Abstract We perform searches for gravitational-wave memory in the data of two major Pulsar Timing Array (PTA) experiments located in Europe and Australia. Supermassive black hole binaries (SMBHBs) are the primary sources of gravitational waves in PTA experiments. We develop and carry out the first search for late inspirals and mergers of these sources based on full numerical relativity waveforms with null (nonlinear) gravitational-wave memory. Additionally, we search for generic bursts of null gravitational-wave memory, exploring the possibilities of reducing the computational costs of these searches through kernel density estimation and normalizing flow approximations of the posteriors. We rule out mergers of SMBHBs with a chirp mass of 10 10 M ⊙ up to 700 Mpc over 18 yr of observation at 95% credibility. We rule out the observation of generic displacement memory bursts with strain amplitudes >10 −14 in brief periods of observation time but across the sky, or over the whole observation time but for certain preferred sky positions, at 95% credibility.

The formation of primordial black holes or other dark matter relics from amplified density fluctuations in the early Universe may also generate scalar-induced gravitational waves (GW), carrying vital information about the primordial power spectrum and the early expansion history of our Universe. We present a Bayesian approach aimed at reconstructing both the shape of the scalar power spectrum and the Universe’s equation of state from GW observations, using interpolating splines to flexibly capture features in the GW data. The optimal number of spline nodes is chosen via Bayesian evidence, aiming at balancing complexity of the model and the fidelity of the reconstruction. We test our method using both representative mock data and recent pulsar timing array measurements, demonstrating that it can accurately reconstruct the curvature power spectrum as well as the underlying equation of state, if different from radiation.

Abstract The nanohertz stochastic gravitational wave background (SGWB), generated by unresolved supermassive black hole binaries (SMBHBs), provides a unique probe of their population and its cosmic evolution. In this work, we explore the potential of uncovering the SMBHB population and its redshift dependence by combining the SGWB signal and its anisotropies with galaxy distribution through cross-correlation analyses. Using a Fisher analysis technique, we show that the SGWB power spectrum alone can not provide any information on the evolutionary history of SMBHBs, whereas the inclusion of the angular power spectrum of the SGWB and its cross-correlation with the galaxy distribution substantially improves constraints on the redshift evolution parameters. Assuming pulsar timing array configurations achievable in the Square Kilometre Array era, we find that the combined use of isotropic and anisotropic SGWB signals, together with galaxy surveys, can provide valuable measurements of the redshift evolution of the SMBH–galaxy connection and the frequency distribution of SMBHBs. These results highlight the potential of joint gravitational wave–galaxy studies to address the long-standing open question of SMBH growth and evolution across cosmic time.

A bstract Supercooled phase transitions, as predicted, e.g., in near-conformal and confining extensions of the Standard Model (SM), are established sources of strong stochastic gravitational wave backgrounds (SGWBs). In this work, we investigate another facet of such transitions: their significant and largely uncharted impact on gravitational wave spectra originating from independent cosmological sources. Focusing on gravitational waves produced by a metastable cosmic string network, we show that an intervening supercooled phase, initiating thermal inflation, can reshape and suppress the high-frequency part of the spectrum. This mechanism reopens regions of string parameter space previously excluded by LIGO’s null results, while remaining compatible with the nanohertz SGWB signal reported by pulsar timing arrays (PTAs). The resulting total spectrum typically exhibits a dual-component structure, sourced by both string decay and the phase transition itself, rendering the scenario observationally distinctive. We systematically classify the viable parameter space and identify regions accessible to upcoming detectors such as Advanced LIGO, LISA, and ET.

Pulsar timing arrays (PTAs) are ensembles of millisecond pulsars observed for years to decades. The primary goal of PTAs is to study gravitational-wave astronomy at nanohertz frequencies, with secondary goals of undertaking other fundamental tests of physics and astronomy. Recently, compelling evidence has emerged in established PTA experiments for the presence of a gravitational-wave background. To accelerate a confident detection of such a signal and then study gravitational-wave emitting sources, it is necessary to observe a larger number of millisecond pulsars to greater timing precision. The SKA telescopes, which will be a factor of three to four greater in sensitivity compared to any other southern hemisphere facility, is poised to make such an impact. In this chapter, we motivate an SKAO pulsar timing array (SKAO PTA) experiment. We discuss the classes of gravitational waves present in PTA observations and how an SKAO PTA can detect and study them. We then describe the sources that can produce these signals. We discuss the astrophysical noise sources that must be mitigated to undertake the most sensitive searches. We then describe a realistic PTA experiment implemented with the SKA and place it in context alongside other PTA experiments likely ongoing in the 2030s. We describe the techniques necessary to search for gravitational waves in the SKAO PTA and motivate how very long baseline interferometry can improve the sensitivity of an SKAO PTA. The SKAO PTA will provide a view of the Universe complementary to those of the other large facilities of the 2030s.

The ionised media that permeate the Milky Way have been active topics of research since the discovery of pulsars in 1967. In fact, pulsars allow one to study several aspects of said plasma, such as their column density, turbulence, scattering measures, and discrete, intervening structures in between the neutron star and the observer, and aspects of the magnetic field throughout. Such sources of information allow us to characterise the electron distribution in the terrestrial ionosphere, the Solar Wind, and our Galaxy and the impact on other experiments involving pulsars such as Pulsar Timing Arrays. In this article, we review the state-of-the-art of plasma research using pulsars, the aspects that should be taken into consideration for optimal plasma studies, and we provide future perspectives on improvements to those enabled by the SKA.

Spatial correlations between pulsars for interfering gravitational-wave sources in pulsar timing array

Pulsar timing array (PTA) experiments have the potential to unveil continuous gravitational wave (CGW) signals from individual low-redshift massive black hole binaries (MBHBs). Detecting these objects in both gravitational waves (GWs) and the electromagnetic (EM) spectrum will open a new chapter in multimessenger astronomy. We investigate the feasibility of conducting multimessenger studies by combining the CGW detections from an idealized 30 year Square Kilometer Array Mid telescope PTA and the optical data from the forthcoming Legacy Survey of Space and Time (LSST). To this end, we employed the semi-analytical model applied to the simulation. We generated 200 different all-sky light cones that include galaxies, massive black holes, and MBHBs whose emission is consistently modeled based on their star formation histories and gas accretion physics. Our results predict an average of ≈33 CGW detections, with signal-to-noise ratios greater than five. The MBHBs associated with the detections are typically at z, L-Galaxies Millennium < ,0.5, with masses of ̊m ∼,3, ,10^ 9 , M_⊙, mass ratios $ > ,0.6$, and eccentricities $ łesssim ,0.2$. In terms of EM counterparts, we find less than 15% of these systems to be connected with an active galactic nucleus detectable by LSST, while their host galaxies are easily detectable ($ < ,23, ̊m mag$) massive (̊m M_⋆, > ,10^ 11 , ̊m M_⊙) ellipticals with typical star formation rates (10^ -15 , ̊m yr ^ -1 , < ,̊m sSRF, < ,10^ -10 , ̊m yr ^ -1 ). Although the CGW-EM counterpart association is complicated by poor sky localization (only 35% of these CGWs are localized within ̊m 100, deg^2), the number of galaxy host candidates can be considerably reduced (from thousands to several tens, depending on the CGW S/N) by applying priors based on the galaxy-MBH correlations. However, picking the actual host among these candidates is highly non-trivial, as they occupy a similar region in any optical color-color diagram. Our findings highlight the considerable challenges entailed in opening the low-frequency multimessenger GW sky.

Opportunities and challenges of noise suppression technology for radio pulsar timing array

Accurate pulsar timing array residual variances and correlation of the stochastic gravitational-wave background

Wide-band timing noise in pulsar timing arrays

Special topic: Detecting nanohertz gravitational waves with pulsar timing arrays

Detecting nanohertz gravitational wave bursts with pulsar timing arrays

Abstract Pulsar timing arrays have recently found evidence for nanohertz gravitational waves that are consistent with being produced by a cosmological population of binary supermassive black holes (SMBHs). However, the amplitude of this gravitational-wave background is larger than predicted from theoretical and empirical models of SMBH binary populations. We investigate preferential accretion onto the secondary, less massive SMBH of the binary as a potential solution to this discrepancy. We carry out the first observationally based analysis of the effect of preferential accretion on the SMBH binary population, and we find that preferential accretion onto the secondary SMBH increases the binary SMBH mass ratio, causing many minor galaxy mergers to lead to major SMBH mergers. The fraction of SMBH mergers that are major mergers increases by a factor of 2–3 when preferential accretion is included. Further, we find that only a small amount of preferential accretion (10% total SMBH mass growth) is needed to bring the predicted gravitational-wave background amplitude into agreement with observations. Preferential accretion has an even larger effect on gravitational-wave signals detected by LISA, which will probe SMBH binaries at higher redshifts where the environment is more gas-rich, and can also help explain the rapid buildup of overmassive black holes at high redshifts observed by the James Webb Space Telescope. It also shortens the time to the first detection of an individual SMBH binary emitting continuous waves. Preferential accretion strengthens the gravitational-wave signals produced by any binary embedded in a circumbinary disk, including LIGO sources.

Realistic assessment of a single gravitational wave source localization taking into account precise pulsar distances with pulsar timing arrays

We used the hagn cosmological simulation to study the properties of supermassive black hole binaries (MBHBs) with the largest contribution to the gravitational wave background (GWB) signal expected for the pulsar timing array (PTA) band. We developed a pipeline to generate realistic populations of MBHBs, which enabled us to estimate both the characteristic strain and GWB time series observable by PTA experiments. We identified potential continuous wave (CW) candidates standing above the background noise, using toy PTA sensitivities representing the current EPTA and future SKA. We estimated the probability of detecting at least one CW with a signal-to-noise ratio of S/N $>3$ to be $4%$ ($20%$) for EPTA (SKA)-like sensitivities, assuming a ten-year baseline. We found that the GWB is dominated by hundreds to thousands of binaries at redshifts in the range $0.05-1$, with chirp masses of $10^ primarily hosted in quiescent massive galaxies residing in halos of mass ∼ 10^ CW candidates have larger masses and lower redshifts, and they tend to be found in even more massive halos, typical of galaxy groups and clusters. The majority of these systems would appear as active galactic nuclei (AGNs), rather than quasars, because of their low Eddington ratios. Nevertheless, CW candidates with f_ Edd can still outshine their hosts, particularly in radio and X-ray bands, suggesting that they could serve as the most promising route for identification. Our findings imply that optical and near-infrared (NIR) searches based on light curve variability are challenging and biased toward more luminous systems. Finally, we highlight important caveats in the common method used to compare PTA observations with theoretical models. We find that GWB spectral inferences used by PTAs could be biased toward shallower slopes and higher amplitudes at f=1/ yr, thereby reducing the apparent tension between astrophysical expectations and PTA observations.

Abstract This study investigates the gravitational waves (GWs) generated by the emergence of magnetic flux tubes in the solar convection zone. We focus on the upward buoyancy of magnetic flux tubes, which leads to significant magnetic activity and the formation of active region sunspots. This study adopts parameters representative of a moderate-sized solar active region to estimate the GWs generated by the emergence of magnetic flux tubes. Our results indicate that the GW strain amplitude, achievable through signal superposition and detection at close proximity (e.g., approximately one solar radius from the solar surface), may reach $\sim$10$^{-29}$. The characteristic GW frequency is estimated at $\sim$10$^{-5}$ Hz, placing it at the high-frequency end of the sensitivity band of Pulsar Timing Array (PTA) methods. \textcolor{RedAdd}{However, the estimated strain amplitudes remain orders of magnitude below the sensitivity thresholds of current and foreseeable gravitational wave detectors. Notably, reducing the cadence $\Delta t$ of Pulsar Timing Array (PTA) observations to approximately 2 hours ($\Delta t = 2\text{hours}$) would raise the maximum detectable frequency to about $5.8 \times 10^{-5} \text{Hz}$, thereby encompassing the dominant spectral component of solar activity-related GWs predicted in this study, offering a potential pathway for future detection.} Successful detection in the future may help to predict the super solar active region emergence in space weather forecasting.

We present a systematic study of likelihood functions used for stochastic gravitational wave background (SGWB) searches. By dividing the data into many short segments, one customarily takes advantage of the central limit theorem to justify a Gaussian cross-correlation likelihood. We show, with a hierarchy of ever more realistic examples—beginning with a single frequency bin and one detector, and then moving to two and three detectors with white and colored signal and noise—that approximating the exact Whittle likelihood by various Gaussian alternatives can induce systematic biases in the estimation of the SGWB parameters. We derive several approximations for the full likelihood and identify regimes where Gaussianity breaks down. We also discuss the possibility of conditioning the full likelihood on fiducial noise estimates to produce unbiased SGWB parameter estimation. We show that for some segment durations and bandwidths, particularly in space-based and pulsar-timing arrays, the bias can exceed the statistical uncertainty. Our results provide practical guidance for segment choice, likelihood selection, and data-compression strategies to ensure robust SGWB inference in current and next-generation gravitational wave detectors.

Abstract The turbulent nature of the ionised interstellar medium (IISM) causes dispersion measure (DM) and scattering variations in pulsar timing measurements. To improve precision of gravitational wave measurements, pulsar timing array (PTA) collaborations have begun the use of sophisticated and intricate noise modelling techniques such as modelling stochastic variations induced by the turbulent IISM and quasi-deterministic processes attributed to discrete structures. However, the reliability of these techniques has not been studied in detail, and it is unclear whether the recovered processes are physical or if they are impacted by misspecification. In this work, we present an analysis to test the efficacy of IISM noise models based on the data from the MeerKAT Pulsar Timing Array (MPTA) 4.5-year data release. We first performed multi-frequency, long-length (500 refractive length scale) simulations of multipath propagation in the IISM to study the properties of scattering variations under a variety of scattering conditions. The results of our simulations show the possibility of significant radio-frequency decorrelation in the scattering variations, particularly for the anisotropic scattering medium. Our analysis of the observed DM and scattering variations using the MPTA 4.5-year data set shows that there can be apparent anticorrelations between DM and scattering variations, which we attribute to the model fitting methods. We also report a possibility that plasma underdensities might exist along the sight lines of PSR J1431−5740 and PSR J1802−2124. Finally, using simulations, we show that the IISM noise models can result in the apparent measurement of strong frequency dependence of scattering variations observed in the MPTA data set. Our analysis shows that improvements in the IISM noise modelling techniques are necessary to accurately measure the IISM properties.

Pulsar Timing Array (PTA) projects have reported various lines of evidence suggesting the presence of a stochastic gravitational wave (GW) background in their data. One key line of evidence involves a detection statistic sensitive to interpulsar correlations, such as those induced by GWs. A p -value is then calculated to assess how unlikely it is for the observed signal to arise under the null hypothesis H 0 , purely by chance. However, PTAs cannot empirically draw samples from H 0 . As a workaround, various techniques are used in the literature to approximate p -values under H 0 . One such technique, which has been characterized as a model-independent method, is the use of “scrambling” transformations that modify the data to cancel out pulsar correlations, thereby simulating realizations from H 0 . In this work, scrambling methods and the detection statistic are investigated from first principles. The p -value methodology that is discussed is general, but the discussions regarding a specific detection statistic apply to the detection of a stochastic background of gravitational waves with PTAs. All methods in the literature to calculate p -values for such a detection statistic are rigorously analyzed, and analytical expressions are derived for the distribution of the detection statistic and the corresponding p -values. All this leads to the conclusion that scrambling methods are model independent and thus not completely empirical. With a single realization of data our results are necessarily always model dependent, which any analysis will need to accept. Instead of scrambling approaches, rigorous Bayesian and Frequentist p -value calculation methods are advocated, the evaluation of which depend on the generalized χ 2 distribution. This view is consistent with the posterior predictive p -value approach that is already in the literature. Efficient expressions are derived to evaluate the generalized χ 2 distribution of the detection statistic on real data. It is highlighted that no Frequentist p -values have been calculated correctly in the PTA literature to date.