Stochastic Gravitational Wave Signal Research Articles

The quark chemical potential of QCD phase transition and the stochastic background of gravitational waves

The detection of stochastic background of gravitational waves (GWs), produced by cosmological phase transitions (PTs), is of fundamental importance because allows to probe the physics related to PT energy scales. Motivated by the decisive role of non-zero quark chemical potential towards understanding physics in the core of neutron stars, quark stars and heavy-ion collisions, in this paper we qualitatively explore the stochastic background of GW spectrum generated by a cosmological source such as high-density QCD first order PT during the early Universe. Specifically, we calculate the frequency peak fpeak redshifted at today time and the fractional energy density Ωgwh2 in light of equation-of-state improved by the finite quark (baryon) chemical potential (we consider an effective three flavor chiral quarks model of QCD). Our calculations reveal a striking increase in fpeak and Ωgwh2 due to the quark chemical potential, which means to improve the chances of detection, in possible future observations (in particular SKA/PTA experiments), of the stochastic background of GWs from QCD first order PT. Even if the improvements could be weak, by updating the sensitivity of relevant detectors in the future, we can still remain hopeful. Concerning the phenomenological contribution of QCD equation-of-state, and in particular the possibility to detect a stochastic GW signal, we further show that the role of the quark chemical potential is model-dependent. This feature allows to discriminate among possible QCD effective models depending on their capability to shed light on the dynamic of QCD-PT through future observations of primordial GWs. In this perspective, the results are indeed encouraging to employ the GWs to study the QCD PT in high density strong interaction matter.

Impact of correlated magnetic noise on the detection of stochastic gravitational waves: Estimation based on a simple analytical model

After the first direct detection of gravitational waves (GW), detection of stochastic background of GWs is an important next step, and the first GW event suggests that it is within the reach of the second-generation ground-based GW detectors. Such a GW signal is typically tiny, and can be detected by cross-correlating the data from two spatially separated detectors if the detector noise is uncorrelated. It has been advocated, however, that the global magnetic fields in the Earth-ionosphere cavity produce the environmental disturbances at low-frequency bands, known as Schumann resonances, which potentially couple with GW detectors. In this paper, we present a simple analytical model to estimate its impact on the detection of stochastic GWs. The model crucially depends on the geometry of the detector pair through the directional coupling, and we investigate the basic properties of the correlated magnetic noise based on the analytic expressions. The model reproduces the major trend of the recently measured global correlation between the GW detectors via magnetometer. The estimated values of the impact of correlated noise also match those obtained from the measurement. Finally, we give an implication to the detection of stochastic GWs including upcoming detectors, KAGRA and LIGO India. The model suggests that LIGO Hanford-Virgo and Virgo-KAGRA pairs are possibly less sensitive to the correlated noise, and can achieve a better sensitivity to the stochastic GW signal in the most pessimistic case.

Upper Limits on the Stochastic Gravitational-Wave Background from Advanced LIGO's First Observing Run.

A wide variety of astrophysical and cosmological sources are expected to contribute to a stochastic gravitational-wave background. Following the observations of GW150914 and GW151226, the rate and mass of coalescing binary black holes appear to be greater than many previous expectations. As a result, the stochastic background from unresolved compact binary coalescences is expected to be particularly loud. We perform a search for the isotropic stochastic gravitational-wave background using data from Advanced Laser Interferometer Gravitational Wave Observatory's (aLIGO) first observing run. The data display no evidence of a stochastic gravitational-wave signal. We constrain the dimensionless energy density of gravitational waves to be Ω_{0}<1.7×10^{-7} with 95%confidence, assuming a flat energy density spectrum in the most sensitive part of the LIGO band (20-86Hz). This is a factor of ∼33 times more sensitive than previous measurements. We also constrain arbitrary power-law spectra. Finally, we investigate the implications of this search for the background of binary black holes using an astrophysical model for the background.

All correlations must die: Assessing the significance of a stochastic gravitational-wave background in pulsar timing arrays

We present two methods for determining the significance of a stochastic gravitational-wave (GW) background affecting a pulsar-timing array, where detection is based on evidence for quadrupolar spatial correlations between pulsars. Rather than constructing noise simulations, we eliminate the GWB spatial correlations in the true datasets to assess detection significance with all real data features intact. In our first method, we perform random phase shifts in the signal-model basis functions. This phase shifting eliminates signal phase coherence between pulsars, while keeping the statistical properties of the pulsar timing residuals intact. We then explore a method to null correlations between pulsars by using a "scrambled" overlap-reduction function in the signal model for the array. This scrambled function is orthogonal to what we expect of a real GW background signal. We demonstrate the efficacy of these methods using Bayesian model selection on a set of simulated datasets that contain a stochastic GW signal, timing noise, undiagnosed glitches, and uncertainties in the Solar system ephemeris. Finally, we introduce an overarching formalism under which these two techniques are naturally linked. These methods are immediately applicable to all current pulsar-timing array datasets, and should become standard tools for future analyses.

Towards robust gravitational wave detection with pulsar timing arrays

Precision timing of highly stable milli-second pulsars is a promising technique for the detection of very low frequency sources of gravitational waves. In any single pulsar, a stochastic gravitational wave signal appears as an additional source of timing noise that can be absorbed by the noise model, and so it is only by considering the coherent response across a network of pulsars that the signal can be distinguished from other sources of noise. In the limit where there are many gravitational wave sources in the sky, or many pulsars in the array, the signals produce a unique tensor correlation pattern that depends only on the angular separation between each pulsar pair. It is this distinct fingerprint that is used to search for gravitational waves using pulsar timing arrays. Here we consider how the prospects for detection are diminished when the statistical isotropy of the timing array or the gravitational wave signal is broken by having a finite number of pulsars and a finite number of sources. We find the standard tensor-correlation analysis to be remarkably robust, with a mild impact on detectability compared to the isotropic limit. Only when there are very few sources and very few pulsars does the standard analysis begin to fail. Having established that the tensor correlations are a robust signature for detection, we study the use of "sky-scrambles" to break the correlations as a way to increase confidence in a detection. This approach is analogous to the use of "time-slides" in the analysis of data from ground based interferometric detectors.

Constraining the solution to the last parsec problem with pulsar timing

The detection of a stochastic gravitational-wave signal from the superposition of many inspiraling supermassive black holes with pulsar timing arrays (PTAs) is likely to occur within the next decade. With this detection will come the opportunity to learn about the processes that drive black-hole-binary systems toward merger through their effects on the gravitational-wave spectrum. We use Bayesian methods to investigate the extent to which effects other than gravitational-wave emission can be distinguished using PTA observations. We show that, even in the absence of a detection, it is possible to place interesting constraints on these dynamical effects for conservative predictions of the population of tightly bound supermassive black-hole binaries. For instance, if we assume a relatively weak signal consistent with a low number of bound binaries and a low black-hole-mass to galaxy-mass correlation, we still find that a non-detection by a simulated array, with a sensitivity that should be reached in practice within a few years, disfavors gravitational-wave-dominated evolution with an odds ratio of $\sim$30:1. Such a finding would suggest either that all existing astrophysical models for the population of tightly bound binaries are overly optimistic, or else that some dynamical effect other than gravitational-wave emission is actually dominating binary evolution even at the relatively high frequencies/small orbital separations probed by PTAs.

Searching for stochastic gravitational waves using data from the two colocated LIGO Hanford detectors

Searches for a stochastic gravitational-wave background (SGWB) using terrestrial detectors typically involve cross-correlating data from pairs of detectors. The sensitivity of such cross-correlation analyses depends, among other things, on the separation between the two detectors: the smaller the separation, the better the sensitivity. Hence, a co-located detector pair is more sensitive to a gravitational-wave background than a non-co-located detector pair. However, co-located detectors are also expected to suffer from correlated noise from instrumental and environmental effects that could contaminate the measurement of the background. Hence, methods to identify and mitigate the effects of correlated noise are necessary to achieve the potential increase in sensitivity of co-located detectors. Here we report on the first SGWB analysis using the two LIGO Hanford detectors and address the complications arising from correlated environmental noise. We apply correlated noise identification and mitigation techniques to data taken by the two LIGO Hanford detectors, H1 and H2, during LIGO's fifth science run. At low frequencies, 40 - 460 Hz, we are unable to sufficiently mitigate the correlated noise to a level where we may confidently measure or bound the stochastic gravitational-wave signal. However, at high frequencies, 460-1000 Hz, these techniques are sufficient to set a $95%$ confidence level (C.L.) upper limit on the gravitational-wave energy density of \Omega(f)<7.7 x 10^{-4} (f/ 900 Hz)^3, which improves on the previous upper limit by a factor of $\sim 180$. In doing so, we demonstrate techniques that will be useful for future searches using advanced detectors, where correlated noise (e.g., from global magnetic fields) may affect even widely separated detectors.

Improved upper limits on the stochastic gravitational-wave background from 2009-2010 LIGO and Virgo data.

Gravitational waves from a variety of sources are predicted to superpose to create a stochastic background. This background is expected to contain unique information from throughout the history of the Universe that is unavailable through standard electromagnetic observations, making its study of fundamental importance to understanding the evolution of the Universe. We carry out a search for the stochastic background with the latest data from the LIGO and Virgo detectors. Consistent with predictions from most stochastic gravitational-wave background models, the data display no evidence of a stochastic gravitational-wave signal. Assuming a gravitational-wave spectrum of Ω_{GW}(f)=Ω_{α}(f/f_{ref})^{α}, we place 95% confidence level upper limits on the energy density of the background in each of four frequency bands spanning 41.5-1726Hz. In the frequency band of 41.5-169.25Hz for a spectral index of α=0, we constrain the energy density of the stochastic background to be Ω_{GW}(f)<5.6×10^{-6}. For the 600-1000Hz band, Ω_{GW}(f)<0.14(f/900 Hz)^{3}, a factor of 2.5 lower than the best previously reported upper limits. We find Ω_{GW}(f)<1.8×10^{-4} using a spectral index of zero for 170-600Hz and Ω_{GW}(f)<1.0(f/1300 Hz)^{3} for 1000-1726Hz, bands in which no previous direct limits have been placed. The limits in these four bands are the lowest direct measurements to date on the stochastic background. We discuss the implications of these results in light of the recent claim by the BICEP2 experiment of the possible evidence for inflationary gravitational waves.

Cosmological signatures of a UV-conformal standard model.

Quantum scale invariance in the UV has been recently advocated as an attractive way of solving the gauge hierarchy problem arising in the standard model. We explore the cosmological signatures at the electroweak scale when the breaking of scale invariance originates from a hidden sector and is mediated to the standard model by gauge interactions (gauge mediation). These scenarios, while being hard to distinguish from the standard model at LHC, can give rise to a strong electroweak phase transition leading to the generation of a large stochastic gravitational wave signal in possible reach of future space-based detectors such as eLISA and BBO. This relic would be the cosmological imprint of the breaking of scale invariance in nature.

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.

Pulsar timing signal from ultralight scalar dark matter

An ultralight free scalar field with mass around 10−23−10−22 eV is a viable dark mater candidate, which can help to resolve some of the issues of the cold dark matter on sub-galactic scales. We consider the gravitational field of the galactic halo composed out of such dark matter. The scalar field has oscillating in time pressure, which induces oscillations of gravitational potential with amplitude of the order of 10−15 and frequency in the nanohertz range. This frequency is in the range of pulsar timing array observations. We estimate the magnitude of the pulse arrival time residuals induced by the oscillating gravitational potential. We find that for a range of dark matter masses, the scalar field dark matter signal is comparable to the stochastic gravitational wave signal and can be detected by the planned SKA pulsar timing array experiment.

An atomic gravitational wave interferometric sensor in low earth orbit (AGIS-LEO)

We propose an atom interferometer gravitational wave detector in low Earth orbit (AGIS-LEO). Gravitational waves can be observed by comparing a pair of atom interferometers separated by a 30 km baseline. In the proposed configuration, one or three of these interferometer pairs are simultaneously operated through the use of two or three satellites in formation flight. The three satellite configuration allows for the increased suppression of multiple noise sources and for the detection of stochastic gravitational wave signals. The mission will offer a strain sensitivity of $${<10^{-18}/\sqrt{{\rm Hz}}}$$ in the 50mHz–10Hz frequency range, providing access to a rich scientific region with substantial discovery potential. This band is not currently addressed with the LIGO, VIRGO, or LISA instruments. We analyze systematic backgrounds that are relevant to the mission and discuss how they can be mitigated at the required levels. Some of these effects do not appear to have been considered previously in the context of atom interferometry, and we therefore expect that our analysis will be broadly relevant to atom interferometric precision measurements. Finally, we present a brief conceptual overview of shorter-baseline $$({\lesssim100\,{\rm m}})$$ atom interferometer configurations that could be deployed as proof-of-principle instruments on the International Space Station (AGIS-ISS) or an independent satellite.

GRAVITATIONAL RADIATION FROM HYDRODYNAMIC TURBULENCE IN A DIFFERENTIALLY ROTATING NEUTRON STAR

(Abridged.) The mean-square current quadrupole moment associated with vorticity fluctuations in high-Reynolds-number turbulence in a differentially rotating neutron star is calculated analytically, as are the amplitude and decoherence time of the resulting, stochastic gravitational wave signal. The calculation resolves the subtle question of whether the signal is dominated by the smallest or largest turbulent eddies: for the Kolmogorov-like power spectrum observed in superfluid spherical Couette simulations, the wave strain is controlled by the largest eddies, and the decoherence time approximately equals the maximum eddy turnover time. For a neutron star with spin frequency $\nu_s$ and Rossby number $Ro$, at a distance $d$ from Earth, the root-mean-square wave strain reaches $h_{RMS} \approx 3\times 10^{-24} Ro^3 (\nu_s / 30 Hz)^3 (d/1 kpc)^{-1}$. A cross-correlation search can detect such a source in principle, because the signal decoheres over the time-scale $\tau_c \approx 10^{-3} Ro^{-1} (\nu_s / 30 Hz)^{-1} s$, which is adequately sampled by existing long-baseline interferometers. Hence hydrodynamic turbulence imposes a fundamental noise floor on gravitational wave observations of neutron stars, although its polluting effect may be muted by partial decoherence in the hectohertz band, where current continuous-wave searches are concentrated, for the highest frequency (and hence most powerful) sources.

Search for a stochastic gravitational-wave signal in the second round of the Mock LISA Data Challenges

The analysis method currently proposed to search for isotropic stochastic radiation with the Laser Interferometer Space Antenna (LISA) relies on the combined use of two LISA channels, one of which is insensitive to gravitational waves, such as the symmetrized Sagnac. For this method to work, it is essential to know how the instrumental noise power in the two channels are related to one another; however, no quantitative estimates of this key information are available to date. The purpose of our study is to assess the performance of the symmetrized Sagnac method for different levels of prior information regarding the instrumental noise. We develop a general approach in the framework of Bayesian inference and an end-to-end analysis algorithm based on Markov chain Monte Carlo methods to compute the posterior probability density functions of the relevant model parameters. We apply this method to data released as part of the second round of the Mock LISA Data Challenges. For the selected (and somewhat idealized) example cases considered here, we find that for a signal whose amplitude dominates the instrumental noise by a factor ≈25, a prior uncertainty of a factor ≈2 in the ratio between the power of the instrumental noise contributions in the two channels allows for the detection of isotropic stochastic radiation. More importantly, we provide a framework for more realistic studies of LISA's performance and development of analysis techniques in the context of searches for stochastic signals.

Cross-correlation search for periodic gravitational waves

In this paper we study the use of cross correlations between multiple gravitational wave (GW) data streams for detecting long-lived periodic signals. Cross-correlation searches between data from multiple detectors have traditionally been used to search for stochastic GW signals, but recently they have also been used in directed searches for periodic GWs. Here we further adapt the cross-correlation statistic for periodic GW searches by taking into account both the nonstationarity and the long-term-phase coherence of the signal. We study the statistical properties and sensitivity of this search and its relation to existing periodic wave searches, and describe the precise way in which the cross-correlation statistic interpolates between semicoherent and fully coherent methods. Depending on the maximum duration over which we wish to preserve phase coherence, the cross-correlation statistic can be tuned to go from a standard cross-correlation statistic using data from distinct detectors, to the semicoherent time-frequency methods with increasing coherent time baselines, and all the way to a full coherent search. This leads to a unified framework for studying periodic wave searches and can be used to make informed trade-offs between computational cost, sensitivity, and robustness against signal uncertainties.

Preparing GEO 600 for gravitational wave astronomy—a status report

A number of gravitational wave detectors throughout the world are currently moving from the final stages of commissioning to a more continuous observational mode. Together, these detectors form a global network which will search for gravitational waves from various astrophysical sources, such as continuous wave signals from rotating neutron stars, transient signals from, for example, inspiralling compact objects and supernovae explosions, and stochastic gravitational wave signals from the early universe. GEO 600 is a long baseline laser-interferometric gravitational wave detector which employs advanced optical and suspension techniques to reach its design sensitivity. Almost all of the major installation work at GEO 600 is already completed and the detector is currently being commissioned to prepare it for extended observation periods. The commissioning process involves many activities in the areas of noise reduction, calibration, operational stability and characterization. This report highlights some of the major commissioning steps that have contributed to the increase in sensitivity of the instrument over the period from December 2003 to December 2004. In addition, recent extensions to the on-line calibration scheme used in GEO 600 are briefly discussed.

A technique to modulate the signature of a stochastic gravitational wave background

Detecting a stationary, stochastic gravitational wave signal is complicated by the impossibility of observing detector noise independently of the signal. Here we describe a method of identifying this source of systematic error by varying the orientation of one of the detectors, leading to separate and independent modulations of the signal and noise contribution to the cross-correlation. The method can be applied to measurements of a stochastic gravitational wave background by the ALLEGRO/LIGO Livingston Observatory detector pair. We explore—in the context of this detector pair—how this new measurement technique is insensitive to a cross-correlated detector noise component that can confound a conventional measurement.

Modulating the experimental signature of a stochastic gravitational wave background

Detecting a stationary, stochastic gravitational wave signal is complicated by the impossibility of observing the detector noise independently of the signal. One consequence is that we require at least two detectors to observe the signal, which will be apparent in the cross-correlation of the detector outputs. A corollary is that there remains a systematic error, associated with the possible presence of correlated instrumental noise, in any observation aimed at estimating or limiting a stochastic gravitational wave signal. Here we describe a method of identifying this systematic error by varying the orientation of one of the detectors, leading to separate and independent modulations of the signal and noise contribution to the cross-correlation. Our method can be applied to measurements of a stochastic gravitational wave background by the ALLEGRO-LIGO Livingston Observatory detector pair. We explore---in the context of this detector pair---how this new measurement technique is insensitive to a cross-correlated detector noise component that can confound a conventional measurement.