Towards Rapid Parameter Estimation on Gravitational Waves from Compact Binaries using Interpolated Waveforms

Accurate parameter estimation of gravitational waves from coalescing compact binary sources is a key requirement for gravitational-wave astronomy. Evaluating the posterior probability density function of the binary's parameters (component masses, sky location, distance, etc.) requires computing millions of waveforms. The computational expense of parameter estimation is dominated by waveform generation and scales linearly with the waveform computational cost. Previous work showed that gravitational waveforms from non-spinning compact binary sources are amenable to a truncated singular value decomposition, which allows them to be reconstructed via interpolation at fixed computational cost. However, the accuracy requirement for parameter estimation is typically higher than for searches, so it is crucial to ascertain that interpolation does not lead to significant errors. Here we provide a proof of principle to show that interpolated waveforms can be used to recover posterior probability density functions with negligible loss in accuracy with respect to non-interpolated waveforms. This technique has the potential to significantly increase the efficiency of parameter estimation.Comment: 7 pages, 2 figure

Rapidly evaluating the compact-binary likelihood function via interpolation

Bayesian parameter estimation on gravitational waves from compact-binary coalescences (CBCs) typically requires millions of template waveform computations at different values of the parameters describing the binary. Sampling techniques such as Markov chain Monte Carlo and nested sampling evaluate likelihoods and, hence, compute template waveforms, serially; thus, the total computational time of the analysis scales linearly with that of template generation. Here we address the issue of rapidly computing the likelihood function of CBC sources with nonspinning components. We show how to efficiently compute the continuous likelihood function on the three-dimensional subspace of parameters on which it has a nontrivial dependence—the chirp mass, symmetric mass ratio and coalescence time—via interpolation. Subsequently, sampling this interpolated likelihood function is a significantly cheaper computational process than directly evaluating the likelihood; we report improvements in computational time of two to three orders of magnitude while keeping likelihoods accurate to ≲0.025%. Generating the interpolant of the likelihood function over a significant portion of the CBC mass space is computationally expensive but highly parallelizable, so the wall time can be very small relative to the time of a full parameter-estimation analysis

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

Early Advanced LIGO binary neutron-star sky localization and parameter estimation

2015 will see the first observations of Advanced LIGO and the start of the gravitational-wave (GW) advanced-detector era. One of the most promising sources for ground-based GW detectors are binary neutron-star (BNS) coalescences. In order to use any detections for astrophysics, we must understand the capabilities of our parameter-estimation analysis. By simulating the GWs from an astrophysically motivated population of BNSs, we examine the accuracy of parameter inferences in the early advanced-detector era. We find that sky location, which is important for electromagnetic follow-up, can be determined rapidly (~5 s), but that sky areas may be hundreds of square degrees. The degeneracy between component mass and spin means there is significant uncertainty for measurements of the individual masses and spins; however, the chirp mass is well measured (typically better than 0.1%).Comment: 4 pages, 2 figures. Published in the proceedings of Amaldi 1

Fatal infantile mitochondrial encephalomyopathy, hypertrophic cardiomyopathy and optic atrophy associated with a homozygous OPA1 mutation.

BACKGROUND: Infantile-onset encephalopathy and hypertrophic cardiomyopathy caused by mitochondrial oxidative phosphorylation defects are genetically heterogeneous with defects involving both the mitochondrial and nuclear genomes. OBJECTIVE: To identify the causative genetic defect in two sisters presenting with lethal infantile encephalopathy, hypertrophic cardiomyopathy and optic atrophy. METHODS: We describe a comprehensive clinical, biochemical and molecular genetic investigation of two affected siblings from a consanguineous family. Molecular genetic analysis was done by a combined approach involving genome-wide autozygosity mapping and next-generation exome sequencing. Biochemical analysis was done by enzymatic analysis and Western blot. Evidence for mitochondrial DNA (mtDNA) instability was investigated using long-range and real-time PCR assays. Mitochondrial cristae morphology was assessed with transmission electron microscopy. RESULTS: Both affected sisters presented with a similar cluster of neurodevelopmental deficits marked by failure to thrive, generalised neuromuscular weakness and optic atrophy. The disease progression was ultimately fatal with severe encephalopathy and hypertrophic cardiomyopathy. Mitochondrial respiratory chain complex activities were globally decreased in skeletal muscle biopsies. They were found to be homozygous for a novel c.1601T>G (p.Leu534Arg) mutation in the OPA1 gene, which resulted in a marked loss of steady-state levels of the native OPA1 protein. We observed severe mtDNA depletion in DNA extracted from the patients' muscle biopsies. Mitochondrial morphology was consistent with abnormal mitochondrial membrane fusion. CONCLUSIONS: We have established, for the first time, a causal link between a pathogenic homozygous OPA1 mutation and human disease. The fatal multisystemic manifestations observed further extend the complex phenotype associated with pathogenic OPA1 mutations, in particular the previously unreported association with hypertrophic cardiomyopathy. Our findings further emphasise the vital role played by OPA1 in mitochondrial biogenesis and mtDNA maintenance