Isotropic Stochastic Gravitational-wave Background Research Articles

Observing gravitational waves with solar system astrometry

The subtle influence of gravitational waves on the apparent positioning of celestial bodies offers novel observational windows [1,2,3,4]. We calculate the expected astrometric signal induced by an isotropic Stochastic Gravitational Wave Background (SGWB) in the short distance limit. Our focus is on the resultant proper motion of Solar System objects, a signal on the same time scales addressed by Pulsar Timing Arrays (PTA). We derive the corresponding astrometric deflection patterns, finding that they manifest as distinctive dipole and quadrupole correlations or, in some cases, may not be present. Our analysis encompasses both Einsteinian and non-Einsteinian polarisations. We estimate the upper limits for the amplitude of SGWBs that could be obtained by tracking the proper motions of large numbers of solar system objects such as asteroids. We find that for SGWBs with negative spectral indices, such as that generated by Super Massive Black Hole Binaries (SMBHB), the constraints from these observations could rival those from PTAs. With the Gaia satellite and the Vera C. Rubin Observatory poised to track an extensive sample of asteroids — ranging from 𝒪(105) to 𝒪(106), we highlight the significant future potential for similar surveys to contribute to our understanding of the SGWB.

The second data release from the European Pulsar Timing Array

We present the results of the search for an isotropic stochastic gravitational wave background (GWB) at nanohertz frequencies using the second data release of the European Pulsar Timing Array (EPTA) for 25 millisecond pulsars and a combination with the first data release of the Indian Pulsar Timing Array (InPTA). A robust GWB detection is conditioned upon resolving the Hellings-Downs angular pattern in the pairwise cross-correlation of the pulsar timing residuals. Additionally, the GWB is expected to yield the same (common) spectrum of temporal correlations across pulsars, which is used as a null hypothesis in the GWB search. Such a common-spectrum process has already been observed in pulsar timing data. We analysed (i) the full 24.7-year EPTA data set, (ii) its 10.3-year subset based on modern observing systems, (iii) the combination of the full data set with the first data release of the InPTA for ten commonly timed millisecond pulsars, and (iv) the combination of the 10.3-year subset with the InPTA data. These combinations allowed us to probe the contributions of instrumental noise and interstellar propagation effects. With the full data set, we find marginal evidence for a GWB, with a Bayes factor of four and a false alarm probability of 4%. With the 10.3-year subset, we report evidence for a GWB, with a Bayes factor of 60 and a false alarm probability of about 0.1% (≳3σ significance). The addition of the InPTA data yields results that are broadly consistent with the EPTA-only data sets, with the benefit of better noise modelling. Analyses were performed with different data processing pipelines to test the consistency of the results from independent software packages. The latest EPTA data from new generation observing systems show non-negligible evidence for the GWB. At the same time, the inferred spectrum is rather uncertain and in mild tension with the common signal measured in the full data set. However, if the spectral index is fixed at 13/3, the two data sets give a similar amplitude of (2.5 ± 0.7) × 10−15 at a reference frequency of 1 yr−1. Further investigation of these issues is required for reliable astrophysical interpretations of this signal. By continuing our detection efforts as part of the International Pulsar Timing Array (IPTA), we expect to be able to improve the measurement of spatial correlations and better characterise this signal in the coming years.

Search for an Isotropic Gravitational-wave Background with the Parkes Pulsar Timing Array

Pulsar timing arrays aim to detect nanohertz-frequency gravitational waves (GWs). A background of GWs modulates pulsar arrival times and manifests as a stochastic process, common to all pulsars, with a signature spatial correlation. Here we describe a search for an isotropic stochastic gravitational-wave background (GWB) using observations of 30 millisecond pulsars from the third data release of the Parkes Pulsar Timing Array (PPTA), which spans 18 yr. Using current Bayesian inference techniques we recover and characterize a common-spectrum noise process. Represented as a strain spectrum , we measure and α = −0.45 ± 0.20, respectively (median and 68% credible interval). For a spectral index of α = −2/3, corresponding to an isotropic background of GWs radiated by inspiraling supermassive black hole binaries, we recover an amplitude of . However, we demonstrate that the apparent signal strength is time-dependent, as the first half of our data set can be used to place an upper limit on A that is in tension with the inferred common-spectrum amplitude using the complete data set. We search for spatial correlations in the observations by hierarchically analyzing individual pulsar pairs, which also allows for significance validation through randomizing pulsar positions on the sky. For a process with α = −2/3, we measure spatial correlations consistent with a GWB, with an estimated false-alarm probability of p ≲ 0.02 (approx. 2σ). The long timing baselines of the PPTA and the access to southern pulsars will continue to play an important role in the International Pulsar Timing Array.

Measuring the maximally allowed polarization states of the isotropic stochastic gravitational wave background with the ground-based detectors

We discuss the polarizational study of isotropic gravitational wave backgrounds with the second-generation detector network, paying special attention to the impacts of adding LIGO-India. The backgrounds can be characterized by at most five spectral components (three parity-even ones and two parity-odd ones). They can be algebraically decomposed through the difference of the corresponding overlap reduction functions defined for the individual spectra. We newly identify two interesting relations between the overlap reduction functions, and these relations generally hamper the algebraic decomposition in the low-frequency regime $f\ensuremath{\lesssim}30\text{ }\text{ }\mathrm{Hz}$. We also find that LIGO-India can significantly improve the network sensitives to the odd spectral components.

Primordial black holes and scalar-induced gravitational waves from the perturbations on the inflaton potential in peak theory

A perturbation on the background inflaton potential can lead inflation into the ultraslow-roll stage and can thus remarkably enhance the power spectrum ${\cal P}_{\cal R}(k)$ of the primordial curvature perturbation on small scales. Such an enhanced ${\cal P}_{\cal R}(k)$ will result in primordial black holes (PBHs), contributing a significant fraction of dark matter, and will simultaneously generate sizable scalar-induced gravitational waves (SIGWs) as a secondorder effect. In this work, we calculate the PBH abundances $f_{\rm PBH}(M)$ and SIGW spectra $\Omega_{\rm GW}(f)$ in peak theory. We obtain the PBHs with desirable abundances in one or two typical mass windows at $10^{-17}\, M_\odot$, $10^{-13}\, M_\odot$, and $30\, M_\odot$, respectively. At the same time, the relevant SIGWs are expected to be observed by the next-generation gravitational wave detectors, without spoiling the current constraint. Especially, the SIGW associated with the PBH of $30\, M_\odot$ can also interpret the potential isotropic stochastic gravitational wave background from the NANOGrav 12.5-year dataset.

Stochastic gravitational wave background phenomenology in a pulsar timing array

Pulsar timing offers an independent avenue to test general relativity and alternative gravity theories. This requires an understanding of how metric polarizations beyond the familiar transverse tensor ones imprint as a stochastic gravitational wave background and correlate the arrival time of radio pulses from a pair of millisecond pulsars. In this work, we focus on an isotropic stochastic gravitational wave background and present a straightforward, self-contained formalism for obtaining the power spectrum and the overlap reduction function, the relevant physical observable in a pulsar timing array, for generic gravitational degrees of freedom featuring both transverse and longitudinal modes off the light cone. We additionally highlight our consideration of finite pulsar distances, which we find significant in two ways: first, making all the modes well defined, and second, keeping the small-scale power that is contained by pulsars of subdegree separations in the sky. We discuss this for tensor, vector, and scalar polarizations, for each one focusing on the angular power spectrum and the overlap reduction function for an isotropic stochastic gravitational wave background. Our results pave the road for an efficient numerical method for examining the gravitational wave-induced spatial correlations across millisecond pulsars in a pulsar timing array.

Upper limits on the polarized isotropic stochastic gravitational-wave background from advanced LIGO-Virgo's first three observing runs

Parity violation is expected to generate an asymmetry between the amplitude of left and right-handed gravitational-wave modes which leads to a circularly polarized stochastic gravitational-wave background (SGWB). Due to the three independent baselines in the LIGO-Virgo network, we focus on the amplitude difference in strain power characterized by Stokes' parameters and do maximum-likelihood estimation to constrain the polarization degree of SGWB. Our results indicate that there is no evidence for the circularly polarized SGWB in the data. Furthermore, by modeling the SGWB as a power-law spectrum, we place upper limit on the normalized energy density Ωgw(25 Hz) < 5.3 × 10-9 at 95% confidence level after marginalizing over the polarization degree and spectral index.

Searching for isotropic stochastic gravitational-wave background in the international pulsar timing array second data release

We search for isotropic stochastic gravitational-wave background (SGWB) in the International Pulsar Timing Array second data release. By modeling the SGWB as a power-law, we find very strong Bayesian evidence for a common-spectrum process, and further this process has scalar transverse (ST) correlations allowed in general metric theory of gravity as the Bayes factor in favor of the ST-correlated process versus the spatially uncorrelated common-spectrum process is 30 ± 2. The median and the 90% equal-tail amplitudes of ST mode are , or equivalently the energy density parameter per logarithm frequency is , at frequency of 1 year−1. However, we do not find any statistically significant evidence for the tensor transverse (TT) mode and then place the 95% upper limits as , or equivalently , at frequency of 1 year−1.

Search for the Gravitational-wave Background from Cosmic Strings with the Parkes Pulsar Timing Array Second Data Release

We perform a direct search for an isotropic stochastic gravitational-wave background (SGWB) produced by cosmic strings in the Parkes Pulsar Timing Array (PPTA) Data Release 2 (DR2). We find no evidence for such an SGWB, and therefore place a 95% confidence level upper limit on the cosmic string tension, G μ, as a function of the reconnection probability, p, which can be less than 1 in the string-theory-inspired models or pure Yang–Mills theory. The upper bound on the cosmic string tension is G μ ≲ 5.1 × 10−10 for p = 1, which is about five orders of magnitude tighter than the bound derived from the null search of individual gravitational-wave bursts from cosmic string cusps in the PPTA DR2, and comparable to previous bounds derived from the null search of the SGWB from cosmic strings.

Searches for Gravitational Waves from Supermassive Black Hole Binaries using Hamiltonian Monte Carlo

Pulsar timing arrays (PTAs) can detect low-frequency gravitational waves by looking for correlated deviations in pulse arrival times. Current Bayesian searches using PTAs are hampered by the large number of parameters needed to be sampled concurrently with Markov Chain Monte Carlo methods. As the data span increases, this problem will only worsen. An alternative Monte Carlo sampling method, Hamiltonian Monte Carlo (HMC), utilizes Hamiltonian dynamics to produce sample proposals informed by first-order gradients of the model likelihood. This in turn allows it to converge faster to high dimensional distributions. We implement HMC as an alternative sampling method in our search for an isotropic stochastic gravitational wave background, and present the accuracy and efficiency of the algorithm for this analysis. We also discuss implications of tailoring this algorithm to additional gravitational wave searches.

The International Pulsar Timing Array second data release: Search for an isotropic gravitational wave background

ABSTRACTWe searched for an isotropic stochastic gravitational wave background in the second data release of the International Pulsar Timing Array, a global collaboration synthesizing decadal-length pulsar-timing campaigns in North America, Europe, and Australia. In our reference search for a power-law strain spectrum of the form $h_c = A(f/1\, \mathrm{yr}^{-1})^{\alpha }$, we found strong evidence for a spectrally similar low-frequency stochastic process of amplitude $A = 3.8^{+6.3}_{-2.5}\times 10^{-15}$ and spectral index α = −0.5 ± 0.5, where the uncertainties represent 95 per cent credible regions, using information from the auto- and cross-correlation terms between the pulsars in the array. For a spectral index of α = −2/3, as expected from a population of inspiralling supermassive black hole binaries, the recovered amplitude is $A = 2.8^{+1.2}_{-0.8}\times 10^{-15}$. None the less, no significant evidence of the Hellings–Downs correlations that would indicate a gravitational-wave origin was found. We also analysed the constituent data from the individual pulsar timing arrays in a consistent way, and clearly demonstrate that the combined international data set is more sensitive. Furthermore, we demonstrate that this combined data set produces comparable constraints to recent single-array data sets which have more data than the constituent parts of the combination. Future international data releases will deliver increased sensitivity to gravitational wave radiation, and significantly increase the detection probability.

Constraining the Polarization of Gravitational Waves with the Parkes Pulsar Timing Array Second Data Release

Abstract We search for the isotropic stochastic gravitational-wave background, including the nontensorial polarizations that are allowed in general metric theories of gravity, in the Parkes Pulsar Timing Array (PPTA) second data release (DR2). We find no statistically significant evidence that the common-spectrum process reported by the PPTA collaboration has tensor transverse, scalar transverse, vector longitudinal, or scalar longitudinal correlations in PPTA DR2. Therefore, we place a 95% upper limit on the amplitude of each polarization mode, as  TT ≲ 3.2 × 10 − 15 ,  ST ≲ 1.8 × 10 − 15 ,  VL ≲ 3.5 × 10 − 16 , and  SL ≲ 4.2 × 10 − 17 ; or, equivalently, a 95% upper limit on the energy density parameter per logarithm frequency, as Ω GW TT ≲ 1.4 × 10 − 8 , Ω GW ST ≲ 4.5 × 10 − 9 , Ω GW VL ≲ 1.7 × 10 − 10 , and Ω GW SL ≲ 2.4 × 10 − 12 , at a frequency of 1/yr.

Common-spectrum process versus cross-correlation for gravitational-wave searches using pulsar timing arrays

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported strong statistical evidence for a common-spectrum red-noise process for all pulsars, as seen in their 12.5-yr analysis for an isotropic stochastic gravitational-wave background. However, there is currently very little evidence for quadrupolar spatial correlations across the pulsars in the array, which is needed to make a confident claim of detection of a stochastic background. Here we give a frequentist analysis of a very simple signal+noise model showing that the current lack of evidence for spatial correlations is consistent with the magnitude of the correlation coefficients for pairs of Earth-pulsar baselines in the array, and the fact that pulsar timing arraysbare most-likely operating in the intermediate-signal regime. We derive analytic expressions that allow one to compare the expected values of the signal-to-noise ratios for both the common-spectrum and cross-correlation estimators.

Measuring parity violation in the Stochastic Gravitational Wave Background with the LISA-Taiji network

Parity violation is a powerful observable to distinguish a cosmological background of Gravitational Waves (GWs) from an astrophysical one. Planar single GW interferometers, both on ground and in space, are unable to measure the net circular polarization of an isotropic Stochastic Gravitational Wave Background (SGWB). In this paper, we explore the possibility of detecting circular polarization of an isotropic SGWB by cross-correlating two space-based detectors planned to be launched around 2034: LISA and Taiji. We compute the response of such a network to chirality and we perform a Fisher forecast analysis on the I and V Stokes parameters for the SGWB. We find that a clear measurement of chirality can be claimed for a maximally chiral flat signal with amplitude h 2 ΩGW ≃ 10−12 at the frequency scales of LISA and Taiji.

The NANOGrav 12.5 yr Data Set: Search for an Isotropic Stochastic Gravitational-wave Background

Abstract We search for an isotropic stochastic gravitational-wave background (GWB) in the 12.5 yr pulsar-timing data set collected by the North American Nanohertz Observatory for Gravitational Waves. Our analysis finds strong evidence of a stochastic process, modeled as a power law, with common amplitude and spectral slope across pulsars. Under our fiducial model, the Bayesian posterior of the amplitude for an f −2/3 power-law spectrum, expressed as the characteristic GW strain, has median 1.92 × 10−15 and 5%–95% quantiles of 1.37–2.67 × 10−15 at a reference frequency of f yr = 1 yr − 1 ; the Bayes factor in favor of the common-spectrum process versus independent red-noise processes in each pulsar exceeds 10,000. However, we find no statistically significant evidence that this process has quadrupolar spatial correlations, which we would consider necessary to claim a GWB detection consistent with general relativity. We find that the process has neither monopolar nor dipolar correlations, which may arise from, for example, reference clock or solar system ephemeris systematics, respectively. The amplitude posterior has significant support above previously reported upper limits; we explain this in terms of the Bayesian priors assumed for intrinsic pulsar red noise. We examine potential implications for the supermassive black hole binary population under the hypothesis that the signal is indeed astrophysical in nature.

The NANOGrav 11 Year Data Set: Pulsar-timing Constraints on the Stochastic Gravitational-wave Background

Abstract We search for an isotropic stochastic gravitational-wave background (GWB) in the newly released 11 year data set from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). While we find no evidence for a GWB, we place constraints on a population of inspiraling supermassive black hole (SMBH) binaries, a network of decaying cosmic strings, and a primordial GWB. For the first time, we find that the GWB constraints are sensitive to the solar system ephemeris (SSE) model used and that SSE errors can mimic a GWB signal. We developed an approach that bridges systematic SSE differences, producing the first pulsar-timing array (PTA) constraints that are robust against SSE errors. We thus place a 95% upper limit on the GW-strain amplitude of A GWB &lt; 1.45 × 10−15 at a frequency of f = 1 yr−1 for a fiducial f −2/3 power-law spectrum and with interpulsar correlations modeled. This is a factor of ∼2 improvement over the NANOGrav nine-year limit calculated using the same procedure. Previous PTA upper limits on the GWB (as well as their astrophysical and cosmological interpretations) will need revision in light of SSE systematic errors. We use our constraints to characterize the combined influence on the GWB of the stellar mass density in galactic cores, the eccentricity of SMBH binaries, and SMBH–galactic-bulge scaling relationships. We constrain the cosmic-string tension using recent simulations, yielding an SSE-marginalized 95% upper limit of Gμ &lt; 5.3 × 10−11—a factor of ∼2 better than the published NANOGrav nine-year constraints. Our SSE-marginalized 95% upper limit on the energy density of a primordial GWB (for a radiation-dominated post-inflation universe) is ΩGWB(f) h 2 &lt; 3.4 × 10−10.

Gravitational wave searches with pulsar timing arrays: Cancellation of clock and ephemeris noises

We propose a data processing technique to cancel monopole and dipole noise sources (such as clock and ephemeris noises respectively) in pulsar timing array searches for gravitational radiation. These noises are the dominant sources of correlated timing fluctuations in the lower-part ($ \approx 10^{-9} - 10^{-8}$ Hz) of the gravitational wave band accessible by pulsar timing experiments. After deriving the expressions that reconstruct these noises from the timing data, we estimate the gravitational wave sensitivity of our proposed processing technique to single-source signals to be at least one order of magnitude higher than that achievable by directly processing the timing data from an equal-size array. Since arrays can generate pairs of clock and ephemeris-free timing combinations that are no longer affected by correlated noises, we implement with them the cross-correlation statistic to search for an isotropic stochastic gravitational wave background. We find the resulting optimal signal-to-noise ratio to be more than one order of magnitude larger than that obtainable by correlating pairs of timing data from arrays of equal size.

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.

Sensitivity to a frequency-dependent circular polarization in an isotropic stochastic gravitational wave background

We calculate the sensitivity to a circular polarization of an isotropic stochastic gravitational wave background (ISGWB) as a function of frequency for ground- and space-based interferometers and observations of the cosmic microwave background. The origin of a circularly polarized ISGWB may be due to exotic primordial physics (i.e., parity violation in the early universe) and may be strongly frequency dependent. We present calculations within a coherent framework which clarifies the basic requirements for sensitivity to circular polarization, in distinction from previous work which focused on each of these techniques separately. We find that the addition of an interferometer with the sensitivity of the Einstein Telescope in the southern hemisphere improves the sensitivity of the ground-based network to circular polarization by about a factor of two. The sensitivity curves presented in this paper make clear that the wide range in frequencies of current and planned observations ($10^{-18}\ {\rm Hz} \lesssim f \lesssim 100\ {\rm Hz}$) will be critical to determining the physics that underlies any positive detection of circular polarization in the ISGWB. We also identify a desert in circular polarization sensitivity for frequencies between $10^{-15}\ {\rm Hz} \lesssim f \lesssim 10^{-3}\ {\rm Hz}$, given the inability for pulsar timing arrays and indirect-detection methods to distinguish the gravitational wave polarization.

THE NANOGRAV NINE-YEAR DATA SET: LIMITS ON THE ISOTROPIC STOCHASTIC GRAVITATIONAL WAVE BACKGROUND

ABSTRACT We compute upper limits on the nanohertz-frequency isotropic stochastic gravitational wave background (GWB) using the 9 year data set from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration. Well-tested Bayesian techniques are used to set upper limits on the dimensionless strain amplitude (at a frequency of 1 yr−1) for a GWB from supermassive black hole binaries of A gw &lt; 1.5 × 10 − 15 . We also parameterize the GWB spectrum with a broken power-law model by placing priors on the strain amplitude derived from simulations of Sesana and McWilliams et al. Using Bayesian model selection we find that the data favor a broken power law to a pure power law with odds ratios of 2.2 and 22 to one for the Sesana and McWilliams prior models, respectively. Using the broken power-law analysis we construct posterior distributions on environmental factors that drive the binary to the GW-driven regime including the stellar mass density for stellar-scattering, mass accretion rate for circumbinary disk interaction, and orbital eccentricity for eccentric binaries, marking the first time that the shape of the GWB spectrum has been used to make astrophysical inferences. Returning to a power-law model, we place stringent limits on the energy density of relic GWs, Ω gw ( f ) h 2 &lt; 4.2 × 10 − 10 . Our limit on the cosmic string GWB, Ω gw ( f ) h 2 &lt; 2.2 × 10 − 10 , translates to a conservative limit on the cosmic string tension with G μ &lt; 3.3 × 10 − 8 , a factor of four better than the joint Planck and high-l cosmic microwave background data from other experiments.