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

Astrophysical Sources of Stochastic Gravitational-Wave Background

We review the spectral properties of stochastic backgrounds of astrophysical origin and discuss how they may differ from the primordial contribution by their statistical properties. We show that stochastic searches with the next generation of terrestrial interferometers could put interesting constrains on the physical properties of astrophysical populations, such as the ellipticity and magnetic field of magnetars, or the coalescence rate of compact binaries.Comment: 12 pages, 3 figures,accepted for publication in CQG, GWDAW12 conference proceedings version corrected in comparison published version where we found an error in equation (4

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.

Second Einstein Telescope Mock Science Challenge : Detection of the GW Stochastic Background from Compact Binary Coalescences

We present the results of the search for an astrophysical gravitational-wave stochastic background during the second Einstein Telescope mock data and science challenge. Assuming that the loudest sources can be detected individually and removed from the data, we show that the residual background can be recovered with an accuracy of $1$ with the standard cross-correlation statistic, after correction of a systematic bias due to the non-isotropy of the sources.Comment: 15 pages, 4 figures, accepted for publication in Physical Review

Searching Gravitational Waves from Pulsars, Using Laser Beam Interferometers

We use recent population synthesis results to investigate the distribution of pulsars in the frequency space, having a gravitational strain high enough to be detected by the future generations of laser beam interferometers. We find that until detectors become able to recover the entire population, the frequency distribution of the 'detectable' population will be very dependent on the detector noise curve. Assuming a mean equatorial deformation $\epsilon =10^{-6}$, the optimal frequency is around 450 Hz for interferometers of the first generation (LIGO or VIRGO) and shifts toward 85 Hz for advanced detectors. An interesting result for future detection stategies is the significant narrowing of the distribution when improving the sensitivity: with an advanced detector, it is possible to have 90% of detection probability while exploring less than 20% of the parameter space (7.5% in the case of $\epsilon =10^{-5}$). In addition, we show that in most cases the spindown of 'detectable' pulsars represents a period shift of less than a tens of nanoseconds after one year of observation, making them easier to follow in the frequency space.Comment: 5 pages, 3 figures accepted for publication in Astronomy & Astrophysic

Stochastic Gravitational Wave Background from Coalescing Binary Black Holes

We estimate the stochastic gravitational wave (GW) background signal from the field population of coalescing binary stellar mass black holes (BHs) throughout the Universe. This study is motivated by recent observations of BH-Wolf-Rayet star systems and by new estimates in the metallicity abundances of star forming galaxies that imply BH-BH systems are more common than previously assumed. Using recent analytical results of the inspiral-merger-ringdown waveforms for coalescing binary BH systems, we estimate the resulting stochastic GW background signal. Assuming average quantities for the single source energy emissions, we explore the parameter space of chirp mass and local rate density required for detection by advanced and third generation interferometric GW detectors. For an average chirp mass of 8.7$M_{\odot}$, we find that detection through 3 years of cross-correlation by two advanced detectors will require a rate density, $r_0 \geq 0.5 \rm{Mpc}^{-3} \rm{Myr}^{-1}$. Combining data from multiple pairs of detectors can reduce this limit by up to 40%. Investigating the full parameter space we find that detection could be achieved at rates $r_0 \sim 0.1 \rm{Mpc}^{-3} \rm{Myr}^{-1}$ for populations of coalescing binary BH systems with average chirp masses of $\sim 15M_{\odot}$ which are predicted by recent studies of BH-Wolf-Rayet star systems. While this scenario is at the high end of theoretical estimates, cross-correlation of data by two Einstein Telescopes could detect this signal under the condition $r_0 \geq 10^{-3} \rm{Mpc}^{-3} \rm{Myr}^{-1}$. Such a signal could potentially mask a primordial GW background signal of dimensionless energy density, $\Omega_{\rm{GW}}\sim 10^{-10}$, around the (1--500) Hz frequency range.Comment: 22 pages, 5 figures, 2 tables, Accepted for publication by Ap

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

Gravitation Wave Emission from Radio Pulsars Revisited

We report a new pulsar population synthesis based on Monte Carlo techniques, aiming to estimate the contribution of galactic radio pulsars to the continuous gravitational wave emission. Assuming that the rotation periods of pulsars at birth have a Gaussian distribution, we find that the average initial period is 290 ms. The number of objects with periods equal to or less than 0.4 s, and therefore capable of being detected by an interferometric gravitational antenna like VIRGO, is of the order of 5100-7800. With integration times lasting between 2 and 3 yr, our simulations suggest that about two detections should be possible, if the mean equatorial ellipticity of the pulsars is $\epsilon$ =10$^{-6}$. A mean ellipticity an order of magnitude higher increases the expected number of detections to 12-18, whereas for $\epsilon < 10^{-6}$, no detections are expectedComment: accepted for publication in A&A, 9 pages, 8 figure