Effects of calibration uncertainties on the detection and parameter estimation of isotropic gravitational-wave backgrounds

Gravitational-wave backgrounds are expected to arise from the superposition of gravitational wave signals from a large number of unresolved sources and also from the stochastic processes that occurred in the Early universe. So far, we have not detected any gravitational wave background, but with the improvements in the detectors' sensitivities, such detection is expected in the near future. The detection and inferences we draw from the search for a gravitational-wave background will depend on the source model, the type of search pipeline used, and the data generation in the gravitational-wave detectors. In this work, we focus on the effect of the data generation process, specifically the calibration of the detectors' digital output into strain data used by the search pipelines. Using the calibration model of the current LIGO detectors as an example, we show that for power-law source models and calibration uncertainties $\lesssim 10 \%$, the detection of isotropic gravitational wave background is not significantly affected. We also show that the source parameter estimation and upper limits calculations get biased. For calibration uncertainties of $\lesssim 5 \%$, the biases are not significant ($\lesssim 2 \%$), but for larger calibration uncertainties, they might become significant, especially when trying to differentiate between different models of isotropic gravitational-wave backgrounds.Comment: 11 pages, 7 figure

Wiener filtering with a seismic underground array at the Sanford Underground Research Facility

A seismic array has been deployed at the Sanford Underground Research Facility in the former Homestake mine, South Dakota, to study the underground seismic environment. This includes exploring the advantages of constructing a third-generation gravitational-wave detector underground. A major noise source for these detectors would be Newtonian noise, which is induced by fluctuations in the local gravitational field. The hope is that a combination of a low-noise seismic environment and coherent noise subtraction using seismometers in the vicinity of the detector could suppress the Newtonian noise to below the projected noise floor for future gravitational-wave detectors. In this paper, we use Wiener filtering techniques to subtract coherent noise in a seismic array in the frequency band 0.05 -- 1\,Hz. This achieves more than an order of magnitude noise cancellation over a majority of this band. We show how this subtraction would benefit proposed future low-frequency gravitational wave detectors. The variation in the Wiener filter coefficients over the course of the day, including how local activities impact the filter, is analyzed. We also study the variation in coefficients over the course of a month, showing the stability of the filter with time. How varying the filter order affects the subtraction performance is also explored. It is shown that optimizing filter order can significantly improve subtraction of seismic noise, which gives hope for future gravitational-wave detectors to address Newtonian noise

Method for estimation of gravitational-wave transient model parameters in frequency-time maps

A common technique for detection of gravitational-wave signals is searching for excess power in frequency-time maps of gravitational-wave detector data. In the event of a detection, model selection and parameter estimation will be performed in order to explore the properties of the source. In this paper, we develop a Bayesian statistical method for extracting model-dependent parameters from observed gravitational-wave signals in frequency-time maps. We demonstrate the method by recovering the parameters of model gravitational-wave signals added to simulated advanced LIGO noise. We also characterize the performance of the method and discuss prospects for future work

A Mock Data and Science Challenge for Detecting an Astrophysical Stochastic Gravitational-Wave Background with Advanced LIGO and Advanced Virgo

The purpose of this mock data and science challenge is to prepare the data analysis and science interpretation for the second generation of gravitational-wave experiments Advanced LIGO-Virgo in the search for a stochastic gravitational-wave background signal of astrophysical origin. Here we present a series of signal and data challenges, with increasing complexity, whose aim is to test the ability of current data analysis pipelines at detecting an astrophysically produced gravitational-wave background, test parameter estimation methods and interpret the results. We introduce the production of these mock data sets that includes a realistic observing scenario data set where we account for different sensitivities of the advanced detectors as they are continuously upgraded toward their design sensitivity. After analysing these with the standard isotropic cross-correlation pipeline we find that we are able to recover the injected gravitational-wave background energy density to within $2\sigma$ for all of the data sets and present the results from the parameter estimation. The results from this mock data and science challenge show that advanced LIGO and Virgo will be ready and able to make a detection of an astrophysical gravitational-wave background within a few years of operations of the advanced detectors, given a high enough rate of compact binary coalescing events

Long gravitational-wave transients and associated detection strategies for a network of terrestrial interferometers

Searches for gravitational waves (GWs) traditionally focus on persistent sources (e.g., pulsars or the stochastic background) or on transients sources (e.g., compact binary inspirals or core-collapse supernovae), which last for time scales of milliseconds to seconds. We explore the possibility of long GW transients with unknown waveforms lasting from many seconds to weeks. We propose a novel analysis technique to bridge the gap between short O(s) “burst” analyses and persistent stochastic analyses. Our technique utilizes frequency-time maps of GW strain cross power between two spatially separated terrestrial GW detectors. The application of our cross power statistic to searches for GW transients is framed as a pattern recognition problem, and we discuss several pattern-recognition techniques. We demonstrate these techniques by recovering simulated GW signals in simulated detector noise. We also recover environmental noise artifacts, thereby demonstrating a novel technique for the identification of such artifacts in GW interferometers. We compare the efficiency of this framework to other techniques such as matched filtering

Calibration Uncertainty for Advanced LIGO's First and Second Observing Runs

Calibration of the Advanced LIGO detectors is the quantification of the detectors' response to gravitational waves. Gravitational waves incident on the detectors cause phase shifts in the interferometer laser light which are read out as intensity fluctuations at the detector output. Understanding this detector response to gravitational waves is crucial to producing accurate and precise gravitational wave strain data. Estimates of binary black hole and neutron star parameters and tests of general relativity require well-calibrated data, as miscalibrations will lead to biased results. We describe the method of producing calibration uncertainty estimates for both LIGO detectors in the first and second observing runs.Comment: 15 pages, 21 figures, LIGO DCC P160013

Characterization of systematic error in Advanced LIGO calibration

The raw outputs of the detectors within the Advanced Laser Interferometer Gravitational-Wave Observatory need to be calibrated in order to produce the estimate of the dimensionless strain used for astrophysical analyses. The two detectors have been upgraded since the second observing run and finished the year-long third observing run. Understanding, accounting, and/or compensating for the complex-valued response of each part of the upgraded detectors improves the overall accuracy of the estimated detector response to gravitational waves. We describe improved understanding and methods used to quantify the response of each detector, with a dedicated effort to define all places where systematic error plays a role. We use the detectors as they stand in the first half (six months) of the third observing run to demonstrate how each identified systematic error impacts the estimated strain and constrain the statistical uncertainty therein. For this time period, we estimate the upper limit on systematic error and associated uncertainty to be $< 7\%$ in magnitude and $< 4$ deg in phase ($68\%$ confidence interval) in the most sensitive frequency band 20-2000 Hz. The systematic error alone is estimated at levels of $< 2\%$ in magnitude and $< 2$ deg in phase