Improving analytical templates and searching for gravitational waves from coalescing black hole binaries

The Laser Interferometer Gravitational-wave Observatory (LIGO) and Virgo are taking data at design sensitivity. They will be upgraded to Advanced LIGO and Virgo within the next 5 years and the detection of gravitational waves will be very likely. Binaries of two compact objects which inspiral and coalesce are one of the most promising sources for LIGO and Virgo. Most searches have focused solely on the inspiral portion of the waveform, and are consequently limited to low total mass. Recent breakthroughs in numerical relativity allow one to construct complete inspiral-merger-ringdown waveforms and search for the whole signal. This thesis will review some of the basic characteristics of gravitational waves from compact binaries and methods of searching for them. Analytical template waveforms for such systems will be presented including a comparison of different families of analytical waveforms, a study on the inclusion of spin effects in such waveforms, and a study of inspiral-merger-ringdown waveforms with amplitude corrections and the importance of these effects for parameter estimation. The thesis will culminate with a presentation of the first gravitational wave search to use inspiral-merger-ringdown templates, which was performed on data from the fifth science run of LIGO

A more effective coordinate system for parameter estimation of precessing compact binaries from gravitational waves

Ground-based gravitational wave detectors are sensitive to a narrow range of frequencies, effectively taking a snapshot of merging compact-object binary dynamics just before merger. We demonstrate that by adopting analysis parameters that naturally characterize this 'picture', the physical parameters of the system can be extracted more efficiently from the gravitational wave data, and interpreted more easily. We assess the performance of MCMC parameter estimation in this physically intuitive coordinate system, defined by (a) a frame anchored on the binary's spins and orbital angular momentum and (b) a time at which the detectors are most sensitive to the binary's gravitational wave emission. Using anticipated noise curves for the advanced-generation LIGO and Virgo gravitational wave detectors, we find that this careful choice of reference frame and reference time significantly improves parameter estimation efficiency for BNS, NS-BH, and BBH signals.Comment: 11 pages, 5 figures, submitted to Phys. Rev.

Asymptotic frame selection for binary black hole spacetimes II: Post-Newtonian limit

One way to select a preferred frame from gravitational radiation is via the principal axes of , an average of the action of rotation group generators on the Weyl tensor at asymptotic infinity. In this paper we evaluate this time-domain average for a quasicircular binary using approximate (post-Newtonian) waveforms. For nonprecessing unequal-mass binaries, we show the dominant eigenvector of this tensor lies along the orbital angular momentum. For precessing binaries, this frame is not generally aligned with either the orbital or total angular momentum, working to leading order in the spins. The difference between these two quantities grows with time, as the binary approaches the end of the inspiral and both precession and higher harmonics become more significant.Comment: 12 pages, 4 figure

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. 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 non-rotating black hole. 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. 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 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 no-hair theorem for certain systems.Comment: 21 pages, 7 figures, 6 table

Gravitational waves from BH-NS 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 plane's 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 detector's sensitive band.Comment: 19 pages, 11 figure

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 non-precessing binary black hole inspirals, which constitutes a four dimensional parameter space (two masses, two spin magnitudes). Compared to the non-spinning case, we find that only a {\it marginal} increase in the (already relatively small) number of reduced basis elements is required to represent any non-precessing 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 {\it 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 non-spinning binaries selected by the algorithm are mostly in the interval $[1,3]$ and that the median of the distribution follows a power-law behavior $\sim (m_1/m_2)^{-5.25}$

Higher-order spin effects in the amplitude and phase of gravitational waveforms emitted by inspiraling compact binaries: Ready-to-use gravitational waveforms

We provide ready-to-use time-domain gravitational waveforms for spinning compact binaries with precession effects through 1.5PN order in amplitude and compute their mode decomposition using spin-weighted -2 spherical harmonics. In the presence of precession, the gravitational-wave modes (l,m) contain harmonics originating from combinations of the orbital frequency and precession frequencies. We find that the gravitational radiation from binary systems with large mass asymmetry and large inclination angle can be distributed among several modes. For example, during the last stages of inspiral, for some maximally spinning configurations, the amplitude of the (2,0) and (2,1) modes can be comparable to the amplitude of the (2,2) mode. If the mass ratio is not too extreme, the l=3 and l=4 modes are generally one or two orders of magnitude smaller than the l = 2 modes. Restricting ourselves to spinning, non-precessing compact binaries, we apply the stationary-phase approximation and derive the frequency-domain gravitational waveforms including spin-orbit and spin(1)- spin(2) effects through 1.5PN and 2PN order respectively in amplitude, and 2.5PN order in phase. Since spin effects in the amplitude through 2PN order affect only the first and second harmonics of the orbital phase, they do not extend the mass reach of gravitational-wave detectors. However, they can interfere with other harmonics and lower or raise the signal-to-noise ratio depending on the spin orientation. These ready-to-use waveforms could be employed in the data-analysis of the spinning, inspiraling binaries as well as in comparison studies at the interface between analytical and numerical relativity.Comment: 43 pages, 10 Postscript figures. submitted to Physical Review D. Includes corrections due to errat

Comparison of post-Newtonian templates for compact binary inspiral signals in gravitational-wave detectors

The two-body dynamics in general relativity has been solved perturbatively using the post-Newtonian (PN) approximation. The evolution of the orbital phase and the emitted gravitational radiation are now known to a rather high order up to O(v^8), v being the characteristic velocity of the binary. The orbital evolution, however, cannot be specified uniquely due to the inherent freedom in the choice of parameter used in the PN expansion as well as the method pursued in solving the relevant differential equations. The goal of this paper is to determine the (dis)agreement between different PN waveform families in the context of initial and advanced gravitational-wave detectors. The waveforms employed in our analysis are those that are currently used by Initial LIGO/Virgo, that is the time-domain PN models TaylorT1, TaylorT2, TaylorT3, TaylorT4 and TaylorEt, the effective one-body (EOB) model, and the Fourier-domain representation TaylorF2. We examine the overlaps of these models with one another and with the prototype effective one-body model (calibrated to numerical relativity simulations, as currently used by initial LIGO) for a number of different binaries at 2PN, 3PN and 3.5PN orders to quantify their differences and to help us decide whether there exist preferred families that are the most appropriate as search templates. We conclude that as long as the total mass remains less than a certain upper limit M_crit, all template families at 3.5PN order (except TaylorT3 and TaylorEt) are equally good for the purpose of detection. The value of M_crit is found to be ~ 12M_Sun for Initial, Enhanced and Advanced LIGO. From a purely computational point of view we recommend that 3.5PN TaylorF2 be used below Mcrit and EOB calibrated to numerical relativity simulations be used for total binary mass M > Mcrit.Comment: 27 pages, 8 figures, 4 tables, submitted to PR

A New Waveform Consistency Test for Gravitational Wave Inspiral Searches

Searches for binary inspiral signals in data collected by interferometric gravitational wave detectors utilize matched filtering techniques. Although matched filtering is optimal in the case of stationary Gaussian noise, data from real detectors often contains "glitches" and episodes of excess noise which cause filter outputs to ring strongly. We review the standard \chi^2 statistic which is used to test whether the filter output has appropriate contributions from several different frequency bands. We then propose a new type of waveform consistency test which is based on the time history of the filter output. We apply one such test to the data from the first LIGO science run and show that it cleanly distinguishes between true inspiral waveforms and large-amplitude false signals which managed to pass the standard \chi^2 test.Comment: 10 pages, 6 figures, submitted to Classical and Quantum Gravity for the proceedings of the Eighth Gravitational Wave Data Analysis Workshop (GWDAW-8

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