The Advanced LIGO and Advanced Virgo gravitational wave (GW) detectors will begin operation in the coming years, with compact binary coalescence events a likely source for the first detections. The gravitational waveforms emitted directly encode information about the sources, including the masses and spins of the compact objects. Recovering the physical parameters of the sources from the GW observations is a key analysis task. This work describes the LALInference software library for Bayesian parameter estimation of compact binary signals, which builds on several previous methods to provide a well-tested toolkit which has already been used for several studies. We show that our implementation is able to correctly recover the parameters of compact binary signals from simulated data from the advanced GW detectors. We demonstrate this with a detailed comparison on three compact binary systems: a binary neutron star, a neutron star black hole binary and a binary black hole, where we show a cross-comparison of results obtained using three independent sampling algorithms. These systems were analysed with non-spinning, aligned spin and generic spin configurations respectively, showing that consistent results can be obtained even with the full 15-dimensional parameter space of the generic spin configurations. We also demonstrate statistically that the Bayesian credible intervals we recover correspond to frequentist confidence intervals under correct prior assumptions by analysing a set of 100 signals drawn from the prior. We discuss the computational cost of these algorithms, and describe the general and problem-specific sampling techniques we have used to improve the efficiency of sampling the compact binary coalescence parameter space.
Within the next five years, it is expected that the Advanced LIGO/Virgo network will have reached a sensitivity sufficient to enable the routine detection of gravitational waves. Beyond the initial detection, the scientific promise of these instruments relies on the effectiveness of our physical parameter estimation capabilities. The majority of this effort has been towards the detection and characterization of gravitational waves from compact binary coalescence, e.g. the coalescence of binary neutron stars. While several previous studies have investigated the accuracy of parameter estimation with advanced detectors, the majority have relied on approximation techniques such as the Fisher Matrix. Here we report the statistical uncertainties that will be achievable for optimal detection candidates (SNR = 20) using the full parameter estimation machinery developed by the LIGO/Virgo Collaboration via Markov-Chain Monte Carlo methods. We find the recovery of the individual masses to be fractionally within 9% (15%) at the 68% (95%) credible intervals for equal-mass systems, and within 1.9% (3.7%) for unequal-mass systems. We also find that the Advanced LIGO/Virgo network will constrain the locations of binary neutron star mergers to a median uncertainty of 5.1 deg^2 (13.5 deg^2) on the sky. This region is improved to 2.3 deg^2 (6 deg^2) with the addition of the proposed LIGO India detector to the network. We also report the average uncertainties on the luminosity distances and orbital inclinations of ideal detection candidates that can be achieved by different network configurations.
During the fifth science run of the Laser Interferometer Gravitational-wave Observatory (LIGO), signals modelling the gravitational waves emitted by coalescing non-spinning compact-object binaries were injected into the LIGO data stream. We analysed the data segments into which such injections were made using a Bayesian approach, implemented as a Markov-chain Monte-Carlo technique in our code SPINspiral. This technique enables us to determine the physical parameters of such a binary inspiral, including masses and spin, following a possible detection trigger. For the first time, we publish the results of a realistic parameter-estimation analysis of waveforms embedded in real detector noise. We used both spinning and non-spinning waveform templates for the data analysis and demonstrate that the intrinsic source parameters can be estimated with an accuracy of better than 1-3% in the chirp mass and 0.02-0.05 (8-20%) in the symmetric mass ratio if non-spinning waveforms are used. We also find a bias between the injected and recovered parameters, and attribute it to the difference in the post-Newtonian orders of the waveforms used for injection and analysis.
We present a Markov-chain Monte-Carlo (MCMC) technique to study the source parameters of gravitational-wave signals from the inspirals of stellar-mass compact binaries detected with ground-based gravitational-wave detectors such as LIGO and Virgo, for the case where spin is present in the more massive compact object in the binary. We discuss aspects of the MCMC algorithm that allow us to sample the parameter space in an efficient way. We show sample runs that illustrate the possibilities of our MCMC code and the difficulties that we encounter.
