The optimal search for an astrophysical gravitational-wave background

Roughly every 2-10 minutes, a pair of stellar mass black holes merge somewhere in the Universe. A small fraction of these mergers are detected as individually resolvable gravitational-wave events by advanced detectors such as LIGO and Virgo. The rest contribute to a stochastic background. We derive the statistically optimal search strategy for a background of unresolved binaries. Our method applies Bayesian parameter estimation to all available data. Using Monte Carlo simulations, we demonstrate that the search is both "safe" and effective: it is not fooled by instrumental artefacts such as glitches, and it recovers simulated stochastic signals without bias. Given realistic assumptions, we estimate that the search can detect the binary black hole background with about one day of design sensitivity data versus $\approx 40$ months using the traditional cross-correlation search. This framework independently constrains the merger rate and black hole mass distribution, breaking a degeneracy present in the cross-correlation approach. The search provides a unified framework for population studies of compact binaries, which is cast in terms of hyper-parameter estimation. We discuss a number of extensions and generalizations including: application to other sources (such as binary neutron stars and continuous-wave sources), simultaneous estimation of a continuous Gaussian background, and applications to pulsar timing.Comment: 16 pages, 9 figure

Fast Simulation of Gaussian-Mode Scattering for Precision Interferometry

Understanding how laser light scatters from realistic mirror surfaces is crucial for the design, com- missioning and operation of precision interferometers, such as the current and next generation of gravitational-wave detectors. Numerical simulations are indispensable tools for this task but their utility can in practice be limited by the computational cost of describing the scattering process. In this paper we present an efficient method to significantly reduce the computational cost of optical simulations that incorporate scattering. This is accomplished by constructing a near optimal representation of the complex, multi-parameter 2D overlap integrals that describe the scattering process (referred to as a reduced order quadrature). We demonstrate our technique by simulating a near-unstable Fabry-Perot cavity and its control signals using similar optics to those installed in one of the LIGO gravitational-wave detectors. We show that using reduced order quadrature reduces the computational time of the numerical simulation from days to minutes (a speed-up of $\approx 2750 \times$) whilst incurring negligible errors. This significantly increases the feasibility of modelling interferometers with realistic imperfections to overcome current limits in state-of-the-art optical systems. Whilst we focus on the Hermite-Gaussian basis for describing the scattering of the optical fields, our method is generic and could be applied with any suitable basis. An implementation of this reduced order quadrature method is provided in the open source interferometer simulation software Finesse.Comment: 15 pages, 11 figure

Parallelized Inference for Gravitational-Wave Astronomy

Bayesian inference is the workhorse of gravitational-wave astronomy, for example, determining the mass and spins of merging black holes, revealing the neutron star equation of state, and unveiling the population properties of compact binaries. The science enabled by these inferences comes with a computational cost that can limit the questions we are able to answer. This cost is expected to grow. As detectors improve, the detection rate will go up, allowing less time to analyze each event. Improvement in low-frequency sensitivity will yield longer signals, increasing the number of computations per event. The growing number of entries in the transient catalog will drive up the cost of population studies. While Bayesian inference calculations are not entirely parallelizable, key components are embarrassingly parallel: calculating the gravitational waveform and evaluating the likelihood function. Graphical processor units (GPUs) are adept at such parallel calculations. We report on progress porting gravitational-wave inference calculations to GPUs. Using a single code - which takes advantage of GPU architecture if it is available - we compare computation times using modern GPUs (NVIDIA P100) and CPUs (Intel Gold 6140). We demonstrate speed-ups of $\sim 50 \times$ for compact binary coalescence gravitational waveform generation and likelihood evaluation and more than $100\times$ for population inference within the lifetime of current detectors. Further improvement is likely with continued development. Our python-based code is publicly available and can be used without familiarity with the parallel computing platform, CUDA.Comment: 5 pages, 4 figures, submitted to PRD, code can be found at https://github.com/ColmTalbot/gwpopulation https://github.com/ColmTalbot/GPUCBC https://github.com/ADACS-Australia/ADACS-SS18A-RSmith Add demonstration of improvement in BNS spi

Measuring eccentricity in binary black hole inspirals with gravitational waves

When binary black holes form in the field, it is expected that their orbits typically circularize before coalescence. In galactic nuclei and globular clusters, binary black holes can form dynamically. Recent results suggest that $\approx5\%$ of mergers in globular clusters result from three-body interactions. These three-body interactions are expected to induce significant orbital eccentricity $\gtrsim 0.1$ when they enter the Advanced LIGO band at a gravitational-wave frequency of 10 Hz. Measurements of binary black hole eccentricity therefore provide a means for determining whether or not dynamic formation is the primary channel for producing binary black hole mergers. We present a framework for performing Bayesian parameter estimation on gravitational-wave observations of black hole inspirals. Using this framework, and employing the non-spinning, inspiral-only EccentricFD waveform approximant, we determine the minimum detectable eccentricity for an event with masses and distance similar to GW150914. At design sensitivity, we find that the current generation of advanced observatories will be sensitive to orbital eccentricities of $\gtrsim0.05$ at a gravitational-wave frequency of 10 Hz, demonstrating that existing detectors can use eccentricity to distinguish between circular field binaries and globular cluster triples. We compare this result to eccentricity distributions predicted to result from three black hole binary formation channels, showing that measurements of eccentricity could be used to infer the population properties of binary black holes.Comment: 12 pages, 7 figures, 2 table

An analysis and visualization of the output mode-matching requirements for squeezing in Advanced LIGO and future gravitational wave detectors

The sensitivity of ground-based gravitational wave (GW) detectors will be improved in the future via the injection of frequency-dependent squeezed vacuum. The achievable improvement is ultimately limited by losses of the interferometer electromagnetic field that carries the GW signal. The analysis and reduction of optical loss in the GW signal chain will be critical for optimal squeezed light-enhanced interferometry. In this work we analyze a strategy for reducing output-side losses due to spatial mode mismatch between optical cavities with the use of adaptive optics. Our goal is not to design a detector from the top down, but rather to minimize losses within the current design. Accordingly, we consider actuation on optics already present and one transmissive optic to be added between the signal recycling mirror and the output mode cleaner. The results of our calculation show that adaptive mode-matching with the current Advanced LIGO design is a suitable strategy for loss reduction that provides less than 2% mean output mode-matching loss. The range of actuation required is +47 uD on SR3, +140 mD on OM1 and OM2, +50 mD on the SRM substrate, and -50 mD on the added new transmissive optic. These requirements are within the demonstrated ranges of real actuators in similar or identical configurations to the proposed implementation. We also present a novel technique that graphically illustrates the matching of interferometer modes and allows for a quantitative comparison of different combinations of actuators.Comment: Matches version accepted in PR