Search

Leveraging the features of the GstLAL pipeline, we present the results of a matched filtering search for asymmetric binary black hole systems with heavily mis-aligned spins in LIGO and Virgo data taken during the third observing run. Our target systems show strong imprints of precession and current searches have non-optimal sensitivity in detecting them. After measuring the sensitivity improvement brought by our search over standard spin-aligned searches, we report the detection of 30 gravitational wave events already discovered in the latest Gravitational Wave Transient Catalogues. However, we do not find any additional significant gravitational wave candidates. Our results allow us to place an upper limit of $R_{90\%} = 0.28^{+0.33}_{-0.04}\;\; \mathrm{Gpc^{-3}yr^{-1}}$ on the merger rate of a hypothetical subpopulation of asymmetric, heavily precessing signals, not identified by other searches. Since our upper limit is consistent with the latest rate estimates from the LIGO-Virgo-KAGRA collaboration, our findings rule out the existence of a yet-to-be-discovered population of precessing binaries.

Astrophysically motivated population models for binary black hole observables are often insufficient to capture the imprints of multiple formation channels. This is mainly due to the strongly parametrized nature of such investigations. Using a non-parametric model for the joint population-level distributions of binary black hole component masses and effective inspiral spins, we find hints of multiple subpopulations in the third gravitational wave transient catalog. The higher (more positive) spin subpopulation is found to have a mass-spectrum without any feature at the $30-40M_{\odot}$, which is consistent with the predictions of isolated stellar binary evolution, simulations for which place the pile up due to pulsational pair-instability supernovae near $50M_{\odot}$ or higher. The other sub-population with effective spins closer to zero shows a feature at $30-40M_{\odot}$ and is consistent with binary black holes formed dynamically in globular clusters, which are expected to peak around $30M_{\odot}$. We also compute merger rates for these two subpopulations and find that they are consistent with the theoretical predictions of the corresponding formation channels. We validate our results by checking their robustness against variations of several model configurations and by analyzing large simulated catalogs with the same model.

Precession in Binary Black Holes (BBH) is caused by the failure of the Black Hole spins to be aligned and its study can open up new perspectives in gravitational waves (GW) astronomy, providing, among other advancements, a precise measure of distance and an accurate characterization of the BBH spins. However, detecting precessing signals is a highly non-trivial task, as standard matched filtering pipelines for GW searches are built on many assumptions that do not hold in the precessing case. This work details the upgrades made to the GstLAL pipeline to facilitate the search for precessing BBH signals. The implemented changes in the search statistics and in the signal consistency test are then described in detail. The performance of the upgraded pipeline is evaluated through two extensive searches of precessing signals, targeting two different regions in the mass space, and the consistency of the results is examined. Additionally, the benefits of the upgrades are assessed by comparing the sensitive volume of the precessing searches with two corresponding traditional aligned-spin searches. While no significant sensitivity improvement is observed for precessing binaries with mass ratio $q\lesssim 6$, a volume increase of up to 100\% is attainable for heavily asymmetric systems with largely misaligned spins. Furthermore, our findings suggest that the primary cause of degraded performance in an aligned-spin search targeting precessing signals is not a poor signal-to-noise-ratio recovery but rather the failure of the $\xi^2$ signal-consistency test. Our work paves the way for a large-scale search for precessing signals, which could potentially result in exciting future detections.

Multi-messenger searches for BNS and NSBH mergers are currently one of the most exciting areas of astronomy. The search for joint electromagnetic and neutrino counterparts to GWs has resumed with O4. To support this effort, public semi-automated data products are sent in near real-time and include localization and source properties to guide complementary observations. In preparation for O4, we have conducted a study using a simulated population of compact binaries and a MDC in the form of a real-time replay to optimize and profile the software infrastructure and scientific deliverables. End-to-end performance was tested, including data ingestion, running online search pipelines, performing annotations, and issuing alerts to the astrophysics community. We present an overview of the low-latency infrastructure and the performance of the data products that are now being released during O4 based on the MDC. We report the expected median latency for the preliminary alert of full bandwidth searches (29.5s) and show consistency and accuracy of released data products using the MDC. For the first time, we report the expected median latency for triggers from early warning searches (-3.1s), which are new in O4 and target neutron star mergers during inspiral phase. This paper provides a performance overview for LVK low-latency alert infrastructure and data products using the MDC and serves as a useful reference for the interpretation of O4 detections.

The speed of gravitational waves $v_g$ can be measured with the time delay between gravitational-wave detectors. Our study provides a more precise measurement of $v_g$ using gravitational-wave signals only, compared with previous studies. We select 52 gravitational-wave events that were detected with high confidence by at least two detectors in the first three observing runs (O1, O2, and O3) of Advanced LIGO and Advanced Virgo. We use Markov chain Monte Carlo and nested sampling to estimate the $v_g$ posterior distribution for each of those events. We then combine their posterior distributions to find the 90% credible interval of the combined $v_g$ distribution for which we obtain $0.99^{+0.02}_{-0.02}c$ without the use of more accurate sky localization from the electromagnetic signal associated with GW170817. Restricting attention to the 50 binary black hole events generates the same result, while the use of the electromagnetic sky localization for GW170817 gives a tighter constraint of $0.99^{+0.01}_{-0.02}c$. The abundance of gravitational wave events allows us to apply hierarchical Bayesian inference on the posterior samples to simultaneously constrain all nine coefficients for Lorentz violation in the nondispersive, nonbirefringent limit of the gravitational sector of the Standard-Model Extension test framework. We compare the hierarchical Bayesian inference method with other methods of combining limits on Lorentz violation in the gravity sector that are found in the literature., Comment: 17 pages, 4 figures, 3 tables

We develop a robust and self-consistent framework to extract and classify gravitational wave candidates from noisy data, for the purpose of assisting in real-time multi-messenger follow-ups during LIGO-Virgo-KAGRA's fourth observing run~(O4). Our formalism implements several improvements to the low latency calculation of the probability of astrophysical origin~(\PASTRO{}), so as to correctly account for various factors such as the sensitivity change between observing runs, and the deviation of the recovered template waveform from the true gravitational wave signal that can strongly bias said calculation. We demonstrate the high accuracy with which our new formalism recovers and classifies gravitational wave triggers, by analyzing replay data from previous observing runs injected with simulated sources of different categories. We show that these improvements enable the correct identification of the majority of simulated sources, many of which would have otherwise been misclassified. We carry out the aforementioned analysis by implementing our formalism through the \GSTLAL{} search pipeline even though it can be used in conjunction with potentially any matched filtering pipeline. Armed with robust and self-consistent \PASTRO{} values, the \GSTLAL{} pipeline can be expected to provide accurate source classification information for assisting in multi-messenger follow-up observations to gravitational wave alerts sent out during O4., Comment: v2 upload was accidental. revert back to v1

Starting from May 2023, the LIGO Scientific, Virgo and KAGRA Collaboration is planning to conduct the fourth observing run with improved detector sensitivities and an expanded detector network including KAGRA. Accordingly, it is vital to optimize the detection algorithm of low-latency search pipelines, increasing their sensitivities to gravitational waves from compact binary coalescences. In this work, we discuss several new features developed for ranking statistics of GstLAL-based inspiral pipeline, which mainly consist of: the signal contamination removal, the bank-$\xi^2$ incorporation, the upgraded $\rho-\xi^2$ signal model and the integration of KAGRA. An injection study demonstrates that these new features improve the pipeline's sensitivity by approximately 15% to 20%, paving the way to further multi-messenger observations during the upcoming observing run., Comment: 13pages, 6figures

GstLAL is a stream-based matched-filtering search pipeline aiming at the prompt discovery of gravitational waves from compact binary coalescences such as the mergers of black holes and neutron stars. Over the past three observation runs by the LIGO, Virgo, and KAGRA (LVK) collaboration, the GstLAL search pipeline has participated in several tens of gravitational wave discoveries. The fourth observing run (O4) is set to begin in May 2023 and is expected to see the discovery of many new and interesting gravitational wave signals which will inform our understanding of astrophysics and cosmology. We describe the current configuration of the GstLAL low-latency search and show its readiness for the upcoming observation run by presenting its performance on a mock data challenge. The mock data challenge includes 40 days of LIGO Hanford, LIGO Livingston, and Virgo strain data along with an injection campaign in order to fully characterize the performance of the search. We find an improved performance in terms of detection rate and significance estimation as compared to that observed in the O3 online analysis. The improvements are attributed to several incremental advances in the likelihood ratio ranking statistic computation and the method of background estimation., Comment: 19 pages, 21 figures

Next-generation ground-based gravitational-wave detectors, such as Cosmic Explorer (CE), are expected to be sensitive to gravitational-wave signals with frequencies as low as 5 Hz, allowing signals to spend a significant amount of time in the detector frequency band. As a result, the effects caused by the rotation of the Earth become increasingly important for such signals. Additionally, the length of the arms of these detectors can be comparable to the wavelength of detectable gravitational waves, which introduces frequency-dependent effects that are not significant in current-generation detectors. These effects are expected to improve the ability to localize compact binary coalescences in the sky even when using only one detector. This study aims to understand how much these effects can help in localization. We present the first comprehensive Bayesian parameter estimation framework that accounts for all these effects using \textsc{Bilby}, a commonly used Bayesian parameter estimation tool. We focus on sky localization constraints for binary neutron star events with an optimal signal-to-noise ratio of 1000 with one detector at the projected CE sensitivity. We find that these effects help localize sources using one detector with sky areas as low as 10 square degrees. Moreover, we explore and discuss how ignoring these effects in the parameter estimation can lead to biases in the inference., Comment: Version accepted by PRD

The observation of gravitational waves from multiple compact binary coalescences by the LIGO-Virgo-KAGRA detector networks has enabled us to infer the underlying distribution of compact binaries across a wide range of masses, spins, and redshifts. In light of the new features found in the mass spectrum of binary black holes and the uncertainty regarding binary formation models, non-parametric population inference has become increasingly popular. In this work, we develop a data-driven clustering framework that can identify features in the component mass distribution of compact binaries simultaneously with those in the corresponding redshift distribution, from gravitational wave data in the presence of significant measurement uncertainties, while making very few assumptions on the functional form of these distributions. Our generalized model is capable of inferring correlations among various population properties such as the redshift evolution of the shape of the mass distribution itself, in contrast to most existing non-parametric inference schemes. We test our model on simulated data and demonstrate the accuracy with which it can re-construct the underlying distributions of component masses and redshifts. We also re-analyze public LIGO-Virgo-KAGRA data from events in GWTC-3 using our model and compare our results with those from some alternative parametric and non-parametric population inference approaches. Finally, we investigate the potential presence of correlations between mass and redshift in the population of binary black holes in GWTC-3 (those observed by the LIGO-Virgo-KAGRA detector network in their first 3 observing runs), without making any assumptions about the specific nature of these correlations., Comment: Upload accepted version

Matched-filtering gravitational wave search pipelines identify gravitational wave signals by computing correlations, i.e., signal-to-noise ratios, between gravitational wave detector data and gravitational wave template waveforms. Intrinsic parameters, the component masses and spins, of the gravitational wave waveforms are often stored in "template banks", and the construction of a densely populated template bank is essential for some gravitational wave search pipelines. This paper presents a template bank that is currently being used by the GstLAL-based compact binary search pipeline in the fourth observing run of the LIGO, Virgo, and KAGRA collaboration, and was generated with a new binary tree approach of placing templates, {\fontfamily{qcr}\selectfont manifold}. The template bank contains $1.8 \times 10^6$ sets of template parameters covering plausible neutron star and black hole systems up to a total mass of $400$ $M_\odot$ with component masses between $1$-$200$ $M_\odot$ and mass ratios between $1$ and $20$ under the assumption that each component object's angular momentum is aligned with the orbital angular momentum. We validate the template bank generated with our new method, {\fontfamily{qcr}\selectfont manifold}, by comparing it with a template bank generated with the previously used stochastic template placement method. We show that both template banks have similar effectualness. The {\fontfamily{qcr}\selectfont GstLAL} search pipeline performs singular value decomposition (SVD) on the template banks to reduce the number of filters used. We describe a new grouping of waveforms that improves the computational efficiency of SVD by nearly $5$ times as compared to previously reported SVD sorting schemes.

Bayesian hierarchical inference of phenomenological parameterized neutron star equations of state (EoS) from multiple gravitational wave observations of binary neutron star mergers is of fundamental importance in improving our understanding of neutron star structure, the general properties of matter at supra nuclear densities and the strong nuclear force. However, such an analysis is computationally costly as it is unable to re-use single-event EoS agnostic parameter estimation runs that are carried out regardless for generating gravitational wave transient catalogs. With the number of events expected to be observable during the 4th observing run (O4) of LIGO/Virgo/KAGRA, this problem can only be expected to worsen. We develop a novel and robust algorithm for rapid and computationally cheap hierarchical inference of parameterized EoSs from gravitational wave data which re-uses single event EoS agnostic parameter estimation samples to significantly reduce computational cost. We efficiently include a priori knowledge of neutron star physics as Bayesian priors on the EoS parameters. The high speed and low computational cost of our method allow for efficient re-computation of EoS inference every time a new binary neutron star event is discovered or whenever new observations and theoretical discoveries change the prior on EoS parameters. We test our method on both real and simulated gravitational wave data to demonstrate its accuracy. We show that our computationally cheap method produces EoS constraints that are completely consistent with existing analysis for real data, the chosen fiducial EoS for simulated data. Armed with our fast analysis scheme, we also study the variability of EoS constraints with binary neutron star properties for sets of simulated events drawn in different signal-to-noise ratio and mass ranges.

We demonstrate a new geometric method for fast template placement for searches for gravitational waves from the inspiral, merger and ringdown of compact binaries. The method is based on a binary tree decomposition of the template bank parameter space into non-overlapping hypercubes. We use a numerical approximation of the signal overlap metric at the center of each hypercube to estimate the number of templates required to cover the hypercube and determine whether to further split the hypercube. As long as the expected number of templates in a given cube is greater than a given threshold, we split the cube along its longest edge according to the metric. When the expected number of templates in a given hypercube drops below this threshold, the splitting stops and a template is placed at the center of the hypercube. Using this method, we generate aligned-spin template banks covering the mass range suitable for a search of Advanced LIGO data. The aligned-spin bank required ~24 CPU-hours and produced 2 million templates. In general, we find that other methods, namely stochastic placement, produces a more strictly bounded loss in match between waveforms, with the same minimal match between waveforms requiring about twice as many templates with our proposed algorithm. Though we note that the average match is higher, which would lead to a higher detection efficiency. Our primary motivation is not to strictly minimize the number of templates with this algorithm, but rather to produce a bank with useful geometric properties in the physical parameter space coordinates. Such properties are useful for population modeling and parameter estimation.

Pulsar timing arrays (PTAs) are searching for gravitational waves from supermassive black hole binaries (SMBHBs). Here we show how future PTAs could use a detection of gravitational waves from individually resolved SMBHB sources to produce a purely gravitational wave-based measurement of the Hubble constant. This is achieved by measuring two separate distances to the same source from the gravitational wave signal in the timing residual: the luminosity distance $D_L$ through frequency evolution effects, and the parallax distance $D_\mathrm{par}$ through wavefront curvature (Fresnel) effects. We present a generalized timing residual model including these effects in an expanding universe. Of these two distances, $D_\mathrm{par}$ is challenging to measure due to the pulsar distance wrapping problem, a degeneracy in the Earth-pulsar distance and gravitational wave source parameters that requires highly precise, sub-parsec level, pulsar distance measurements to overcome. However, in this paper we demonstrate that combining the knowledge of two SMBHB sources in the timing residual largely removes the wrapping cycle degeneracy. Two sources simultaneously calibrate the PTA by identifying the distances to the pulsars, which is useful in its own right, and allow recovery of the source luminosity and parallax distances which results in a measurement of the Hubble constant. We find that, with optimistic PTAs in the era of the Square Kilometer Array, two SMBHB sources within a few hundred Mpc could be used to measure the Hubble constant with a relative uncertainty on the order of 10 per cent., Comment: 23 pages, 11 figures. Published by the Monthly Notices of the Royal Astronomical Society. arXiv admin note: text overlap with arXiv:2109.07603

We present a novel gravitational wave detection algorithm that conducts a matched filter search stochastically across the compact binary parameter space rather than relying on a fixed bank of template waveforms. This technique is competitive with standard template-bank-driven pipelines in both computational cost and sensitivity. However, the complexity of the analysis is simpler allowing for easy configuration and horizontal scaling across heterogeneous grids of computers. To demonstrate the method we analyze approximately one month of public LIGO data from July 27 00:00 2017 UTC - Aug 25 22:00 2017 UTC and recover eight known confident gravitational wave candidates. We also inject simulated binary black hole (BBH) signals to demonstrate the sensitivity., Comment: 12 pages, 6 figures

We present ${\tt nimbus}$ : a hierarchical Bayesian framework to infer the intrinsic luminosity parameters of kilonovae (KNe) associated with gravitational-wave (GW) events, based purely on non-detections. This framework makes use of GW 3-D distance information and electromagnetic upper limits from multiple surveys for multiple events, and self-consistently accounts for finite sky-coverage and probability of astrophysical origin. The framework is agnostic to the brightness evolution assumed and can account for multiple electromagnetic passbands simultaneously. Our analyses highlight the importance of accounting for model selection effects, especially in the context of non-detections. We show our methodology using a simple, two-parameter linear brightness model, taking the follow-up of GW190425 with the Zwicky Transient Facility (ZTF) as a single-event test case for two different prior choices of model parameters -- (i) uniform/uninformative priors and (ii) astrophysical priors based on surrogate models of Monte Carlo radiative transfer simulations of KNe. We present results under the assumption that the KN is within the searched region to demonstrate functionality and the importance of prior choice. Our results show consistency with ${\tt simsurvey}$ -- an astronomical survey simulation tool used previously in the literature to constrain the population of KNe. While our results based on uniform priors strongly constrain the parameter space, those based on astrophysical priors are largely uninformative, highlighting the need for deeper constraints. Future studies with multiple events having electromagnetic follow-up from multiple surveys should make it possible to constrain the KN population further., Comment: 18 pages, 5 figures, accepted for publication in ApJ

The discovery of the coalescence of binary neutron star GW170817 was a watershed moment in the field of gravitational wave astronomy. Among the rich variety of information that we were able to uncover from this discovery was the first non-electromagnetic measurement of the neutron star radius, and the cold nuclear equation of state. It also led to a large equation of state model-selection study from gravitational-wave data. In those studies Bayesian nested sampling runs were conducted for each candidate equation of state model to compute their evidence in the gravitational-wave data. Such studies, though invaluable, are computationally expensive and require repeated, redundant, computation for any new models. We present a novel technique to conduct model-selection of equation of state in an extremely rapid fashion (~minutes) on any arbitrary model. We test this technique against the results of a nested-sampling model-selection technique published earlier by the LIGO/Virgo collaboration, and show that the results are in good agreement with a median fractional error in Bayes factor of about 10%, where we assume that the true Bayes factor is calculated in the aforementioned nested sampling runs. We found that the highest fractional error occurs for equation of state models that have very little support in the posterior distribution, thus resulting in large statistical uncertainty. We then used this method to combine multiple binary neutron star mergers to compute a joint-Bayes factor between equation of state models. This is achieved by stacking the evidence of the individual events and computing the Bayes factor from these stacked evidences for each pairs of equation of state., Comment: Dataset produced in this study https://zenodo.org/record/4679013#.YHuUnJNKhsA

Merging supermassive black hole binaries produce low-frequency gravitational waves, which pulsar timing experiments are searching for. Much of the current theory is developed within the plane-wave formalism, and here we develop the more general Fresnel formalism. We show that Fresnel corrections to gravitational wave timing residual models allow novel measurements to be made, such as direct measurements of the source distance from the timing residual phase and frequency, as well as direct measurements of chirp mass from a monochromatic source. Probing the Fresnel corrections in these models will require future pulsar timing arrays with more distant pulsars across our Galaxy (ideally at the distance of the Magellanic Clouds), timed with precisions less than $100$ ns, with distance uncertainties reduced to the order of the gravitational wavelength. We find that sources with chirp mass of order $10^9 \ \mathrm{M}_\odot$ and orbital frequency $\omega_0 > 10$ nHz are good candidates for probing Fresnel corrections. With these conditions met, the measured source distance uncertainty can be made less than 10 per cent of the distance to the source for sources out to $\sim 100$ Mpc, source sky localization can be reduced to sub-arcminute precision, and source volume localization can be made to less than $1 \ \text{Mpc}^3$ for sources out to 1-Gpc distances., Comment: 28 pages, 11 figures, 1 supplementary document. Published by the Monthly Notices of the Royal Astronomical Society

The accurate localization of gravitational-wave (GW) events in low-latency is a crucial element in the search for further multimessenger signals from these cataclysmic events. The localization of these events in low-latency uses signal-to-noise ratio (SNR) time-series from matched-filtered searches which identify candidate events. Here we report on an improvement to the GstLAL-based inspiral pipeline, the low-latency pipeline that identified GW170817 and GW190425, which automates the use of SNRs from all detectors in the network in rapid localization of GW events. This improvement was incorporated into the detection pipeline prior to the recent third observing run of the Advanced LIGO and Advanced Virgo detector network. Previously for this pipeline, manual intervention was required to use SNRs from all detectors if a candidate GW event was below an SNR threshold for any detector in the network. The use of SNRs from subthreshold events can meaningfully decrease the area of the 90% confidence region estimated by rapid localization. To demonstrate this, we present a study of the simulated detections of $\mathcal{O}(2\times10^4)$ binary neutron stars using a network mirroring the second observational run of the Advanced LIGO and Virgo detectors. When incorporating subthreshold SNRs in rapid localization, we find that the fraction of events that can be localized down to $100~\mathrm{deg}^2$ or smaller increases by a factor 1.18.

We present updates to GstLAL, a matched filter gravitational-wave search pipeline, in Advanced LIGO and Virgo's third observing run. We discuss the incorporation of statistical data quality information into GstLAL's multi-dimensional likelihood ratio ranking statistic and additional improvements to search for gravitational wave candidates found in only one detector. Statistical data quality information is provided by iDQ, a data quality pipeline that infers the presence of short-duration transient noise in gravitational-wave data using the interferometer's auxiliary state, which has operated in near real-time since before LIGO's first observing run in 2015. We look at the performance and impact on noise rejection by the inclusion of iDQ information in GstLAL's ranking statistic, and discuss GstLAL results in the GWTC-2 catalog, focusing on two case studies; GW190424A, a single-detector gravitational-wave event found by GstLAL and a period of time in Livingston impacted by a thunderstorm., Comment: 8 pages, 5 figures

The GstLAL library, derived from Gstreamer and the LIGO Algorithm Library, supports a stream-based approach to gravitational-wave data processing. Although GstLAL was primarily designed to search for gravitational-wave signatures of merging black holes and neutron stars, it has also contributed to other gravitational-wave searches, data calibration, and detector-characterization efforts. GstLAL has played an integral role in all of the LIGO-Virgo collaboration detections, and its low-latency configuration has enabled rapid electromagnetic follow-up for dozens of compact binary candidates.

We perform Bayesian model selection with parameter estimation to identify potentially lensed gravitational-wave images from the second observing run (O2) of Advanced LIGO and Advanced Virgo. Specifically, we compute the Bayesian evidence for a pair of events being lensed or not lensed (unlensed) using nested sampling. We consider the discrete coalescence phase shifts that can be induced if the gravitational-wave signal interacts with the lens caustics in the model selection. We find that the pair of events, GW170104 and GW170814 with a $\pi/2$ coalescence phase shift, has a significant Bayes factor ($B^L_{U}$ $\sim 1.98 \times 10^4$) favoring the lensing hypothesis. However, after taking into account the long time delay of approximately 7 months between events, the timing Bayes factor is significantly small ($B_t \sim 8.7\times10^{-2}$). The prior probability for detecting strongly lensed pairs at O2 sensitivity are exceedingly small for both galaxy and galaxy cluster lensing. Combining the lensing and timing Bayes factors with the prior odds on lensing gives an odds ratio of $O^L_{U} \sim 20$. However, the model dependence of the timing and prior odds factors does not provide strong evidence to demonstrate that the pair is strongly lensed., Comment: 8 pages, 4 figures; references added; figures updated

Binary neutron stars (BNSs) will spend $\simeq 10$ -- 15 minutes in the band of Advanced LIGO and Virgo detectors at design sensitivity. Matched-filtering of gravitational-wave (GW) data could in principle accumulate enough signal-to-noise ratio (SNR) to identify a forthcoming event tens of seconds before the companions collide and merge. Here we report on the design and testing of an early warning gravitational-wave detection pipeline. Early warning alerts can be produced for sources that are at low enough redshift so that a large enough SNR accumulates $\sim 10 - 60\,\rm s$ before merger. We find that about 7% (respectively, 49%) of the total detectable BNS mergers will be detected $60\, \rm s$ ($10\, \rm s$) before the merger. About 2% of the total detectable BNS mergers will be detected before merger and localized to within $100\, \rm \text{deg}^2$ (90% credible interval). Coordinated observing by several wide-field telescopes could capture the event seconds before or after the merger. LIGO-Virgo detectors at design sensitivity could facilitate observing at least one event at the onset of merger., Comment: small update in numbers caused by using a more updated local BNS rate estimate

The speed of gravitational waves for a single observation can be measured by the time delay among gravitational-wave detectors with Bayesian inference. Then multiple measurements can be combined to produce a more accurate result. From the near simultaneous detection of gravitational waves and gamma rays originating from GW170817/GRB 170817A, the speed of gravitational wave signal was found to be the same as the the speed of the gamma rays to approximately one part in $10^{15}$. Here we present a different method of measuring the speed of gravitational waves, not based on an associated electromagnetic signal but instead by the measured transit time across a geographically separated network of detectors. While this method is far less precise, it provides an independent measurement of the speed of gravitational waves. For GW170817 a binary neutron star inspiral observed by Advanced LIGO and Advanced Virgo, by fixing sky localization of the source at the electromagnetic counterpart the speed of gravitational waves is constrained to 90% confidence interval (0.97c, 1.02c), where c is the speed of light in a vacuum. By combing seven BBH events and the BNS event from the second observing run of Advanced LIGO and Advanced Virgo, the 90% confidence interval is narrowed down to (0.97c, 1.01c). The accurate measurement of the speed of gravitational waves allows us to test the general theory of relativity. We further interpret these results within the test framework provided by the gravitational Standard-Model Extension (SME). In doing so, we obtain simultaneous constraints on 4 of the 9 nonbirefringent, nondispersive coefficients for Lorentz violation in the gravity sector of the SME and place limits on the anisotropy of the speed of gravity., Comment: 8 pages, 6 figures

The recently published GWTC-1 - a journal article summarizing the search for gravitational waves (GWs) from coalescing compact binaries in data produced by the LIGO-Virgo network of ground-based detectors during their first and second observing runs - quoted estimates for the rates of binary neutron star, neutron star black hole binary, and binary black hole mergers, as well as assigned probabilities of astrophysical origin for various significant and marginal GW candidate events. In this paper, we delineate the formalism used to compute these rates and probabilities, which assumes that triggers above a low ranking statistic threshold, whether of terrestrial or astrophysical origin, occur as independent Poisson processes. In particular, we include an arbitrary number of astrophysical categories by redistributing, via mass-based template weighting, the foreground probabilities of candidate events, across source classes. We evaluate this formalism on synthetic GW data, and demonstrate that this method works well for the kind of GW signals observed during the first and second observing runs., Comment: 19 pages, 5 figures

After their successful first observing run (September 12, 2015 - January 12, 2016), the Advanced LIGO detectors were upgraded to increase their sensitivity for the second observing run (November 30, 2016 - August 26, 2017). The Advanced Virgo detector joined the second observing run on August 1, 2017. We discuss the updates that happened during this period in the GstLAL-based inspiral pipeline, which is used to detect gravitational waves from the coalescence of compact binaries both in low latency and an offline configuration. These updates include deployment of a zero-latency whitening filter to reduce the over-all latency of the pipeline by up to 32 seconds, incorporation of the Virgo data stream in the analysis, introduction of a single-detector search to analyze data from the periods when only one of the detectors is running, addition of new parameters to the likelihood ratio ranking statistic, increase in the parameter space of the search, and introduction of a template mass-dependent glitch-excision thresholding method., Comment: 12 pages, 7 figures, to be submitted to Phys. Rev. D, comments welcome

Gravitational waves searches for compact binary mergers with LIGO and Virgo are presently a two stage process. First, a gravitational wave signal is identified. Then, an exhaustive search over possible signal parameters is performed. It is critical that the identification stage is efficient in order to maximize the number of gravitational wave sources that are identified. Initial identification of gravitational wave signals with LIGO and Virgo happens in real-time which requires that less than one second of computational time must be used for each one second of gravitational wave data collected. In contrast, subsequent parameter estimation may require hundreds of hours of computational time to analyze the same one second of gravitational wave data. The real-time identification requirement necessitates efficient and often approximate methods for signal analysis. We describe one piece of real-time gravitational-wave identification: an efficient method for ascertaining a signal's consistency between multiple gravitational wave detectors suitable for real-time gravitational wave searches for compact binary mergers. This technique was used in analyses of Advanced LIGO's second observing run and Advanced Virgo's first observing run.

We describe the methods used to construct the aligned-spin template bank of gravitational waveforms used by the GstLAL-based inspiral pipeline to analyze data from the second observing run of Advanced LIGO and the first observing run of advanced Virgo. The bank expands upon the parameter space covered during the first observing run, including coverage for merging compact binary systems with total mass between 2 $\mathrm{M}_{\odot}$ and 400 $\mathrm{M}_{\odot}$ and mass ratios between 1 and 97.988. Thus the systems targeted include merging neutron star-neutron star systems, neutron star-black hole binaries, and black hole-black hole binaries expanding into the intermediate-mass range. Component masses less than 2 $\mathrm{M}_{\odot}$ have allowed (anti-)aligned spins between $\pm0.05$ while component masses greater than 2 $\mathrm{M}_{\odot}$ have allowed (anti-)aligned between $\pm0.999$. The bank placement technique combines a stochastic method with a new grid-bank method to better isolate noisy templates, resulting in a total of 677,000 templates., Comment: 9 pages, 13 figures

We present quantities which characterize the sensitivity of gravitational-wave observatories to sources at cosmological distances. In particular, we introduce and generalize the horizon, range, response, and reach distances. These quantities incorporate a number of important effects, including cosmologically well-defined distances and volumes, cosmological redshift, cosmological time dilation, and rate density evolution. In addition, these quantities incorporate unique aspects of gravitational wave detectors, such as the variable sky sensitivity of the detectors and the scaling of the sensitivity with inverse distance. An online calculator (https://users.rcc.uchicago.edu/~dholz/gwc/) and python notebook (https://github.com/hsinyuc/distancetool) to determine GW distances are available. We provide answers to the question: "How far can gravitational-wave detectors hear?", Comment: Classical and Quantum Gravity accepted version

We describe a stream-based analysis pipeline to detect gravitational waves from the merger of binary neutron stars, binary black holes, and neutron-star-black-hole binaries within ~ 1 minute of the arrival of the merger signal at Earth. Such low-latency detection is crucial for the prompt response by electromagnetic facilities in order to observe any fading electromagnetic counterparts that might be produced by mergers involving at least one neutron star. Even for systems expected not to produce counterparts, low-latency analysis of the data is useful for deciding when not to point telescopes, and as feedback to observatory operations. Analysts using this pipeline were the first to identify GW151226, the second gravitational-wave event ever detected. The pipeline also operates in an offline mode, in which it incorporates more refined information about data quality and employs acausal methods that are inapplicable to the online mode. The pipeline's offline mode was used in the detection of the first two gravitational-wave events, GW150914 and GW151226, as well as the identification of a third candidate, LVT151012.

Supermassive black hole binaries, cosmic strings, relic gravitational waves from inflation, and first order phase transitions in the early universe are expected to contribute to a stochastic background of gravitational waves in the 10^(-9) Hz-10^(-7) Hz frequency band. Pulsar timing arrays (PTAs) exploit the high precision timing of radio pulsars to detect signals at such frequencies. Here we present a time-domain implementation of the optimal cross-correlation statistic for stochastic background searches in PTA data. Due to the irregular sampling typical of PTA data as well as the use of a timing model to predict the times-of-arrival of radio pulses, time-domain methods are better suited for gravitational wave data analysis of such data. We present a derivation of the optimal cross-correlation statistic starting from the likelihood function, a method to produce simulated stochastic background signals, and a rigorous derivation of the scaling laws for the signal-to-noise ratio of the cross-correlation statistic in the two relevant PTA regimes: the weak signal limit where instrumental noise dominates over the gravitational wave signal at all frequencies, and a second regime where the gravitational wave signal dominates at the lowest frequencies., Comment: 12 pages, 3 figures, submitted to Physical Review D

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., Comment: 14 pages, submitted to Phys. Rev. D

Using an extended set of equations of state and a multiple-group multiple-code collaborative effort to generate waveforms, we improve numerical-relativity-based data-analysis estimates of the measurability of matter effects in neutron-star binaries. We vary two parameters of a parameterized piecewise-polytropic equation of state (EOS) to analyze the measurability of EOS properties, via a parameter {\Lambda} that characterizes the quadrupole deformability of an isolated neutron star. We find that, to within the accuracy of the simulations, the departure of the waveform from point-particle (or spinless double black-hole binary) inspiral increases monotonically with {\Lambda}, and changes in the EOS that did not change {\Lambda} are not measurable. We estimate with two methods the minimal and expected measurability of {\Lambda} in second- and third- generation gravitational-wave detectors. The first estimate, using numerical waveforms alone, shows two EOS which vary in radius by 1.3km are distinguishable in mergers at 100Mpc. The second estimate relies on the construction of hybrid waveforms by matching to post-Newtonian inspiral, and estimates that the same EOS are distinguishable in mergers at 300Mpc. We calculate systematic errors arising from numerical uncertainties and hybrid construction, and we estimate the frequency at which such effects would interfere with template-based searches., Comment: 21 pages, 13 figures

We study the ability of the advanced Laser Interferometer Gravitational-wave Observatory (aLIGO) to detect apparent violations of the cosmic censorship conjecture and the no-hair theorem. The cosmic censorship conjecture, which is believed to be true in the theory of general relativity, limits the spin-to-mass-squared ratio of a Kerr black hole. The no-hair theorem, which is also believed to be true in the theory of general relativity, suggests a particular value for the tidal Love number of a non-rotating black hole. Using the Fisher matrix formalism, we examine the measurability of the spin and tidal deformability of compact binary systems involving at least one putative black hole. Using parameter measurement errors and correlations obtained from the Fisher matrix, we determine the smallest detectable violation of bounds implied by the cosmic censorship conjecture and the no-hair theorem. We examine the effect of excluding unphysical areas of parameter space when determining the smallest detectable apparent violations, and we examine the effect of different post-Newtonian corrections to the amplitude of the compact binary coalescence gravitational waveform. In addition, we perform a brief study of how the recently calculated 3.0 pN and 3.5 pN spin-orbit corrections to the phase affect spin and mass parameter measurability. We find that physical priors on the symmetric mass ratio and higher harmonics in the gravitational waveform could significantly affect the ability of aLIGO to investigate cosmic censorship and the no-hair theorem for certain systems., Comment: 21 pages, 7 figures, 6 tables

Supermassive black hole binaries (SMBHBs) are expected to emit continuous gravitational waves in the pulsar timing array (PTA) frequency band ($10^{-9}$--$10^{-7}$ Hz). The development of data analysis techniques aimed at efficient detection and characterization of these signals is critical to the gravitational wave detection effort. In this paper we leverage methods developed for LIGO continuous wave gravitational searches, and explore the use of the $\mathcal{F}$-statistic for such searches in pulsar timing data. Babak & Sesana 2012 have already used this approach in the context of PTAs to show that one can resolve multiple SMBHB sources in the sky. Our work improves on several aspects of prior continuous wave search methods developed for PTA data analysis. The algorithm is implemented fully in the time domain, which naturally deals with the irregular sampling typical of PTA data and avoids spectral leakage problems associated with frequency domain methods. We take into account the fitting of the timing model, and have generalized our approach to deal with both correlated and uncorrelated colored noise sources. We also develop an incoherent detection statistic that maximizes over all pulsar dependent contributions to the likelihood. To test the effectiveness and sensitivity of our detection statistics, we perform a number of monte-carlo simulations. We produce sensitivity curves for PTAs of various configurations, and outline an implementation of a fully functional data analysis pipeline. Finally, we present a derivation of the likelihood maximized over the gravitational wave phases at the pulsar locations, which results in a vast reduction of the search parameter space., Comment: 11 pages, 5 figures

Gravitational wave observations can potentially measure properties of neutron star equations of state by measuring departures from the point-particle limit of the gravitational waveform produced in the late inspiral of a neutron star binary. Numerical simulations of inspiraling neutron star binaries computed for equations of state with varying stiffness are compared. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly if the neutron stars are more compact. This suggests that gravitational wave observations at frequencies around 1 kHz will be able to measure a compactness parameter and place stringent bounds on possible neutron star equations of state. Advanced laser interferometric gravitational wave observatories will be able to tune their frequency band to optimize sensitivity in the required frequency range to make sensitive measures of the late-inspiral phase of the coalescence., Comment: Talk given at the 13th Conference on Recent Developments in Gravity (NEB XIII), Thessaloniki, Greece, 4-6 Jun 2008

The properties of neutron star matter above nuclear density are not precisely known. Gravitational waves emitted from binary neutron stars during their late stages of inspiral and merger contain imprints of the neutron-star equation of state. Measuring departures from the point-particle limit of the late inspiral waveform allows one to measure properties of the equation of state via gravitational wave observations. This and a companion talk by J. S. Read reports a comparison of numerical waveforms from simulations of inspiraling neutron-star binaries, computed for equations of state with varying stiffness. We calculate the signal strength of the difference between waveforms for various commissioned and proposed interferometric gravitational wave detectors and show that observations at frequencies around 1 kHz will be able to measure a compactness parameter and constrain the possible neutron-star equations of state., Comment: Talk given at the 12th Marcel Grossman Meeting, Paris, France, 12-18 Jul 2009

We report the results of a first study that uses numerical simulations to estimate the accuracy with which one can use gravitational wave observations of double neutron star inspiral to measure parameters of the neutron-star equation of state. The simulations use the evolution and initial-data codes of Shibata and Uryu to compute the last several orbits and the merger of neutron stars, with matter described by a parametrized equation of state. Previous work suggested the use of an effective cutoff frequency to place constraints on the equation of state. We find, however, that greater accuracy is obtained by measuring departures from the point-particle limit of the gravitational waveform produced during the late inspiral. As the stars approach their final plunge and merger, the gravitational wave phase accumulates more rapidly for smaller values of the neutron star compactness (the ratio of the mass of the neutron star to its radius). We estimate that realistic equations of state will lead to gravitational waveforms that are distinguishable from point particle inspirals at an effective distance (the distance to an optimally oriented and located system that would produce an equivalent waveform amplitude) of 100 Mpc or less. As Lattimer and Prakash observed, neutron-star radius is closely tied to the pressure at density not far above nuclear. Our results suggest that broadband gravitational wave observations at frequencies between 500 and 1000 Hz will constrain this pressure, and we estimate the accuracy with which it can be measured. Related first estimates of radius measurability show that the radius can be determined to an accuracy of ~1 km at 100 Mpc., Comment: 12 pages, 5 figures, to be submitted to Phys. Rev. D

A low frequency stochastic background of gravitational waves may be detected by pulsar timing experiments in the next five to ten years. Using methods developed to analyze interferometric gravitational wave data, in this paper we lay out the optimal techniques to detect a background of gravitational waves using a pulsar timing array. We show that for pulsar distances and gravitational wave frequencies typical of pulsar timing experiments, neglecting the effect of the metric perturbation at the pulsar does not result in a significant deviation from optimality. We discuss methods for setting upper limits using the optimal statistic, show how to construct skymaps using the pulsar timing array, and consider several issues associated with realistic analysis of pulsar timing data., Comment: 20 pages, 6 figures. Added figure with sky sensitivity for Parkes Pulsar Timing Array, included dipole overlap reduction function and derivation in appendix, extended likelihood discussion

A new generation of observatories is looking for gravitational waves. These waves, emitted by highly relativistic systems, will open a new window for ob- servation of the cosmos when they are detected. Among the most promising sources of gravitational waves for these observatories are compact binaries in the final min- utes before coalescence. In this article, we review in brief interferometric searches for gravitational waves emitted by neutron star binaries, including the theory, instru- mentation and methods. No detections have been made to date. However, the best direct observational limits on coalescence rates have been set, and instrumentation and analysis methods continue to be refined toward the ultimate goal of defining the new field of gravitational wave astronomy., Comment: 30 pages, 5 Figures, to appear in "Short-Period Binary Stars: Observations, Analyses, and Results", Ed.s Eugene F. Milone, Denis A. Leahy, David W. Hobill

The use of the loudest observed event to generate statistical statements about rate and strength has become standard in searches for gravitational waves from compact binaries and pulsars. The Bayesian formulation of the method is generalized in this paper to allow for uncertainties both in the background estimate and in the properties of the population being constrained. The method is also extended to allow rate interval construction. Finally, it is shown how to combine the results from multiple experiments and a comparison is drawn between the upper limit obtained in a single search and the upper limit obtained by combining the results of two experiments each of half the original duration. To illustrate this, we look at an example case, motivated by the search for gravitational waves from binary inspiral., Comment: 11 pages, 8 figures

We describe the current status of the search for gravitational waves from inspiralling compact binary systems in LIGO data. We review the result from the first scientific run of LIGO (S1). We present the goals of the search of data taken in the second scientific run (S2) and describe the differences between the methods used in S1 and S2., Comment: 9 pages, 2 figures. Published in proceedings of the 8th Gravitational Wave Data Analysis Workshop, Milwaukee, WI, USA, 17-20 December 2003

Activities in data analysis and numerical simulation of gravitational waves have to date largely proceeded independently. In this work we study how waveforms obtained from numerical simulations could be effectively used within the data analysis effort to search for gravitational waves from black hole binaries. We propose measures to quantify the accuracy of numerical waveforms for the purpose of data analysis and study how sensitive the analysis is to errors in the waveforms. We estimate that ~100 templates (and ~10 simulations with different mass ratios) are needed to detect waves from non-spinning binary black holes with total masses in the range 100 Msun < M < 400 Msun using initial LIGO. Of course, many more simulation runs will be needed to confirm that the correct physics is captured in the numerical evolutions. From this perspective, we also discuss sources of systematic errors in numerical waveform extraction and provide order of magnitude estimates for the computational cost of simulations that could be used to estimate the cost of parameter space surveys. Finally, we discuss what information from near-future numerical simulations of compact binary systems would be most useful for enhancing the detectability of such events with contemporary gravitational wave detectors and emphasize the role of numerical simulations for the interpretation of eventual gravitational-wave observations., Comment: 19 pages, 12 figures

We consider the stochastic background of gravitational waves produced by a network of cosmic strings and assess their accessibility to current and planned gravitational wave detectors, as well as to big bang nucleosynthesis (BBN), cosmic microwave background (CMB), and pulsar timing constraints. We find that current data from interferometric gravitational wave detectors, such as LIGO, are sensitive to areas of parameter space of cosmic string models complementary to those accessible to pulsar, BBN, and CMB bounds. Future more sensitive LIGO runs and interferometers such as Advanced LIGO and LISA will be able to explore substantial parts of the parameter space., Comment: Replaced with version accepted for publication in Physical Review Letters. 4 pages, 2 figures

We discuss data analysis techniques that can be used in the search for gravitational wave bursts from cosmic strings. When data from multiple interferometers are available, we describe consistency checks that can be used to greatly reduce the false alarm rates. We construct an expression for the rate of bursts for arbitrary cosmic string loop distributions and apply it to simple known solutions. The cosmology is solved exactly and includes the effects of a late-time acceleration. We find substantially lower burst rates than previous estimates suggest and explain the disagreement. Initial LIGO is unlikely to detect field theoretic cosmic strings with the usual loop sizes, though it may detect cosmic superstrings as well as cosmic strings and superstrings with non-standard loop sizes (which may be more realistic). In the absence of a detection, we show how to set upper limits based on the loudest event. Using Initial LIGO sensitivity curves, we show that these upper limits may result in interesting constraints on the parameter space of theories that lead to the production of cosmic strings., Comment: Replaced with version accepted for publication in PRD