TIGER: A data analysis pipeline for testing the strong-field dynamics of general relativity with gravitational wave signals from coalescing compact binaries

The direct detection of gravitational waves with upcoming second-generation gravitational wave detectors such as Advanced LIGO and Virgo will allow us to probe the genuinely strong-field dynamics of general relativity (GR) for the first time. We present a data analysis pipeline called TIGER (Test Infrastructure for GEneral Relativity), which is designed to utilize detections of compact binary coalescences to test GR in this regime. TIGER is a model-independent test of GR itself, in that it is not necessary to compare with any specific alternative theory. It performs Bayesian inference on two hypotheses: the GR hypothesis $\mathcal{H}_{\rm GR}$, and $\mathcal{H}_{\rm modGR}$, which states that one or more of the post-Newtonian coefficients in the waveform are not as predicted by GR. By the use of multiple sub-hypotheses of $\mathcal{H}_{\rm modGR}$, in each of which a different number of parameterized deformations of the GR phase are allowed, an arbitrarily large number of 'testing parameters' can be used without having to worry about a model being insufficiently parsimonious if the true number of extra parameters is in fact small. TIGER is well-suited to the regime where most sources have low signal-to-noise ratios, again through the use of these sub-hypotheses. Information from multiple sources can trivially be combined, leading to a stronger test. We focus on binary neutron star coalescences, for which sufficiently accurate waveform models are available that can be generated fast enough on a computer to be fit for use in Bayesian inference. We show that the pipeline is robust against a number of fundamental, astrophysical, and instrumental effects, such as differences between waveform approximants, a limited number of post-Newtonian phase contributions being known, the effects of neutron star spins and tidal deformability on the orbital motion, and instrumental calibration errors.Comment: 12 pages, 9 figures. Version as appears in Phys. Rev.

Nested sampling with normalizing flows for gravitational-wave inference

We present a novel method for sampling iso-likelihood contours in nested sampling using a type of machine learning algorithm known as normalizing flows and incorporate it into our sampler nessai. nessai is designed for problems where computing the likelihood is computationally expensive and therefore the cost of training a normalizing flow is offset by the overall reduction in the number of likelihood evaluations. We validate our sampler on 128 simulated gravitational wave signals from compact binary coalescence and show that it produces unbiased estimates of the system parameters. Subsequently, we compare our results to those obtained with dynesty and find good agreement between the computed log-evidences while requiring 2.07 times fewer likelihood evaluations. We also highlight how the likelihood evaluation can be parallelized in nessai without any modifications to the algorithm. Finally, we outline diagnostics included in nessai and how these can be used to tune the sampler’s settings

Importance nested sampling with normalising flows

We present an improved version of the nested sampling algorithm nessai in which the core algorithm is modified to use importance weights. In the modified algorithm, samples are drawn from a mixture of normalising flows and the requirement for samples to be independently and identically distributed (i.i.d.) according to the prior is relaxed. Furthermore, it allows for samples to be added in any order, independently of a likelihood constraint, and for the evidence to be updated with batches of samples. We call the modified algorithm i-nessai. We first validate i-nessai using analytic likelihoods with known Bayesian evidences and show that the evidence estimates are unbiased in up to 32 dimensions. We compare i-nessai to standard nessai for the analytic likelihoods and the Rosenbrock likelihood, the results show that i-nessai is consistent with nessai whilst producing more precise evidence estimates. We then test i-nessai on 64 simulated gravitational-wave signals from binary black hole coalescence and show that it produces unbiased estimates of the parameters. We compare our results to those obtained using standard nessai and dynesty and find that i-nessai requires 2.68 and 13.3 times fewer likelihood evaluations to converge, respectively. We also test i-nessai of an 80-second simulated binary neutron star signal using a Reduced-Order-Quadrature (ROQ) basis and find that, on average, it converges in 24 minutes, whilst only requiring 1.01 × 106 likelihood evaluations compared to 1.42 × 106 for nessai and 4.30 × 107 for dynesty. These results demonstrate the i-nessai is consistent with nessai and dynesty whilst also being more efficient

The First Two Years of Electromagnetic Follow-Up with Advanced LIGO and Virgo

We anticipate the first direct detections of gravitational waves (GWs) with Advanced LIGO and Virgo later this decade. Though this groundbreaking technical achievement will be its own reward, a still greater prize could be observations of compact binary mergers in both gravitational and electromagnetic channels simultaneously. During Advanced LIGO and Virgo's first two years of operation, 2015 through 2016, we expect the global GW detector array to improve in sensitivity and livetime and expand from two to three detectors. We model the detection rate and the sky localization accuracy for binary neutron star (BNS) mergers across this transition. We have analyzed a large, astrophysically motivated source population using real-time detection and sky localization codes and higher-latency parameter estimation codes that have been expressly built for operation in the Advanced LIGO/Virgo era. We show that for most BNS events the rapid sky localization, available about a minute after a detection, is as accurate as the full parameter estimation. We demonstrate that Advanced Virgo will play an important role in sky localization, even though it is anticipated to come online with only one-third as much sensitivity as the Advanced LIGO detectors. We find that the median 90% confidence region shrinks from ~500 square degrees in 2015 to ~200 square degrees in 2016. A few distinct scenarios for the first LIGO/Virgo detections emerge from our simulations.Comment: 17 pages, 11 figures, 5 tables. For accompanying data, see http://www.ligo.org/scientists/first2year

Parameter estimation on gravitational waves from neutron-star binaries with spinning components

Inspiraling binary neutron stars are expected to be one of the most significant sources of gravitational-wave signals for the new generation of advanced ground-based detectors. We investigate how well we could hope to measure properties of these binaries using the Advanced LIGO detectors, which began operation in September 2015. We study an astrophysically motivated population of sources (binary components with masses $1.2~\mathrm{M}_\odot$--$1.6~\mathrm{M}_\odot$ and spins of less than $0.05$) using the full LIGO analysis pipeline. While this simulated population covers the observed range of potential binary neutron-star sources, we do not exclude the possibility of sources with parameters outside these ranges; given the existing uncertainty in distributions of mass and spin, it is critical that analyses account for the full range of possible mass and spin configurations. We find that conservative prior assumptions on neutron-star mass and spin lead to average fractional uncertainties in component masses of $\sim 16\%$, with little constraint on spins (the median $90\%$ upper limit on the spin of the more massive component is $\sim 0.7$). Stronger prior constraints on neutron-star spins can further constrain mass estimates, but only marginally. However, we find that the sky position and luminosity distance for these sources are not influenced by the inclusion of spin; therefore, if LIGO detects a low-spin population of BNS sources, less computationally expensive results calculated neglecting spin will be sufficient for guiding electromagnetic follow-up.Comment: 10 pages, 9 figure

Parameterized tests of the strong-field dynamics of general relativity using gravitational wave signals from coalescing binary black holes: Fast likelihood calculations and sensitivity of the method

Thanks to the recent discoveries of gravitational wave signals from binary black hole mergers by Advanced Laser Interferometer Gravitational Wave Observatory and Advanced Virgo, the genuinely strong-field dynamics of spacetime can now be probed, allowing for stringent tests of general relativity (GR). One set of tests consists of allowing for parametrized deformations away from GR in the template waveform models and then constraining the size of the deviations, as was done for the detected signals in previous work. In this paper, we construct reduced-order quadratures so as to speed up likelihood calculations for parameter estimation on future events. Next, we explicitly demonstrate the robustness of the parametrized tests by showing that they will correctly indicate consistency with GR if the theory is valid. We also check to what extent deviations from GR can be constrained as information from an increasing number of detections is combined. Finally, we evaluate the sensitivity of the method to possible violations of GR.Comment: 19 pages, many figures. Matches PRD versio

The British Transplantation Society guidelines on ethics, law and consent in relation to deceased donors after circulatory death

The British Transplantation Society (BTS) 'Guideline on transplantation from deceased donors after circulatory death' has recently been updated and this manuscript summarises the relevant recommendations from chapters specifically related to law, ethics, donor consent and informing the recipient

Overview of Advanced LIGO Adaptive Optics

This is an overview of the adaptive optics used in Advanced LIGO (aLIGO), known as the thermal compensation system (TCS). The thermal compensation system was designed to minimize thermally-induced spatial distortions in the interferometer optical modes and to provide some correction for static curvature errors in the core optics of aLIGO. The TCS is comprised of ring heater actuators, spatially tunable CO$_{2}$ laser projectors and Hartmann wavefront sensors. The system meets the requirements of correcting for nominal distortion in Advanced LIGO to a maximum residual error of 5.4nm, weighted across the laser beam, for up to 125W of laser input power into the interferometer