure parameters. For non-precessing binaries, these Fisher matrices separate into intrinsic (mass, spin) and extrinsic (geometrical) parameters; higher harmonics principally improve our knowledge about the line of sight. For the precessing binaries, the extra information provided by higher harmonics is distributed across several parameters. We provide concrete estimates for measurement accuracy, using coordinates adapted to the precession cone in the detectors sensitive band.

Advanced LIGO's ability to detect apparent violations of the cosmic censorship conjecture and the no-hair theorem through compact binary coalescence detections

We study the ability of the Advanced Laser Interferometer Gravitational-Wave Observatory (aLIGO) to detect apparent violations of the cosmic censorship conjecture and the no-hair theorem. The cosmic censorship conjecture, which is believed to be true in the theory of general relativity, limits the spin-to-mass-squared ratio of a Kerr black hole, � � j=m 2 � 1. The no-hair theorem, which is also believed to be true in the theory of general relativity, suggests a particular value for the tidal Love number of a nonrotating black hole (k2 ¼ 0). Using the Fisher matrix formalism, we examine the measurability of the spin and tidal deformability of compact binary systems involving at least one putative black hole. Using parameter measurement errors and correlations obtained from the Fisher matrix, we determine the smallest detectable violation of bounds implied by the cosmic censorship conjecture and the no-hair theorem. We examine the effect of excluding unphysical areas of parameter space when determining the smallest detectable apparent violations, and we examine the effect of different post-Newtonian corrections to the amplitude of the compact binary coalescence gravitational waveform, as given in Arun et al. [Phys. Rev. D79, 104023 (2009)]. In addition, we perform a brief study of how the recently calculated 3.0 pN and 3.5 pN spin-orbit corrections to the phase [Marsat et al., Classical Quantum Gravity 30, 055007 (2013)] affect spin and mass parameter measurability. We find that physical priors on the symmetric mass ratio and higher harmonics in the gravitational waveform could significantly affect the ability of aLIGO to investigate cosmic censorship and the nohair theorem for certain systems.

Towards beating the curse of dimensionality for gravitational waves using reduced basis

Using the reduced basis approach, we efficiently compress and accurately represent the space of waveforms for nonprecessing binary black hole inspirals, which constitutes a four-dimensional parameter space (two masses, two spin magnitudes). Compared to the nonspinning case, we find that only a marginal increase in the (already relatively small) number of reduced basis elements is required to represent any nonprecessing waveform to nearly numerical round-off precision. Most parameters selected by the algorithm are near the boundary of the parameter space, leaving the bulk of its volume sparse. Our results suggest that the full eight-dimensional space (two masses, two spin magnitudes, four spin orientation angles on the unit sphere) may be highly compressible and represented with very high accuracy by a remarkably small number of waveforms, thus providing some hope that the number of numerical relativity simulations of binary black hole coalescences needed to represent the entire space of configurations is not intractable. Finally, we find that the distribution of selected parameters is robust to different choices of seed values starting the algorithm, a property which should be useful for indicating parameters for numerical relativity simulations of binary black holes. In particular, we find that the mass ratios m_1/m_2 of nonspinning binaries selected by the algorithm are mostly in the interval [1,3] and that the median of the distribution follows a power-law behavior ∼(m_1/m_2)^(-5.25).

A method for estimating time–frequency characteristics of compact binary mergers to improve searches for inspiral, merger and ring-down phases separately

Recent advances in the description of compact binary systems have produced gravitational waveforms that include inspiral, merger and ring-down phases. Comparing results from numerical simulations with those of post-Newtonian (PN), and related, expansions has provided motivation for employing PN waveforms in near merger epochs when searching for gravitational waves and has encouraged the development of analytic fits to full numerical waveforms. The models and simulations do not yet cover the full binary coalescence parameter space. For these yet un-simulated regions, data analysts can still conduct separate inspiral, merger and ring-down searches. Improved knowledge about the end of the inspiral phase, the beginning of the merger, and the ring-down frequencies could increase the efficiency of both coherent inspiral-merger-ring-down (IMR) searches and searches over each phase separately. Insight can be gained for all three cases through a recently presented theoretical calculation, which, corroborated by the numerical results, provides an implicit formula for the final spin of the merged black holes, accurate to within 10% over a large parameter space. Knowledge of the final spin allows one to predict the end of the inspiral phase and the quasinormal mode ring-down frequencies, and in turn provides information about the bandwidth and duration of the merger. In this work we will discuss a few of the implications of this calculation for data analysis. ar X iv :0 80 1. 42 97 v2 [ gr -q c] 2 9 Ja n 20 08Recent advances in the description of compact binary systems have produced gravitational waveforms that include inspiral, merger and ring-down phases. Comparing results from numerical simulations with those of post-Newtonian, and related, expansions has provided motivation for employing post-Newtonian waveforms in near merger epochs when searching for gravitational waves and has encouraged the development of analytic fits to full numerical waveforms. Until searches employ full waveforms as templates, data analysts can still conduct separate inspiral, merger and ring-down searches. Improved knowledge about the end of the inspiral phase, the beginning of the merger and the ring-down frequencies will increase the efficiency of searches over each phase separately without needing the exact waveform. We will show that knowledge of the final spin, of which there are many theoretical models and analytic fits to simulations, may give an insight into the time–frequency properites of the merger. We also present implications on the ability to probe the tidal disruption of neutron stars through gravitational waves.

Novel scheme for rapid parallel parameter estimation of gravitational waves from compact binary coalescences

We introduce a highly parallelizable architecture for estimating parameters of compact binary coalescence using gravitational-wave data and waveform models. Using a spherical harmonic mode decomposition, the waveform is expressed as a sum over modes that depend on the intrinsic parameters (e.g., masses) with coefficients that depend on the observer dependent extrinsic parameters (e.g., distance, sky position). The data is then prefiltered against those modes, at fixed intrinsic parameters, enabling efficiently evaluation of the likelihood for generic source positions and orientations, independent of waveform length or generation time. We efficiently parallelize our intrinsic space calculation by integrating over all extrinsic parameters using a Monte Carlo integration strategy. Since the waveform generation and prefiltering happens only once, the cost of integration dominates the procedure. Also, we operate hierarchically, using information from existing gravitational-wave searches to identify the regions of parameter space to emphasize in our sampling. As proof of concept and verification of the result, we have implemented this algorithm using standard time-domain waveforms, processing each event in less than one hour on recent computing hardware. For most events we evaluate the marginalized likelihood (evidence) with statistical errors of