P. R. Brady

Predictions for the Rates of Compact Binary Coalescences Observable by Ground-based Gravitational-wave Detectors

We present an up-to-date, comprehensive summary of the rates for all types of compact binary coalescence sources detectable by the initial and advanced versions of the ground-based gravitational-wave detectors LIGO and Virgo. Astrophysical estimates for compact-binary coalescence rates depend on a number of assumptions and unknown model parameters and are still uncertain. The most confident among these estimates are the rate predictions for coalescing binary neutron stars which are based on extrapolations from observed binary pulsars in our galaxy. These yield a likely coalescence rate of 100 Myr−1 per Milky Way Equivalent Galaxy (MWEG), although the rate could plausibly range from 1 Myr−1 MWEG−1 to 1000 Myr−1 MWEG−1 (Kalogera et al 2004 Astrophys. J. 601 L179; Kalogera et al 2004 Astrophys. J. 614 L137 (erratum)). We convert coalescence rates into detection rates based on data from the LIGO S5 and Virgo VSR2 science runs and projected sensitivities for our advanced detectors. Using the detector sensitivities derived from these data, we find a likely detection rate of 0.02 per year for Initial LIGO–Virgo interferometers, with a plausible range between 2 × 10−4 and 0.2 per year. The likely binary neutron–star detection rate for the Advanced LIGO–Virgo network increases to 40 events per year, with a range between 0.4 and 400 per year.

FINDCHIRP: an algorithm for detection of gravitational waves from inspiraling compact binaries

Matched-filter searches for gravitational waves from coalescing compact binaries by the LIGO Scientific Collaboration use the FINDCHIRP algorithm: an implementation of the optimal filter with innovations to account for unknown signal parameters and to improve performance on detector data that has nonstationary and non-Gaussian artifacts. We provide details on the FINDCHIRP algorithm as used in the search for subsolar mass binaries, binary neutron stars, neutron starblack hole binaries, and binary black holes.

Searching for periodic sources with LIGO

We investigate the computational requirements for all-sky, all-frequency searches for gravitational waves from spinning neutron stars, using archived data from interferometric gravitational wave detectors such as LIGO. These sources are expected to be weak, so the optimal strategy involves coherent accumulation of signal-to-noise using Fourier transforms of long stretches of data (months to years). Earth-motion-induced Doppler shifts, and intrinsic pulsar spindown, will reduce the narrow-band signal-to-noise by spreading power across many frequency bins; therefore, it is necessary to correct for these effects before performing the Fourier transform. The corrections can be implemented by a parametrized model, in which one does a search over a discrete set of parameter values (points in the parameter space of corrections). We define a metric on this parameter space, which can be used to determine the optimal spacing between points in a search; the metric is used to compute the number of independent parameter-space points Np that must be searched, as a function of observation time T. This method accounts automatically for correlations between the spindown and Doppler corrections. The number Np(T) depends on the maximum gravitational wave frequency and the minimum spindown age τ=f/f that the search can detect. The signal-to-noise ratio required, in order to have 99% confidence of a detection, also depends on Np(T). We find that for an all-sky, all-frequency search lasting T=10^7 s, this detection threshold is hc≈(4–5)h3/yr, where h3/yr is the corresponding 99% confidence threshold if one knows in advance the pulsar position and spin period. We define a coherent search, over some data stream of length T, to be one where we apply a correction, followed by a fast Fourier transform of the data, for every independent point in the parameter space. Given realistic limits on computing power, and assuming that data analysis proceeds at the same rate as data acquisition (e.g., 10 days of data gets analyzed in ∼10 days), we can place limitations on how much data can be searched coherently. In an all-sky search for pulsars having gravity-wave frequencies f ~1000 yr, one can coherently search ∼18 days of data on a teraflops computer. In contrast, a teraflops computer can only perform a ∼0.8-day coherent search for pulsars with frequencies f<~1 kHz and spindown ages as low as 40 yr. In addition to all-sky searches we consider coherent directed searches, where one knows in advance the source position but not the period. (Nearby supernova remnants and the galactic center are obvious places to look.) We show that for such a search, one gains a factor of ∼10 in observation time over the case of an all-sky search, given a 1 Tflops computer. The enormous computational burden involved in coherent searches indicates the need for alternative data analysis strategies. As an example we briefly discuss the implementation of a simple hierarchical search in the last section of the paper. Further work is required to determine the optimal approach.

Illuminating gravitational waves: A concordant picture of photons from a neutron star merger

GROWTH observations of GW170817 The gravitational wave event GW170817 was caused by the merger of two neutron stars (see the Introduction by Smith). In three papers, teams associated with the GROWTH (Global Relay of Observatories Watching Transients Happen) project present their observations of the event at wavelengths from x-rays to radio waves. Evans et al. used space telescopes to detect GW170817 in the ultraviolet and place limits on its x-ray flux, showing that the merger generated a hot explosion known as a blue kilonova. Hallinan et al. describe radio emissions generated as the explosion slammed into the surrounding gas within the host galaxy. Kasliwal et al. present additional observations in the optical and infrared and formulate a model for the event involving a cocoon of material expanding at close to the speed of light, matching the data at all observed wavelengths. Science, this issue p. 1565, p. 1579, p. 1559; see also p. 1554 Observations of a binary neutron star merger at multiple wavelengths can be explained by an off-axis relativistic cocoon model. Merging neutron stars offer an excellent laboratory for simultaneously studying strong-field gravity and matter in extreme environments. We establish the physical association of an electromagnetic counterpart (EM170817) with gravitational waves (GW170817) detected from merging neutron stars. By synthesizing a panchromatic data set, we demonstrate that merging neutron stars are a long-sought production site forging heavy elements by r-process nucleosynthesis. The weak gamma rays seen in EM170817 are dissimilar to classical short gamma-ray bursts with ultrarelativistic jets. Instead, we suggest that breakout of a wide-angle, mildly relativistic cocoon engulfing the jet explains the low-luminosity gamma rays, the high-luminosity ultraviolet-optical-infrared, and the delayed radio and x-ray emission. We posit that all neutron star mergers may lead to a wide-angle cocoon breakout, sometimes accompanied by a successful jet and sometimes by a choked jet.

A Case Study on the Use of Workflow Technologies for Scientific Analysis: Gravitational Wave Data Analysis

Modern scientific experiments acquire large amounts of data that must be analyzed in subtle and complicated ways to extract the best results. The Laser Interferometer Gravitational Wave Observatory (LIGO) is an ambitious effort to detect gravitational waves produced by violent events in the universe, such as the collision of two black holes or the explosion of supernovae [37,258]. The experiment records approximately 1 TB of data per day, which is analyzed by scientists in a collaboration that spans four continents. LIGO and distributed computing have grown up side by side over the past decade, and the analysis strategies adopted by LIGO scientists have been strongly influenced by the increasing power of tools to manage distributed computing resources and the workflows to run on them. In this chapter, we use LIGO as an application case study in workflow design and implementation. The software architecture outlined here has been used with great efficacy to analyze LIGO data [2–5] using dedicated computing facilities operated by the LIGO Scientific Collaboration, the LIGO Data Grid. It is just the first step, however. Workflow design and implementation lies at the interface between computing and traditional scientific activities. In the conclusion, we outline a few directions for future development and provide some long-term vision for applications related to gravitational wave data analysis.

Host Galaxies Catalog Used in LIGO Searches for Compact Binary Coalescence Events

An up-to-date catalog of nearby galaxies considered to be hosts of binary compact objects is provided, with complete information about sky position, distance, extinction-corrected blue luminosity, and error estimates. With our current understanding of binary evolution, rates of formation and coalescence for binary compact objects scale with massive-star formation, and hence the (extinction-corrected) blue luminosity of host galaxies. Coalescence events in binary compact objects are among the most promising gravitational-wave sources for ground-based gravitational-wave detectors such as LIGO. Our catalog and associated error estimates are important for the interpretation of analyses carried out for LIGO, in constraining the rates of compact binary coalescence, given an astrophysical population model for the sources considered. We discuss how the notion of effective distance, created to account for the antenna pattern of a gravitational-wave detector, must be used in conjunction with our catalog. We also note that the catalog provided can be used in other astronomical analysis of populations that scale with galaxy blue luminosity.

Testing gravitational-wave searches with numerical relativity waveforms: results from the first Numerical INJection Analysis (NINJA) project

The Numerical INJection Analysis (NINJA) project is a collaborative effort between members of the numerical relativity and gravitational-wave data analysis communities. The purpose of NINJA is to study the sensitivity of existing gravitational-wave search algorithms using numerically generated waveforms and to foster closer collaboration between the numerical relativity and data analysis communities. We describe the results of the first NINJA analysis which focused on gravitational waveforms from binary black hole coalescence. Ten numerical relativity groups contributed numerical data which were used to generate a set of gravitational-wave signals. These signals were injected into a simulated data set, designed to mimic the response of the initial LIGO and Virgo gravitational-wave detectors. Nine groups analysed this data using search and parameter-estimation pipelines. Matched filter algorithms, un-modelled-burst searches and Bayesian parameter estimation and model-selection algorithms were applied to the data. We report the efficiency of these search methods in detecting the numerical waveforms and measuring their parameters. We describe preliminary comparisons between the different search methods and suggest improvements for future NINJA analyses.

Search for gravitational-wave bursts associated with gamma-ray bursts using data from LIGO science run 5 and VIRGO science run 1.

We present the results of a search for gravitational-wave bursts associated with 137 gamma-ray bursts (GRBs) that were detected by satellite-based gamma-ray experiments during the fifth LIGO science run and first Virgo science run. The data used in this analysis were collected from 2005 November 4 to 2007 October 1, and most of the GRB triggers were from the Swift satellite. The search uses a coherent network analysis method that takes into account the different locations and orientations of the interferometers at the three LIGO-Virgo sites. We find no evidence for gravitational-wave burst signals associated with this sample of GRBs. Using simulated short-duration (<1 s) waveforms, we set upper limits on the amplitude of gravitational waves associated with each GRB. We also place lower bounds on the distance to each GRB under the assumption of a fixed energy emission in gravitational waves, with typical limits of D ~ 15 Mpc (E_GW^iso / 0.01 M_o c^2)^1/2 for emission at frequencies around 150 Hz, where the LIGO-Virgo detector network has best sensitivity. We present astrophysical interpretations and implications of these results, and prospects for corresponding searches during future LIGO-Virgo runs.

Radiative falloff in Schwarzschild-de Sitter space-time

We consider the time evolution of a scalar field propagating in Schwarzschild-de Sitter spacetime. At early times, the field behaves as if it were in pure Schwarzschild spacetime; the structure of spacetime far from the black hole has no influence on the evolution. In this early epoch, the fields initial outburst is followed by quasi-normal oscillations, and then by an inverse power-law decay. At intermediate times, the power-law behavior gives way to a faster, exponential decay. At late times, the field behaves as if it were in pure de Sitter spacetime; the structure of spacetime near the black hole no longer influences the evolution in a significant way. In this late epoch, the fields behavior depends on the value of the curvature-coupling constant xi. If xi is less than a critical value 3/16, the field decays exponentially, with a decay constant that increases with increasing xi. If xi > 3/16, the field oscillates with a frequency that increases with increasing xi; the amplitude of the field still decays exponentially, but the decay constant is independent of xi.

Extracting equation of state parameters from black hole-neutron star mergers. I. Nonspinning black holes

The late inspiral, merger, and ringdown of a black hole-neutron star (BHNS) system can provide information about the neutron-star equation of state (EOS). Candidate EOSs can be approximated by a parametrized piecewise-polytropic EOS above nuclear density, matched to a fixed low-density EOS; and we report results from a large set of BHNS inspiral simulations that systematically vary two parameters. To within the accuracy of the simulations, we find that, apart from the neutron-star mass, a single physical parameter Lambda, describing its deformability, can be extracted from the late inspiral, merger, and ringdown waveform. This parameter is related to the radius, mass, and l=2 Love number, k_2, of the neutron star by Lambda = 2k_2 R^5/3M_{NS}^5, and it is the same parameter that determines the departure from point-particle dynamics during the early inspiral. Observations of gravitational waves from BHNS inspiral thus restrict the EOS to a surface of constant Lambda in the parameter space, thickened by the measurement error. Using various configurations of a single Advanced LIGO detector, we find that neutron stars are distinguishable from black holes of the same mass and that Lambda^{1/5} or equivalently R can be extracted to 10-40% accuracy from single events for mass ratios of Q=2 and 3 at a distance of 100 Mpc, while with the proposed Einstein Telescope, EOS parameters can be extracted to accuracy an order of magnitude better.