On the (In)Efficiency of the Cross-Correlation Statistic for Gravitational Wave Stochastic Background Signals with Non-Gaussian Noise and Heterogeneous Detector Sensitivities

Under standard assumptions including stationary and serially uncorrelated Gaussian gravitational wave stochastic background signal and noise distributions, as well as homogenous detector sensitivities, the standard cross-correlation detection statistic is known to be optimal in the sense of minimizing the probability of a false dismissal at a fixed value of the probability of a false alarm. The focus of this paper is to analyze the comparative efficiency of this statistic, versus a simple alternative statistic obtained by cross-correlating the \textit{squared} measurements, in situations that deviate from such standard assumptions. We find that differences in detector sensitivities have a large impact on the comparative efficiency of the cross-correlation detection statistic, which is dominated by the alternative statistic when these differences reach one order of magnitude. This effect holds even when both the signal and noise distributions are Gaussian. While the presence of non-Gaussian signals has no material impact for reasonable parameter values, the relative inefficiency of the cross-correlation statistic is less prominent for fat-tailed noise distributions but it is magnified in case noise distributions have skewness parameters of opposite signs. Our results suggest that introducing an alternative detection statistic can lead to noticeable sensitivity gains when noise distributions are possibly non-Gaussian and/or when detector sensitivities exhibit substantial differences, a situation that is expected to hold in joint detections from Advanced LIGO and Advanced Virgo, in particular in the early phases of development of the detectors, or in joint detections from Advanced LIGO and Einstein Telescope.Comment: 36 pages, 5 figures and 1 table, accepted for publication in Physical Review

A Semi-Parametric Approach to the Detection of Non-Gaussian Gravitational Wave Stochastic Backgrounds

Using a semi-parametric approach based on the fourth-order Edgeworth expansion for the unknown signal distribution, we derive an explicit expression for the likelihood detection statistic in the presence of non-normally distributed gravitational wave stochastic backgrounds. Numerical likelihood maximization exercises based on Monte-Carlo simulations for a set of large tail symmetric non-Gaussian distributions suggest that the fourth cumulant of the signal distribution can be estimated with reasonable precision when the ratio between the signal and the noise variances is larger than 0.01. The estimation of higher-order cumulants of the observed gravitational wave signal distribution is expected to provide additional constraints on astrophysical and cosmological models.Comment: 26 pages, 3 figures, to appear in Phys. Rev.

Measuring neutron-star ellipticity with measurements of the stochastic gravitational-wave background

Galactic neutron stars are a promising source of gravitational waves in the analysis band of detectors such as LIGO and Virgo. Previous searches for gravitational waves from neutron stars have focused on the detection of individual neutron stars, which are either nearby or highly non-spherical. Here we consider the stochastic gravitational-wave signal arising from the ensemble of Galactic neutron stars. Using a population synthesis model, we estimate the single-sigma sensitivity of current and planned gravitational-wave observatories to average neutron star ellipticity $\epsilon$ as a function of the number of in-band Galactic neutron stars $N_\text{tot}$. For the plausible case of $N_\text{tot}\approx 53000$, and assuming one year of observation time with colocated initial LIGO detectors, we find it to be $\sigma_\epsilon=2.1\times10^{-7}$, which is comparable to current bounds on some nearby neutron stars. (The current best $95\%$ upper limits are $\epsilon\lesssim7\times10^{-8}.$) It is unclear if Advanced LIGO can significantly improve on this sensitivity using spatially separated detectors. For the proposed Einstein Telescope, we estimate that $\sigma\epsilon=5.6\times10^{-10}$. Finally, we show that stochastic measurements can be combined with measurements of individual neutron stars in order to estimate the number of in-band Galactic neutron stars. In this way, measurements of stochastic gravitational waves provide a complementary tool for studying Galactic neutron stars

Parameter Estimation in Searches for the Stochastic Gravitational-Wave Background

The stochastic gravitational-wave background (SGWB) is expected to arise from the superposition of many independent and unresolved gravitational-wave signals of either cosmological or astrophysical origin. The spectral content of the SGWB carries signatures of the physics that generated it. We present a Bayesian framework for estimating the parameters associated with different SGWB models using data from gravitational-wave detectors. We apply this technique to recent results from LIGO to produce the first simultaneous 95% confidence level limits on multiple parameters in generic power-law SGWB models and in SGWB models of compact binary coalescences. We also estimate the sensitivity of the upcoming second-generation detectors such as Advanced LIGO/Virgo to these models and demonstrate how SGWB measurements can be combined and compared with observations of individual compact binary coalescences in order to build confidence in the origin of an observed SGWB signal. In doing so, we demonstrate a novel means of differentiating between different sources of the SGWB.Comment: 6 pages, 5 figure

The stochastic background from cosmic (super)strings: popcorn and (Gaussian) continuous regimes

In the era of the next generation of gravitational wave experiments a stochastic background from cusps of cosmic (super)strings is expected to be probed and, if not detected, to be significantly constrained. A popcorn-like background can be, for part of the parameter space, as pronounced as the (Gaussian) continuous contribution from unresolved sources that overlap in frequency and time. We study both contributions from unresolved cosmic string cusps over a range of frequencies relevant to ground based interferometers, such as LIGO/Virgo second generation (AdLV) and Einstein Telescope (ET) third generation detectors, the space antenna LISA and Pulsar Timing Arrays (PTA). We compute the sensitivity (at $2 \sigma$ level) in the parameter space for AdLV, ET, LISA and PTA. We conclude that the popcorn regime is complementary to the continuous background. Its detection could therefore enhance confidence in a stochastic background detection and possibly help determine fundamental string parameters such as the string tension and the reconnection probability.Comment: 21 pages, 11 figures ; revised version after correction of a typo in eq. 4.

Statistical properties of astrophysical gravitational-wave backgrounds

We investigate how a stochastic gravitational-wave background, produced from a discrete set of astrophysical sources, differs from an idealized model consisting of an isotropic, unpolarized, and Gaussian background. We focus, in particular, on the different signatures produced from these two cases, as observed in a cross-correlation search. We show that averaged over many realizations of an astrophysical background, the cross-correlation measurement of an astrophysical background is identical to that of an idealized background. However, any one realization of an astrophysical background can produce a different signature. Using a model consisting of an ensemble of binary neutron star coalescences, we quantify the typical difference between the signal from individual realizations of the astrophysical background and the idealized case. For advanced detectors, we find that, using a cross-correlation analysis, astrophysical backgrounds from many discrete sources are probably indistinguishable from an idealized background

LISACode : A scientific simulator of LISA

A new LISA simulator (LISACode) is presented. Its ambition is to achieve a new degree of sophistication allowing to map, as closely as possible, the impact of the different sub-systems on the measurements. LISACode is not a detailed simulator at the engineering level but rather a tool whose purpose is to bridge the gap between the basic principles of LISA and a future, sophisticated end-to-end simulator. This is achieved by introducing, in a realistic manner, most of the ingredients that will influence LISA's sensitivity as well as the application of TDI combinations. Many user-defined parameters allow the code to study different configurations of LISA thus helping to finalize the definition of the detector. Another important use of LISACode is in generating time series for data analysis developments

Detection regimes of the cosmological gravitational wave background from astrophysical sources

Key targets for gravitational wave (GW) observatories, such as LIGO and the next generation interferometric detector, Advanced LIGO, include core-collapse of massive stars and the final stage of coalescence of compact stellar remnants. The combined GW signal from such events occurring throughout the Universe will produce an astrophysical GW background (AGB), one that is fundamentally different from the GW background by very early Universe processes. One can classify contributions to the AGB for different classes of sources based on the strength of the GW emissions from the individual sources, their peak emission frequency, emission duration and their event rate density distribution. This article provides an overview of the detectability regimes of the AGB in the context of current and planned gravitational wave observatories. We show that there are two important AGB signal detection regimes, which we define as `continuous' and `popcorn noise'. We describe how the `popcorn noise' AGB regime evolves with observation time and we discuss how this feature distinguishes it from the GW background produced from very early Universe processes.Comment: accepted for publication in New Astronomy Reviews; 23 pages and 2 figure

Targeted search for the stochastic gravitational-wave background from the galactic millisecond pulsar population

The millisecond pulsars, old-recycled objects spinning with high frequency $\mathcal{O}$(kHz) sustaining the deformation from their spherical shape, may emit gravitational-waves (GW). These are one of the potential candidates contributing to the anisotropic stochastic gravitational-wave background (SGWB) observable in the ground-based GW detectors. Here, we present the results from a likelihood-based targeted search for the SGWB due to millisecond pulsars in the Milky Way, by analyzing the data from the first three observing runs of Advanced LIGO and Advanced Virgo detector. We assume that the shape of SGWB power spectra and the sky distribution is known a priori from the population synthesis model. The information of the ensemble source properties, i.e., the in-band number of pulsars, $N_{obs}$ and the averaged ellipticity, $\mu_\epsilon$ is encoded in the maximum likelihood statistic. We do not find significant evidence for the SGWB signal from the considered source population. The best Bayesian upper limit with $95\%$ confidence for the parameters are $N_{obs}\leq8.8\times10^{4}$ and $\mu_\epsilon\leq1.1\times10^{-7}$, which is comparable to the bounds on mean ellipticity with the GW observations of the individual pulsars. Finally, we show that for the plausible case of $N_{obs}=40,000$, with the one year of observations, the one-sigma sensitivity on $\mu_\epsilon$ might reach $10^{-8}$ and $2.7\times10^{-9}$ for the second-generation detector network having A+ sensitivity and third-generation detector network respectively.Comment: 13 pages, 3 figures, 1 tabl