Pulsar Timing Array Experiments Research Articles

The behaviour of eccentric sub-pc massive black hole binaries embedded in massive discs

Using the 3D smoothed-particle hydrodynamics code phantom we investigated the evolution of the orbital properties of massive black hole binaries embedded in massive discs where gravitational instabilities (GIs) triggered by the disc's self-gravity are the only significant source of angular momentum transport. In particular, we investigated the evolution of binaries with different initial eccentricities of $e_0=0.05,\,0.5,\,0.8$ and mass ratios of $q=0.1,\,0.3,\,0.9$. Previous studies indicate an equilibrium eccentricity of around $0.6<e<0.8$, where the binary tidal torques and disc self-gravity torque are in dynamical balance. Our simulations suggest that there might not be a universal value of critical eccentricity. We find that binaries that are initially more eccentric attain higher asymptotic eccentricity than more circular ones do. This implies that there is a range of critical eccentricity values that depend on the initial condition and microphysics (initial eccentricity, mass ratio, cooling) of the system. In particular, we find the width of this range to be narrower for more unequal binaries. We furthermore measured preferential accretion on one of the binary components, only finding more accretion onto the primary for the mass ratio $q=0.3$ and eccentricity $e=0.8$. We discuss how this might have implications for the amplitude of the gravitational wave background detected by pulsar timing array (PTA) experiments. We finally measure the corresponding value of the viscosity parameter alpha due to GIs in our simulations and discuss how this depends on the binary properties.

Improving pulsar timing precision through superior time-of-arrival creation

The measurement of pulsar pulse times-of-arrival (ToAs) is a crucial step in detecting low-frequency gravitational waves. To determine ToAs, we can use template-matching to compare each observed pulse profile with a standard template. However, using different combinations of templates and template-matching methods (TMMs) without careful consideration can lead to inconsistent results. In pulsar timing array (PTA) experiments, distinct ToAs from the same observations can be obtained due to the use of diverse templates and TMMs. In other words, employing diverse approaches can yield different timing results and would thus have a significant impact on subsequent gravitational wave searches. In this paper we examine several commonly used combinations to analyze their effect on pulse ToAs. We evaluated the potential impact of template and TMM selection on 13 typical millisecond pulsars within the European PTA. We employed pulsar timing methods, specifically the root mean square and reduced chi-square ($ of the residuals of the best timing solution, to assess the outcomes. Additionally, we evaluated the system-limited noise floor (SLNF) for each pulsar at various telescopes operating around 1.4 GHz using frequency-resolved templates. Our findings suggest that utilizing data-derived and smoothed templates in conjunction with the Fourier-domain with Markov chain Monte Carlo TMM is generally the most effective approach, though there may be exceptions that require further attention. Furthermore, we determine that pulse phase jitter noise does not significantly limit the current precision of the European PTA's timing, as jitter levels derived from other studies are much lower than the SLNF.

Low-frequency pulse-jitter measurement with the uGMRT I : PSR J0437–4715

Abstract High-precision pulsar timing observations are limited in their accuracy by the jitter noise that appears in the arrival time of pulses. Therefore, it is important to systematically characterise the amplitude of the jitter noise and its variation with frequency. In this paper, we provide jitter measurements from low-frequency wideband observations of PSR J0437–4715 using data obtained as part of the Indian Pulsar Timing Array experiment. We were able to detect jitter in both the 300 - 500 MHz and 1260 - 1460 MHz observations of the upgraded Giant Metrewave Radio Telescope (uGMRT). The former is the first jitter measurement for this pulsar below 700 MHz, and the latter is in good agreement with results from previous studies. In addition, at 300 - 500 MHz, we investigated the frequency dependence of the jitter by calculating the jitter for each sub-banded arrival time of pulses. We found that the jitter amplitude increases with frequency. This trend is opposite as compared to previous studies, indicating that there is a turnover at intermediate frequencies. It will be possible to investigate this in more detail with uGMRT observations at 550 - 750 MHz and future high sensitive wideband observations from next generation telescopes, such as the Square Kilometre Array. We also explored the effect of jitter on the high precision dispersion measure (DM) measurements derived from short duration observations. We find that even though the DM precision will be better at lower frequencies due to the smaller amplitude of jitter noise, it will limit the DM precision for high signal-to-noise observations, which are of short durations. This limitation can be overcome by integrating for a long enough duration optimised for a given pulsar.

Revisiting metastable cosmic string breaking

Metastable cosmic strings appear in models of new physics with a two-step symmetry breaking G → H → 1, where π1(H) ≠ 0 and π1(G) = 0. They decay via the monopole-antimonopole pair creation inside. Conventionally, the breaking rate has been estimated by an infinitely thin string approximation, which requires a large hierarchy between the symmetry breaking scales. In this paper, we reexamine it by taking into account the finite sizes of both the cosmic string and the monopole. We obtain a robust lower limit on the tunneling factor e−SB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {e}^{-{S}_B} $$\\end{document} even for regimes the conventional estimate is unreliable. In particular, it is relevant to the cosmic string interpretation of the gravitational wave signals recently reported by pulsar timing array experiments.

Connecting low-redshift LISA massive black hole mergers to the nHz stochastic gravitational wave background

Pulsar Timing Array (PTA) experiments worldwide recently reported evidence of a nHz stochastic gravitational wave background (sGWB) compatible with the existence of slowly inspiralling massive black hole (MBH) binaries (MBHBs). The shape of the signal contains valuable information about the evolution of $z<1$ MBHs above $ odot $, suggesting a faster dynamical evolution of MBHBs towards the gravitational-wave-driven inspiral or a larger MBH growth than usually assumed. In this work, we investigate if the nHz sGWB could also provide constraints on the population of merging lower-mass MBHBs ($ odot $) detectable by LISA. To this end, we use the L-Galaxies semi-analytical model applied to the Millennium suite of simulations. We generate a population of MBHs compatible simultaneously with current electromagnetic and nHz sGWB constraints by including the possibility that, in favourable environments, MBHs can accrete gas beyond the Eddington limit. The predictions of this new model for the sGWB show that the global (integrated up to high-$z$) LISA detection rate is not significantly affected when compared to a fiducial model whose nHz sGWB signal is $ sim \,2$ times smaller. In both cases, the global rate yields sim $ and is dominated by systems of $ odot $. The main differences are limited to low-$z$ ($z<3$), high-mass ($ odot $) LISA MBHBs. The model compatible with the latest PTA results predicts up to $ sim \,1.6$ times more detections, with a rate of sim erg/s$. Hence, in case PTA results are confirmed and given the current MBH modelling, our findings suggest there will be higher chances to perform multimessenger studies with LISA MBHB than previously expected.

Imprint of inflationary gravitational waves and WIMP dark matter in pulsar timing array data

Motivated by the recent release of new results from five different pulsar timing array (PTA) experiments claiming to have found compelling evidence for primordial gravitational waves (GW) at nano-Hz frequencies, we consider the prospects of generating such a signal from inflationary blue-tilted tensor power spectrum in a specific dark matter (DM) scenario dubbed as Miracle-less WIMP. While Miracle-less WIMP, due to insufficient interaction rate with the Standard Model (SM) bath gets thermally overproduced, inflationary blue-tilted gravitational waves (BGW) in compliance with PTA data, conflict cosmological observations if reheat temperature after inflation is sufficiently high. Both these issues are circumvented with late entropy dilution, bringing DM abundance within observational limits and creating a doubly-peaked feature in the BGW spectrum consistent with cosmological observations. The blue-tilted tail of the low-frequency peak can fit NANOGrav 15 yr data, while other parts of the spectrum are within reach of present and future GW experiments.

The NANOGrav 12.5 yr Data Set: A Computationally Efficient Eccentric Binary Search Pipeline and Constraints on an Eccentric Supermassive Binary Candidate in 3C 66B

The radio galaxy 3C 66B has been hypothesized to host a supermassive black hole binary (SMBHB) at its center based on electromagnetic observations. Its apparent 1.05 yr period and low redshift (∼0.02) make it an interesting testbed to search for low-frequency gravitational waves (GWs) using pulsar timing array (PTA) experiments. This source has been subjected to multiple searches for continuous GWs from a circular SMBHB, resulting in progressively more stringent constraints on its GW amplitude and chirp mass. In this paper, we develop a pipeline for performing Bayesian targeted searches for eccentric SMBHBs in PTA data sets, and test its efficacy by applying it to simulated data sets with varying injected signal strengths. We also search for a realistic eccentric SMBHB source in 3C 66B using the NANOGrav 12.5 yr data set employing PTA signal models containing Earth term-only as well as Earth+pulsar term contributions using this pipeline. Due to limitations in our PTA signal model, we get meaningful results only when the initial eccentricity e 0 < 0.5 and the symmetric mass ratio η > 0.1. We find no evidence for an eccentric SMBHB signal in our data, and therefore place 95% upper limits on the PTA signal amplitude of 88.1 ± 3.7 ns for the Earth term-only and 81.74 ± 0.86 ns for the Earth+pulsar term searches for e 0 < 0.5 and η > 0.1. Similar 95% upper limits on the chirp mass are (1.98 ± 0.05) × 109 and (1.81 ± 0.01) × 109 M ☉. These upper limits, while less stringent than those calculated from a circular binary search in the NANOGrav 12.5 yr data set, are consistent with the SMBHB model of 3C 66B developed from electromagnetic observations.

Stochastic Wave Dark Matter with Fermi-LAT γ-Ray Pulsar Timing Array

Pulsar timing arrays (PTAs) can detect disturbances in the fabric of spacetime on a galactic scale by monitoring the arrival time of pulses from millisecond pulsars (MSPs). Recent advancements have enabled the use of γ-ray radiation emitted by MSPs, in addition to radio waves, for PTA experiments. Wave dark matter (DM), a prominent class of DM candidates, can be detected with PTAs due to its periodic perturbations of the spacetime metric. In response to this development, we perform in this Letter a first analysis of applying the γ-ray PTA to detect the ultralight axion-like wave DM, with the data of Fermi Large Area Telescope (Fermi-LAT). Despite its much smaller collecting area, the Fermi-LAT γ-ray PTA demonstrates a promising sensitivity potential. We show that the upper limits not far from those of the dedicated radio-PTA projects can be achieved. Moreover, we initiate a cross-correlation analysis using the data of two Fermi-LAT pulsars. The cross-correlation of phases, while carrying key information on the source of the spacetime perturbations, has been ignored in the existing data analyses for the wave DM detection with PTAs. Our analysis indicates that taking this information into account can improve the sensitivity to wave DM by ≳50% at masses below 10−23 eV.

Massive black hole binaries as sources of low-frequency gravitational waves and X-shaped radio galaxies

ABSTRACT We present the study of multimessenger signatures of massive black hole (MBH) binaries residing in the centres of galaxy merger remnants. In particular, we first focus on the gravitational wave background (GWB) produced by an ensemble of MBH binary inspirals in the frequency range probed by the Pulsar Timing Array (PTA) experiments. The improved estimates of the characteristic strain were obtained with the inclusion of environmental effects on the MBH binary orbital decay within the galaxy merger remnants, added in post-processing to the semi-analytical model of galaxy formation and evolution SHARK. Secondly, we explore two, intriguing in terms of the MBH binary evolution studies, hypotheses aiming to explain the origins of X-shaped radio galaxies – a peculiar type of objects with double lobe structures, constituting approximately 6–10 per cent of known radio loud galaxies. The two considered scenarios involve either an abrupt change in the jet direction after an MBH merger (a spin-flip) or an unresolved close binary, where each of the two components produces a jet. We find that the estimated GWB amplitude at the reference frequency $f_0=1 \, {\rm yr}^{-1}$ is in the range of $A_{\rm { yr^{-1}}} = 1.20\times 10^{-15}{\!-\!}1.46\times 10^{-15}$, which is 50 per cent lower than the strain of the signal detected by the PTA experiments. We also show that the spin-flip scenario considered in gas-poor mergers reproduces the observed properties of X-shaped radio galaxies well in terms of flip angle, redshift, and luminosity distributions.

Enhancement of gravitational waves at Q-ball decay including non-linear density perturbations

The existence of a stochastic gravitational wave background is indicated by the recent pulsar timing array (PTA) experiments. We study the enhanced production of second-order gravitational waves from the scalar perturbations when the universe experiences a transition from the early matter-dominated era to the radiation-dominated era due to Q-ball decay. We extend the analysis in previous work by including the frequency range where density perturbations go non-linear and find that the resultant gravitational wave spectrum can be consistent with that favored by the recent PTA experiment results.

Probing stochastic gravitational wave background from SU(5) × U(1)χ strings in light of NANOGrav 15-year data

A realistic model of SU(5) × U(1)χ, embedded in SO(10) supersymmetric grand unified theory, is investigated for the emergence of a metastable cosmic string network. This network eventually decays via the Schwinger production of monopole-antimonopole pairs, subsequently generating a stochastic gravitational wave background that is compatible with the NANOGrav 15-year data. In order to avoid the monopole problem in the breaking of both SO(10) and SU(5), a non-minimal Higgs inflation scenario is incorporated. The radiative breaking of the U(1)χ symmetry at a slightly lower scale plays a pivotal role in aligning the string tension parameter with the observable range. The resultant gravitational wave spectrum not only accounts for the signal observed in the most recent pulsar timing array (PTA) experiments but is also accessible to both current and future ground-based and space-based experiments.

Decade-long Timing of Four GMRT Discovered Millisecond Pulsars

The discovery and timing follow up of millisecond pulsars (MSPs) are necessary not just for their usefulness in pulsar timing arrays (PTAs) but also for investigating their own intriguing properties. In this work, we provide the findings of the decade-long timing of four MSPs discovered by the Giant Meterwave Radio Telescope (GMRT), including their timing precision, model parameters, and newly detected proper motions. We compare the timing results for these MSPs before and after the GMRT upgrade in 2017 and characterize the improvement in timing precision due to the bandwidth upgrade. We discuss the suitability of these four GMRT MSPs as well as the usefulness of the decade-long timing data for PTA experiments. These data may aid in the global effort to improve the signal-to-noise ratios of recently detected signature of gravitational waves in cross-correlation statistics of residuals of MSPs.

QCD-collapsed domain walls: QCD phase transition and gravitational wave spectroscopy

For a discrete symmetry that is anomalous under QCD, the domain walls produced in the early universe from its spontaneous breaking can naturally annihilate due to QCD instanton effects. The gravitational waves generated from wall annihilation have their amplitude and frequency determined by both the discrete symmetry breaking scale and the QCD scale. The evidence of stochastic gravitational waves at nanohertz observed by pulsar timing array experiments suggests that the discrete-symmetry-breaking scale is around 100 TeV, assuming the domain-wall explanation. The annihilation temperature is about 100 MeV, which could naturally be below the QCD phase transition temperature. We point out that the QCD phase transition within some domains with an effective large QCD θ angle could be a first-order one. To derive the phase diagram in θ and temperature, we adopt a phenomenological linear sigma model with three quark flavors. The domain-wall explanation for the NANOGrav, EPTA, PPTA and CPTA results hints at a first-order QCD phase transition, which predicts additional gravitational waves at higher frequencies. If the initial formation of domain walls is also a first-order process, this class of domain-wall models predicts an interesting gravitational wave spectroscopy with frequencies spanning more than ten orders of magnitude, from nanohertz to 100 Hz.

Scale of Dirac leptogenesis and left-right symmetry in the light of recent PTA results

Motivated by the recent release of new results from five different pulsar timing array (PTA) experiments claiming to have found compelling evidence for primordial gravitational waves (GW) at nano-Hz frequencies, we study the consequences for two popular beyond the Standard Model (SM) frameworks, where such nano-Hz GW can arise due to annihilating domain walls (DW). Minimal framework of Dirac leptogenesis, as well as left-right symmetric model (LRSM) can lead to formation of DW due to spontaneous breaking of Z 2 symmetry. Considering the NANOGrav 15 yr data, we show that the scale of Dirac leptogenesis should be above 107 GeV for conservative choices of Dirac Yukawa couplings with fine-tuning at the level of the SM. The scale of minimal LRSM is found to be more constrained M LR ∼ 106 GeV in order to fit the NANOGrav 15 yr data. On the other hand, the non-minimal LRSM can be compatible with the NANOGrav data for 102 TeV ≲ M LR ≲ 103 TeV but with the corresponding B - L breaking scale violating collider bounds.

Toward Robust Detections of Nanohertz Gravitational Waves

The recent observation of a common red-noise process in pulsar timing arrays (PTAs) suggests that the detection of nanohertz gravitational waves might be around the corner. However, in order to confidently attribute this red process to gravitational waves, one must observe the Hellings–Downs curve—the telltale angular correlation function associated with a gravitational-wave background. This effort is complicated by the complex modeling of pulsar noise. Without proper care, misspecified noise models can lead to false-positive detections. Background estimation using “quasi-resampling” methods such as sky scrambles and phase shifts, which use the data to characterize the noise, are therefore important tools for assessing significance. We investigate the ability of current PTA experiments to estimate their background with “quasi-independent” scrambles—characterized by a statistical “match” below the fiducial value: ∣M∣ < 0.1. We show that sky scrambling is affected by “saturation” after quasi-independent realizations; subsequent scrambles are no longer quasi-independent. We show that phase scrambling saturates after quasi-independent realizations. With so few independent scrambles, it is difficult to make reliable statements about the ≳5σ tail of the null distribution of the detection statistic. We sketch out various methods by which one may increase the number of independent scrambles. We also consider an alternative approach, wherein one reframes the background estimation problem so that the significance is calculated using statistically dependent scrambles. The resulting p-value is in principle well defined, but may be susceptible to failure if assumptions about the data are incorrect.

Dark baryon from pure Yang-Mills theory and its GW signature from cosmic strings

We point out that SO(2N) pure Yang-Mills theory provides a candidate for dark matter (DM) without the explicit need to impose any additional symmetry. The DM candidate is a particular type of glueball, which we refer to as a baryonic glueball, that is naturally stable and produced by a novel production mechanism for a moderately large N. In this case, the intercommutation probability of cosmic strings (or macroscopic color flux tubes) is quite low, which offers characteristic gravitational wave signals to test our model. In particular, our model can simultaneously account for both abundance of DM and the recently reported gravitational wave signals detected in pulsar timing array experiments, including NANOGrav.

Nanohertz gravitational waves from cosmic strings and dark photon dark matter

The recent observations by pulsar timing array (PTA) experiments suggest the existence of stochastic gravitational wave background in the nano-Hz range. It can be a hint for the new physics and cosmic string is one of the promising candidates. In this paper, we study the implication of the PTA result for cosmic strings and dark photon dark matter produced by the decay of cosmic string loops. It can simultaneously explain the PTA result and present dark matter abundance for the dark photon mass m∼10−7–10−5eV. Implications for the gravitational wave detection with multi-frequency bands are also discussed.

Pulsar timing array observations as possible hints for nonsingular cosmology

Recent pulsar timing array (PTA) experiments have reported strong evidence of the stochastic gravitational wave background (SGWB). If interpreted as primordial gravitational waves (GWs), the signal favors a strongly blue-tilted spectrum. Consequently, the nonsingular cosmology, which is able to predict a strongly blue-tilted GW spectrum with n_T simeq 2 on certain scales, offers a potential explanation for the observed SGWB signal. In this paper, we present a Genesis-inflation model capable of explaining the SGWB signal observed by the PTA collaborations while also overcoming the initial singularity problem associated with the inflationary cosmology. Furthermore, our model predicts distinctive features in the SGWB spectrum, which might be examined by forthcoming space-based gravitational wave experiments.

Peaky production of light dark photon dark matter

We explore a mechanism to produce a light dark photon dark matter through a coupling between the dark photon field and a spectator scalar field which plays no role in the inflationary expansion of the Universe while rolling down its potential during the inflation. The motion of the spectator field efficiently produces dark photons with large wavelengths which become non-relativistic before the time of matter-radiation equality. The spectrum of the wavelengths is peaky so that the constraint from the isocurvature perturbation can be evaded. The correct relic abundance is then achieved over a wide range of the dark photon mass down to 10-13 eV. Our mechanism favors high-scale inflation models which can be tested in future observations. Furthermore, fluctuations of the dark photon field during inflation produce gravitational waves detectable at future space-based interferometers and/or pulsar timing array experiments.

Inflationary interpretation of the stochastic gravitational wave background signal detected by pulsar timing array experiments

Various pulsar timing array (PTA) experiments (NANOGrav, EPTA, PPTA, CPTA, including data from InPTA) very recently reported evidence for excess red common-spectrum signals in their latest datasets, with inter-pulsar correlations following the Hellings-Downs pattern, pointing to a stochastic gravitational wave background (SGWB) origin. Focusing for concreteness on the NANOGrav signal (given that all signals are in good agreement between each other), I inspect whether it supports an inflationary SGWB explanation, finding that such an interpretation calls for an extremely blue tensor spectrum, with spectral index nT≃1.8±0.3, while Big Bang Nucleosynthesis limits require a very low reheating scale, Trh≲10GeV. While not impossible, an inflationary origin for the PTA signal is barely tenable: within well-motivated inflationary models it is hard to achieve such a blue tilt, whereas models who do tend to predict sizeable non-Gaussianities, excluded by observations. Intriguingly, ekpyrotic models naturally predict a SGWB with spectral index nT=2, although with an amplitude too suppressed to be able to explain the signal detected by PTA experiments. Finally, I provide explicit expressions for a bivariate Gaussian approximation to the joint posterior distribution for the intrinsic-noise amplitude and spectral index of the NANOGrav signal, which can facilitate extending similar analyses to different theoretical signals.