T. B. Littenberg

Testing general relativity with present and future astrophysical observations

One century after its formulation, Einsteins general relativity (GR) has made remarkable predictions and turned out to be compatible with all experimental tests. Most of these tests probe the theory in the weak-field regime, and there are theoretical and experimental reasons to believe that GR should be modified when gravitational fields are strong and spacetime curvature is large. The best astrophysical laboratories to probe strong-field gravity are black holes and neutron stars, whether isolated or in binary systems. We review the motivations to consider extensions of GR. We present a (necessarily incomplete) catalog of modified theories of gravity for which strong-field predictions have been computed and contrasted to Einsteins theory, and we summarize our current understanding of the structure and dynamics of compact objects in these theories. We discuss current bounds on modified gravity from binary pulsar and cosmological observations, and we highlight the potential of future gravitational wave measurements to inform us on the behavior of gravity in the strong-field regime.

Low-frequency gravitational-wave science with eLISA/NGO

We review the expected science performance of the New Gravitational-Wave Observatory (NGO, a.k.a. eLISA), a mission under study by the European Space Agency for launch in the early 2020s. eLISA will survey the low-frequency gravitational-wave sky (from 0.1 mHz to 1 Hz), detecting and characterizing a broad variety of systems and events throughout the Universe, including the coalescences of massive black holes brought together by galaxy mergers; the inspirals of stellar-mass black holes and compact stars into central galactic black holes; several millions of ultra-compact binaries, both detached and mass transferring, in the Galaxy; and possibly unforeseen sources such as the relic gravitational-wave radiation from the early Universe. eLISAs high signal-to-noise measurements will provide new insight into the structure and history of the Universe, and they will test general relativity in its strong-field dynamical regime.

Parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library

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 analyzed with nonspinning, 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 analyzing 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.

Basic Parameter Estimation of Binary Neutron Star Systems by the Advanced LIGO/Virgo Network

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. A major part of this effort has been toward 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 which are insensitive to the non-Gaussian nature of the gravitational wave posterior distribution function. Here we report average statistical uncertainties that will be achievable for strong detection candidates (S/N = 20) over a comprehensive sample of source parameters. We use the Markov Chain Monte Carlo based parameter estimation software developed by the LIGO/Virgo Collaboration with the goal of updating the previously quoted Fisher Matrix bounds. 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 strong detections that can be achieved by different network configurations.

Tests of Bayesian model selection techniques for gravitational wave astronomy

The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a gravitational wave signal. The analysis of data from ground based gravitational wave detectors is mostly conducted using classical statistics, and methods such as the Neyman-Peterson criteria are used for model selection. Future space based detectors, such as the Laser Interferometer Space Antenna (LISA), are expected to produce rich data streams containing the signals from many millions of sources. Determining the number of sources that are resolvable, and the most appropriate description of each source poses a challenging model selection problem that may best be addressed in a Bayesian framework. An important class of LISA sources are the millions of low-mass binary systems within our own galaxy, tens of thousands of which will be detectable. Not only are the number of sources unknown, but so are the number of parameters required to model the waveforms. For example, a significant subset of the resolvable galactic binaries will exhibit orbital frequency evolution, while a smaller number will have measurable eccentricity. In the Bayesian approach to model selection one needs to compute the Bayes factor between competing models. Here we explore various methods for computing Bayes factors in the context of determining which galactic binaries have measurable frequency evolution. The methods explored include a reverse jump Markov chain Monte Carlo algorithm, Savage-Dickie density ratios, the Schwarz-Bayes information criterion, and the Laplace approximation to the model evidence. We find good agreement between all of the approaches.

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.

Bayesian inference for spectral estimation of gravitational wave detector noise

Gravitational wave data from ground-based detectors is dominated by instrument noise. Signals will be comparatively weak, and our understanding of the noise will influence detection confidence and signal characterization. Mis-modeled noise can produce large systematic biases in both model selection and parameter estimation. Here we introduce a multi-component, variable dimension, parameterized model to describe the Gaussian-noise power spectrum for data from ground-based gravitational wave interferometers. Called BayesLine, the algorithm models the noise power spectral density using cubic splines for smoothly varying broad-band noise and Lorentzians for narrow-band line features in the spectrum. We describe the algorithm and demonstrate its performance on data from the fifth and sixth LIGO science runs. Once fully integrated into LIGO/Virgo data analysis software, BayesLine will produce accurate spectral estimation and provide a means for marginalizing inferences drawn from the data over all plausible noise spectra.

Robust parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library

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 analyzed with nonspinning, 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 analyzing 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.

An overview of the second round of the Mock LISA Data Challenges

The Mock Data Challenges (MLDCs) have the dual purpose of fostering the development of LISA data-analysis tools and capabilities and of demonstrating the technical readiness already achieved by the gravitational-wave community in distilling a rich science payoff from the LISA data. The first round of MLDCs has just been completed and the second-round data sets are being released shortly after this workshop. The second-round data sets contain radiation from an entire Galactic population of stellar-mass binary systems, from massive-black-hole binaries, and from extreme-mass-ratio inspirals. These data sets are designed to capture much of the complexity that is expected in the actual LISA data, and should provide a fairly realistic setting to test advanced data-analysis techniques, and in particular the global aspect of the analysis. Here we describe the second round of MLDCs and provide details about its implementation.

Systematic biases in parameter estimation of binary black-hole mergers

Parameter estimation of binary black-hole merger events in gravitational-wave data relies on matchedfiltering techniques which, in turn, depend on accurate model waveforms. Here we characterize the systematic biases introduced in measuring astrophysical parameters of binary black holes by applying the currently most accurate effective-one-body templates to simulated data containing nonspinning numericalrelativity waveforms. We quantify the systematic bias by using a Markov chain Monte Carlo algorithm to sample the posterior distribution function of noise-free data, and compare the offset of the maximum a priori waveform parameters (the bias) to the width of the distribution, which we refer to as the statistical error. For advanced ground-based detectors, we find that the systematic biases arewell within the statistical error for realistic signal-to-noise ratios. These biases grow to be comparable to the statistical errors at high ground-based-instrument signal-to-noise ratios (SNR � 50), but never dominate the error budget. At the much larger signal-to-noise ratios expected for space-based detectors, these biases will become large compared to the statistical errors, but for astrophysical black hole mass estimates the absolute biases (of at most a few percent) are still fairly small.