The NANOGrav 12.5-year Data Set: Search For An Isotropic Stochastic Gravitational-Wave Background

Abstract

We search for an isotropic stochastic gravitational-wave background (GWB) in the $12.5$-year 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. The Bayesian posterior of the amplitude for an $f^{-2/3}$ power-law spectrum, expressed as the characteristic GW strain, has median $1.92\times 10^{-15}$ and $5\%$--$95\%$ quantiles of $1.37$--$2.67\times 10^{-15}$ at a reference frequency of $f_{\mathrm{yr}}=1{\mathrm{yr}}^{-1}$. 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.

arXiv comment25 pages, 14 figures, 5 tables, 3 appendices. Published in The Astrophysical Journal Letters. Please send any comments/questions to Joseph Simon ([email protected]). Jupyter notebook tutorials and some MCMC chain files are available at https://github.com/nanograv/12p5yr_stochastic_analysis

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• Implication of Pulsar Timing Array Experiments on Cosmological Gravitational Wave Detection
• Black Holes Up Close
• Variable Scintillation Arcs of Millisecond Pulsars observed with the Large European Array for Pulsars
• Constraints on ultra-slow-roll inflation from the third LIGO-Virgo observing run
• Scalar-Induced Gravitational Waves from Ghost Inflation and Parity Violation
• Interaction of supernova neutrinos with stochastic gravitational waves
• Optical follow-up of the tick-tock massive black hole binary candidate
• Induced Gravitational Waves from Multi-Sound Speed Resonances during Cosmological Inflation
• Signatures of a High Temperature QCD Transition in the Early Universe
• Constraining ultralight dark matter using the Fermi-LAT pulsar timing array
• Powerful Radio-Loud Quasars are Triggered by Galaxy Mergers in the Cosmic Bright Ages
• Invoking the virial theorem to understand the impact of (dry) mergers on the $M_{\mathrm{bh}}$-$\sigma$ relation
• Sudden braking and turning with a two-field potential bump: primordial black hole formation
• Looking out for the Galileon in the nanohertz gravitational wave sky
• The NANOGrav 12.5-year data set: A computationally efficient eccentric binary search pipeline and constraints on an eccentric supermassive binary candidate in 3C 66B
• D-term inflation in braneworld models: Consistency with cosmic-string bounds and early-time Hubble tension resolving models
• Timing-residual power spectrum of a polarized stochastic gravitational-wave background in pulsar-timing-array observation
• Primordial black holes generated by fast-roll mechanism in non-canonical natural inflation
• Pulsar Timing Arrays require hierarchical models
• Stochastic gravitational wave background due to gravitational wave memory
• Gravitational waves from holographic QCD phase transition with gluon condensate
• Impact of quasi-periodic and steep-spectrum timing noise on the measurement of pulsar timing parameters
• Detecting Cosmic Strings with Lensed Fast Radio Bursts
• Principles of Gravitational-Wave Detection with Pulsar Timing Arrays
• Collapsing domain walls beyond $Z_2$
• Implications of Gravitational Waves for Supersymmetric Grand Unification
• Enhanced primordial gravitational waves from a stiff post-inflationary era due to an oscillating inflaton
• Spatial and Spectral Characterization of the Gravitational-wave Background with the PTA Optimal Statistic
• Redshift-space fluctuations in stochastic gravitational wave background
• A first order dark $SU(2{)}_D$ phase transition with vector dark matter in the light of NANOGrav 12.5 yr data
• Unveiling the hosts of parsec-scale massive black hole binaries: morphology and electromagnetic signatures
• Astrometric Gravitational-Wave Detection via Stellar Interferometry
• Primordial Black Hole Formation in Non-Standard Post-Inflationary Epochs
• Generalized optimal statistic for characterizing multiple correlated signals in pulsar timing arrays
• "Stairway to Heaven" -- Spectroscopy of Particle Couplings with Gravitational Waves
• The Search for Binary Supermassive Black Holes Amongst Quasars with Offset Broad Lines Using the Very Long Baseline Array
• Using Pulsar Parameter Drifts to Detect Sub-Nanohertz Gravitational Waves
• An estimate of the stochastic gravitational wave background from the MassiveBlackII simulation
• Big Bang Nucleosynthesis Limits and Relic Gravitational Waves Detection Prospects
• Searching for Dark Clumps with Gravitational-Wave Detectors
• A comparative analysis of pulse time-of-arrival creation methods
• Detectability of Primordial Black Hole Binaries at High Redshift
• Tensor Perturbations from Bounce Inflation Scenario in f(Q) Gravity
• Noise analysis of the Indian Pulsar Timing Array data release I
• Simulating relic gravitational waves from inflationary magnetogenesis
• Profile changes associated with DM events in PSR J1713+0747
• Bayesian search for gravitational wave bursts in pulsar timing array data
• Gravitational waves from cosmic strings associated with pseudo-Nambu-Goldstone dark matter
• Toward robust detections of nanohertz gravitational waves
• Unveiling the Graviton Mass Bounds through Analysis of 2023 Pulsar Timing Array Data Releases
• Imprint of PBH domination on gravitational waves generated by cosmic strings
• A single pulse study of a millisecond pulsar PSR J0621+1002
• Discovering new forces with gravitational waves from supermassive black holes
• Generalized $R^p$-attractor Cosmology in the Jordan and Einstein Frames: New Type of Attractors and Revisiting Standard Jordan Frame $R^p$ Inflation
• Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: I. The optimal statistic
• Harmonic analysis for pulsar timing arrays
• Warp factor and the gravitational wave spectrum
• Exploring the Capabilities of Gibbs Sampling in Pulsar Timing Arrays
• On Detecting Nearby Nano-Hertz Gravitational Wave Sources via Pulsar Timing Arrays
• Constraining changes in the merger history of (P)BH binaries with the stochastic gravitational wave background
• NGC 6240 Supermassive Black Hole Binary dynamical evolution based on Chandra data
• Probing ultralight scalar, vector and tensor dark matter with pulsar timing arrays
• Inflation, space-borne interferometers and the expansion history of the Universe
• Constraints on conformal ultralight dark matter couplings from the European Pulsar Timing Array
• Distinguishing black holes with and without spontaneous scalarization in Einstein-scalar-Gauss-Bonnet theories via optical features
• Probing the primordial Universe with 21-cm line from cosmic dawn/epoch of reionization
• Full analytic expression of overlap reduction function for gravitational wave background with pulsar timing arrays
• Premerger detection of massive black hole binaries using deep learning
• Measuring the primordial gravitational wave background in the presence of other stochastic signals
• Gravitational wave non-linearities and pulsar-timing array angular correlations
• Constraining the Gravitational-Wave Spectrum from Cosmological First-Order Phase Transitions Using Data from LIGO-Virgo First Three Observing Runs
• Nonlinear gravitational-wave memory from cusps and kinks on cosmic strings
• The Impact of Black Hole Scaling Relation Assumptions on the Mass Density of Black Holes
• Strongly Magnetized Hot QCD Matter and Stochastic Gravitational Wave Background
• Gravitational Waves from Incomplete Inflationary Phase Transitions
• Sensitivity of third-generation interferometers to extra polarizations in the Stochastic Gravitational Wave Background
• Long-Lived Quasinormal Modes of Brane-Localized Reissner-Nordström--de Sitter Black Holes
• Multimessenger Approaches to Supermassive Black Hole Binary Detection and Parameter Estimation II: Optimal Strategies for a Pulsar Timing Array
• Gravitational waves in neutrino plasma and NANOGrav signal
• Stochastic gravitational wave background: birth from string-wall death
• Stochastic gravitational waves from long cosmic strings
• Gravitational Waves from Phase Transitions
• Implications for Cosmic Domain Walls from LIGO-Virgo First Three Observing Runs
• Boltzmann equations for astrophysical Stochastic Gravitational Wave Backgrounds scattering off of massive objects
• Gravitational Wave Statistics for Pulsar Timing Arrays: Examining Bias from Using a Finite Number of Pulsars
• Post-Newtonian-accurate pulsar timing array signals induced by inspiralling eccentric binaries: accuracy, computational cost, and single-pulsar search
• Fast Likelihood-free Reconstruction of Gravitational Wave Backgrounds
• Extragalactic neutrino emission induced by Supermassive and Stellar Mass Black Hole mergers
• Swampland Criteria and Constraints on Inflation in a $f(R,T)$ Gravity Theory
• Constraining models of Inflationary Magnetogenesis with NANOGrav
• Probing the Delay Time of Supermassive Black Hole Binary Mergers With Gravitational Waves
• The Green Bank North Celestial Cap Survey IX: Timing Follow-up for 128 Pulsars
• Systematic errors in searches for nanohertz gravitational waves
• Cosmic (super)strings with a time-varying tension
• Iterative time-domain method for resolving multiple gravitational wave sources in Pulsar Timing Array data
• Gravitational waves and primordial black holes from chirality imbalanced QCD first-order phase transition with $\mathcal{P}$ and $\mathcal{C}\mathcal{P}$ violation
• Imprint of Early Dark Energy in Stochastic Gravitational Wave Background
• Implementation of an efficient Bayesian search for gravitational wave bursts with memory in pulsar timing array data
• Gauge-Invariant Tensor Perturbations Induced from Baryon-CDM Relative Velocity and the B-mode Polarization of the CMB
• White dwarf binary modulation can help stochastic gravitational wave background search
• Is the black-widow pulsar PSR J1555-2908 in a hierarchical triple system?
• Low frequency tail of gravitational wave spectra from hydromagnetic turbulence
• Induced gravitational waves from statistically anisotropic scalar perturbations
• Predictions for LISA and PTA based on SHARK galaxy simulations
• Gravitational Wave Measurement in the Mid-Band with Atom Interferometers
• Solving the PTA Data Analysis Problem with a Global Gibbs Scheme
• Dynamics of Confined Monopoles and Similarities with Confined Quarks
• Domain Wall Network: A Dual Solution for Gravitational Waves and Hubble Tension?
• Signals of merging supermassive primordial black holes in pulsar timing arrays
• A Study in Frequency-Dependent Effects on Precision Pulsar Timing Parameters with the Pulsar Signal Simulator
• Stellar hardening of massive black hole binaries: the impact of the host rotation
• Deep VLBI Observations Challenge Previous Evidence of a Binary Supermassive Black Hole Residing in the Seyfert Galaxy NGC 7674
• PSR J0437-4715: The Argentine Institute of Radioastronomy 2019-2020 Observational Campaign
• Ensemble noise properties of the European Pulsar Timing Array
• Fundamental Physics and Cosmology with TianQin
• Gravitational Waves from the Cosmological Quark-Hadron Phase Transition Revisited
• Parameter-Estimation Biases for Eccentric Supermassive Binary Black Holes in Pulsar Timing Arrays: Biases Caused by Ignored Pulsar Terms
• Modern Cosmology, an Amuse-Gueule
• The effect of quantum decoherence on inflationary gravitational waves
• Orbit Tomography of Binary Supermassive Black Holes with Very Long Baseline Interferometry
• Seeing the gravitational wave universe
• Implications of Pulsar Timing Array Results for High Frequency Gravitational Waves
• Search for stochastic gravitational-wave background from string cosmology with Advanced LIGO and Virgo's O1$\sim$O3 data
• All-sky analysis of astrochronometric signals induced by gravitational waves
• Posterior predictive checking for gravitational-wave detection with pulsar timing arrays: II. Posterior predictive distributions and pseudo Bayes factors
• Scattering Delay Mitigation in High Accuracy Pulsar Timing: Cyclic Spectroscopy Techniques
• Tracking Down the Route to the SM with Inflation and Gravitational Waves
• Host Galaxy Demographics Of Individually Detectable Supermassive Black-hole Binaries with Pulsar Timing Arrays
• Complex morphology and precession indicators of AGN jets in LoTSS DR2
• Astrometry meets Pulsar Timing Arrays: Synergies for Gravitational Wave Detection
• Reducing instrumental errors in Parkes Pulsar Timing Array data
• Signal of Cosmic Strings in Cross-Correlation of 21-cm Redshift and CMB Polarization Maps
• Minimally modified gravity with auxiliary constraints formalism
• Dark Matter Spike surrounding Supermassive Black Holes Binary and the Nanohertz Stochastic Gravitational Wave Background
• Model-independent search for anisotropies in stochastic gravitational-wave backgrounds and application to LIGO-Virgo's first three observing Runs
• Scalar-Induced Gravitational Waves in a $\Lambda$CDM Cosmology
• Real-Time Nucleation and Off-Equilibrium Effects in High-Temperature Quantum Field Theories
• The refractive index of the relic gravitons and the nHz band
• Astrophysics with the Laser Interferometer Space Antenna
• A Parkes "Murriyang" Search for Pulsars and Transients in the Large Magellanic Cloud
• Gravitational wave background discovered by NANOGrav as evidence of a cyclic universe
• Non-linear corrections of overlap reduction functions for pulsar timing arrays
• Climbing over the potential barrier during inflation via null energy condition violation
• Earth-mass primordial black hole mergers as sources for non-repeating FRBs
• Damping of long wavelength gravitational waves by the intergalactic medium
• Gravitational waves in models with multicritical-point principle
• Imprints of massive black-hole binaries on neighbouring decihertz gravitational-wave sources
• Probing intermediate scale Froggatt-Nielsen models at future gravitational wave observatories
• Implications for Pulsar Timing Arrays of Sub-solar Black Hole Detections: From LVK to Einstein Telescope and Cosmic Explorer
• Never bet against Einstein
• Improving pulsar-timing solutions through dynamic pulse fitting
• Relic gravitons and pulsar timing arrays: a theoretical viewpoint
• Gravitational waves generation in turbulent hypermagnetic fields before the electroweak phase transition
• A VLBI Proper Motion Analysis of the Recoiling Supermassive Black Hole Candidate Mrk 1018
• Massive Black Hole Mergers
• Inflation with two-form field: the production of primordial black holes and gravitational waves
• Modified propagation of gravitational waves from the early radiation era
• Probing Supermassive Black Hole Binaries with Orbital Resonances of Laser-Ranged Satellite
• The NANOGrav 15 yr data set: Posterior predictive checks for gravitational-wave detection with pulsar timing arrays
• Interferences in the Stochastic Gravitational Wave Background
• The Global 21 cm Signal of a Network of Cosmic String Wakes
• Stochastic gravitational wave background from supernovae in massive scalar-tensor gravity
• Detection of eccentric close-binary supermassive black holes with incomplete interferometric data
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme
• On Filaments, Prolate Halos and Rotation Curves
• Can QCD Axion Stars explain Subaru HSC microlensing?
• Cold Atoms in Space: Community Workshop Summary and Proposed Road-Map
• Stability of non-topological string in supersymmetric $SU(2)\times U(1)$ gauge theory
• Stability of the embedded string in the $SU(N)\times U(1)$ Higgs model and its application
• Relic gravitons and non-stationary processes
• Connecting Inflation to the NANOGrav 15-year Data Set via Massive Gravity
• On the nature of cosmic strings in the brane world
• Detecting the heterodyning of gravitational waves
• Reconciling cosmic dipolar tensions with a gigaparsec void
• Tracing the Evolution of SMBHs and Stellar Objects in Galaxy Mergers: An Multi-mass Direct N-body Model
• Testing hilltop supernatural inflation with gravitational waves
• Robust parameter estimation from pulsar timing data
• Anisotropy of Nanohertz Gravitational Wave Background and Source Clustering from Supermassive Binary Black Holes Based on Cosmological Simulation
• Primordial blackholes from Gauss-Bonnet-corrected single field inflation
• Rapid Construction of Joint Pulsar Timing Array Datasets: The Lite Method
• Bounds from multi-messenger astronomy on the Super Heavy Dark Matter
• Gravitational wave induced baryon acoustic oscillations
• Gravitational wave signal from primordial magnetic fields in the Pulsar Timing Array frequency band
• Cosmic Strings-induced CMB anisotropies in light of Weighted Morphology
• Flat spectra of cosmic gravitons in the nHz and audio bands
• Adiabatic Duality: Duality of cosmological models with varying slow-roll parameter and sound speed
• Theoretical Radio Signals from Radio-Band Gravitational Waves Converted from the Neutron Star Magnetic Field
• Simulations of helical inflationary magnetogenesis and gravitational waves
• Search for the non-linearities of gravitational wave background in NANOGrav 15-year data set
• Efficient prescription to search for linear gravitational wave memory from hyperbolic black hole encounters and its application to the NANOGrav 12.5-year dataset
• Non-Gaussianity of Tensor Induced Density Perturbations
• The Indian Pulsar Timing Array Data Release 2: II. Customised Single-Pulsar Noise Analysis and Noise Budget
• An updated constraint for the Gravitational Wave Background from the Gamma-ray Pulsar Timing Array
• Searching for continuous gravitational waves in the Parkes Pulsar Timing Array Data Release 3
• Observation of Gravitational Waves by Invariants for Electromagnetic Waves
• Magnetogenesis from Sawtooth Coupling: Gravitational Wave Probe of Reheating
• Ultra-Low Frequency Gravitational Waves from Massive Clusters at z~1
• Identifying the Quadrupolar Nature of Gravitational Wave Background through Space-based Missions
• Search for Continuous Gravitational Wave Signals in Pulsar Timing Residuals: A New Scalable Approach with Diffusive Nested Sampling
• Stochastic gravitational wave background anisotropies from inflation with non-Bunch-Davies states
• Pulsar Timing Response to Gravitational Waves with Spherical Wavefronts from a Massive Compact Source in the Quadrupole Approximation
• Gravitational Waves in Metastable Supersymmetry Breaking
• Probing Leptophobic Dark Sectors via Gravitational Wave Signatures
• Extending the Observational Frequency Range for Gravitational Waves in a Pulsar Timing Array
• Radio polarization of millisecond pulsars with multipolar magnetic fields
• Smearing of primordial gravitational waves
• Axion Dark Matter Archaeology with Primordial Gravitational Waves
• The impact of outliers on pulsar timing arrays
• Complementary signatures of $\alpha -$attractor inflation in CMB and cosmic string Gravitational Waves
• To observe, or not to observe, quantum-coherent dark matter in the Milky Way, that is a question
• Overlap reduction function for gravitational wave detectors in an expanding Universe
• Relic gravitons at intermediate frequencies and the expansion history of the Universe
• Cosmic Overture Echoed in a Stellar Final Act: Implications of Nanohertz Gravitational Waves for Core Collapse Supernova Neutrinos
• Alternative LISA-TAIJI networks: detectability of the isotropic stochastic gravitational wave background
• Comparison of maximum likelihood mapping methods for gravitational-wave backgrounds
• Gravitational wave astronomy: astrophysical and cosmological inferences
• Cosmic Collider Gravitational Waves sourced by Right-handed Neutrino production from Bubbles: Testing Seesaw, Leptogenesis and Dark Matter
• Mode changing in J1909$-$3744: the most precisely timed pulsar
• Stochastic gravitational wave background from the collisions of dark matter halos
• Covariant transverse-traceless projection for secondary gravitational waves
• Exploring realistic nanohertz gravitational-wave backgrounds
• Detecting White Dwarf Binary Mergers with Gravitational Waves
• Series expansion of the overlap reduction function for scalar and vector polarizations for gravitational wave search with pulsar timing arrays
• Cosmology of the companion-axion model: dark matter, gravitational waves, and primordial black holes
• Upper limits on microhertz gravitational waves from supermassive black-hole binaries using PSR J1909-3744 data from the second IPTA data release
• Gravitational-wave standard sirens and application in cosmology
• Testing Nambu-Goto approximation of cosmic string by lattice field simulations
• Multi-messenger parameter inference of gravitational-wave and electromagnetic observations of white dwarf binaries
• Exploring the parameter space of modified supergravity for double inflation and primordial black hole formation
• A Parallelized Bayesian Approach To Accelerated Gravitational-Wave Background Characterization
• Description and Application of the Surfing Effect
• Fast Bayesian analysis of individual binaries in pulsar timing array data
• Observation of polarized stochastic gravitational-wave background in pulsar-timing-array experiments