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The NANOGrav 11-year Data Set: Pulsar-timing Constraints On The Stochastic Gravitational-wave Background

Z. Arzoumanian, P. T. Baker, A. Brazier, S. Burke-Spolaor, S. J. Chamberlin, S. Chatterjee, B. Christy, J. M. Cordes, N. J. Cornish, F. Crawford, H. Thankful Cromartie, K. Crowter, M. DeCesar, P. B. Demorest, T. Dolch, J. A. Ellis, R. D. Ferdman, E. Ferrara, W. M. Folkner, E. Fonseca, N. Garver-Daniels, P. A. Gentile, R. Haas, J. S. Hazboun, E. A. Huerta, K. Islo, G. Jones, M. L. Jones, D. L. Kaplan, V. M. Kaspi, M. T. Lam, T. J. W. Lazio, L. Levin, A. N. Lommen, D. R. Lorimer, J. Luo, R. S. Lynch, D. R. Madison, M. A. McLaughlin, S. T. McWilliams, C. M. F. Mingarelli, C. Ng, D. J. Nice, R. S. Park, T. T. Pennucci, N. S. Pol, S. M. Ransom, P. S. Ray, A. Rasskazov, X. Siemens, J. Simon, R. Spiewak, I. H. Stairs, D. R. Stinebring, K. Stovall, J. Swiggum, S. R. Taylor, M. Vallisneri, S. Vigeland, W. W. Zhu

TL;DR

This work presents a comprehensive search for an isotropic stochastic GWB in the NANOGrav 11-year data set, demonstrating that Solar System ephemeris uncertainties can mimic GW signals and must be marginalized. By combining Bayesian inference with a Gaussian-process-based spectral modeling of SMBHB populations and a BayesEphem SSE framework, the authors derive SSE-marginalized upper limits and perform robust model comparisons. No definitive GWB detection is found, but the methodology yields stringent constraints on SMBHB environments, cosmic strings, and primordial GWs, with significant improvements over prior limits. The results highlight the importance of accounting for ephemeris systematics in PTA analyses and set the stage for potential detection as datasets grow in duration and precision.

Abstract

We search for an isotropic stochastic gravitational-wave background (GWB) in the newly released $11$-year dataset from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). While we find no significant evidence for a GWB, we place constraints on a GWB from a population of supermassive black-hole binaries, cosmic strings, and a primordial GWB. For the first time, we find that the GWB upper limits and detection statistics 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 PTA constraints that are robust against SSE uncertainties. We thus place a $95\%$ upper limit on the GW strain amplitude of $A_\mathrm{GWB}<1.45\times 10^{-15}$ at a frequency of $f=1$ yr$^{-1}$ for a fiducial $f^{-2/3}$ power-law spectrum, and with inter-pulsar correlations modeled. This is a factor of $\sim 2$ improvement over the NANOGrav $9$-year limit, calculated using the same procedure. Previous PTA upper limits on the GWB will need revision in light of SSE systematic uncertainties. 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 cosmic-string tension using recent simulations, yielding an SSE-marginalized $95\%$ upper limit on the cosmic string tension of $Gμ< 5.3\times 10^{-11}$---a factor of $\sim 2$ better than the published NANOGrav $9$-year constraints. Our SSE-marginalized $95\%$ upper limit on the energy density of a primordial GWB (for a radiation-dominated post-inflation Universe) is $Ω_\mathrm{GWB}(f)h^2<3.4\times10^{-10}$.

The NANOGrav 11-year Data Set: Pulsar-timing Constraints On The Stochastic Gravitational-wave Background

TL;DR

This work presents a comprehensive search for an isotropic stochastic GWB in the NANOGrav 11-year data set, demonstrating that Solar System ephemeris uncertainties can mimic GW signals and must be marginalized. By combining Bayesian inference with a Gaussian-process-based spectral modeling of SMBHB populations and a BayesEphem SSE framework, the authors derive SSE-marginalized upper limits and perform robust model comparisons. No definitive GWB detection is found, but the methodology yields stringent constraints on SMBHB environments, cosmic strings, and primordial GWs, with significant improvements over prior limits. The results highlight the importance of accounting for ephemeris systematics in PTA analyses and set the stage for potential detection as datasets grow in duration and precision.

Abstract

We search for an isotropic stochastic gravitational-wave background (GWB) in the newly released -year dataset from the North American Nanohertz Observatory for Gravitational Waves (NANOGrav). While we find no significant evidence for a GWB, we place constraints on a GWB from a population of supermassive black-hole binaries, cosmic strings, and a primordial GWB. For the first time, we find that the GWB upper limits and detection statistics 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 PTA constraints that are robust against SSE uncertainties. We thus place a upper limit on the GW strain amplitude of at a frequency of yr for a fiducial power-law spectrum, and with inter-pulsar correlations modeled. This is a factor of improvement over the NANOGrav -year limit, calculated using the same procedure. Previous PTA upper limits on the GWB will need revision in light of SSE systematic uncertainties. 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 cosmic-string tension using recent simulations, yielding an SSE-marginalized upper limit on the cosmic string tension of ---a factor of better than the published NANOGrav -year constraints. Our SSE-marginalized upper limit on the energy density of a primordial GWB (for a radiation-dominated post-inflation Universe) is .

Paper Structure

This paper contains 23 sections, 8 equations, 12 figures, 9 tables.

Table of Contents

  1. Introduction
  2. The $11$-year Data Set
  3. Observations
  4. Processing & Time-Of-Arrival Data
  5. Timing Models & Noise Analysis
  6. Data Analysis Methods
  7. Bayesian methods
  8. Gravitational-wave strain spectrum
  9. Solar System ephemeris errors and uncertainties
  10. Data model and likelihood
  11. Optimal Statistic
  12. Software
  13. Results
  14. Bayesian upper limits
  15. Bayesian model-comparison evidence for GWs
  16. ...and 8 more sections

Figures (12)

  • Figure 1: Sky positions of all $45$ pulsars in the NANOGrav $11$-year dataset. The area of each circle is indicative of the number of TOAs, while the color scale indicates the observational baseline. The $34$ pulsars whose baselines are longer than three years are indicated with solid red edges. The Milky Way plane is shown behind as a blue band (thickness is not indicative of Galactic scale height), with the Galactic center shown as a blue star. The longest baseline is given by J$1744$$-$$1134$ with $11.37$ years, while the largest dataset is given by J$1713$$+$$0747$ with 27571 TOAs.
  • Figure 2: GWB-amplitude 95% upper limit for an uncorrelated common process (model 2A) as a function of spectral index $$ (see Eq. \ref{['eq:toaspec']}), for the JPL ephemerides and for BayesEphem. The dotted curve shows a power-law fit to the BayesEphem curve, which is consistent with a similar fit in abb+16.
  • Figure 3: Top panel: GWB-amplitude 95% upper limits for an uncorrelated common process with $= 13/3$ power law (straight black line) or with independently determined free-spectrum components (jagged black line). The thickness of the lines spans the spread of results over different ephemerides. The dash-dotted line shows the expected sensitivity scaling behavior for white-noise. The colored dashed lines and bands show median and one-sigma ranges for the GWB amplitudes predicted in mop14 (green), ss16 (orange), and s16 (blue). Bottom panel: As in the top panel, except showing the results in terms of the stochastic GWB energy density (per logarithmic frequency bin)in the Universe as a fraction of closure density, $\Omega_\mathrm{GWB}(f)h^2$. The relationship between $h_c(f)$ and $\Omega_\mathrm{GWB}(f)h^2$ is given in \ref{['eq:omega_gwb']}.
  • Figure 4: Bayes factors for model comparisons on the 11-year dataset: on the left, evidence of a GWB; on the right, effects of spatially correlated systematics. In these graphs, each model (as described in \ref{['tab:spatialcorr_modeltab']}) is represented by a bubble, and for each pair of models the dots mark on a logarithmic scale the measured Bayes factor in favor of the model at the head of the arrow. Thus, dots are closer to the model favored by the data. The smaller colored dots represent Bayes factors computed by taking one of the DE421, DE430, DE435, and DE436 JPL ephemerides as a fixed-parameter model without uncertainties; the larger black dots represent Bayes factors computed by marginalizing over ephemeris errors (i.e., by adopting BayesEphem). Dots to the left of the arrows correspond to fixing the spectral slope $$ of the GWB to 13/3, as appropriate for a background from SMBHBs evolving purely by GW emission; dots to the right correspond to marginalizing over $$, taken to have uniform prior distribution in $[0,7]$. The graph on the left shows that when adopting the JPL ephemerides as fixed-parameter models, most of the evidence for a GWB accrues from the presence of unexplained red-spectrum residuals in each pulsar (2A--1), with a smaller preference added by modeling Hellings--Downs correlations (3A--2A); neither conclusion is supported by BayesEphem. As for the graph on the right: The bottom row compares a common uncorrelated red process with dipolar and monopolar processes; the former is favored. The top row examines the case for dipolar and monopolar processes in the presence of a Hellings--Downs (GW-like) signal. Comparing the vertical arrows in the left and right graphs we see that (for fixed JPL ephemerides) evidence for a GW-like signal is weakened when the model allows for other spatially correlated processes.
  • Figure 5: Posterior probability distributions for $A_\mathrm{GWB}$ (log-uniform prior, $= 13/3$, and no spatial correlations), as computed for the NANOGrav 11-year dataset under individual JPL ephemerides (dashed lines), and with BayesEphem, taking each of the JPL ephemerides as a starting point (solid lines). This plots demonstrates that BayesEphem bridges the JPL ephemerides successfully; in doing so it removes most evidence for the presence of a GWB.
  • ...and 7 more figures