The NANOGrav 11-year Data Set: Pulsar-timing Constraints On The Stochastic Gravitational-wave Background (1801.02617v2)

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 $G\mu < 5.3\times 10^{-11}$---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 $\Omega_\mathrm{GWB}(f)h^2<3.4\times10^{-10}$.

• The paper introduces advanced Bayesian inference to model red-spectrum gravitational waves while addressing systematic errors from solar system ephemeris variations.
• It establishes robust upper limits on the GW strain amplitude (1.45×10⁻¹⁵) and cosmic string tension (<5.3×10⁻¹¹), tightening constraints on SMBHB and primordial sources.
• The work presents the BayesEphem method to distinguish true GW signals from spurious SSE-induced noise, enhancing the reliability of pulsar timing array analyses.

Overview of the NANOGrav 11-Year Data Set: Pulsar-Timing Constraints on the Stochastic Gravitational-Wave Background

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has released an 11-year data set aiming to constrain the stochastic gravitational-wave background (GWB) using pulsar timing. This paper details the extensive analysis conducted on this data, focusing on various noise and signal models and the imposition of tighter upper limits on potential GW sources. The paper capitalizes on continuous refinements in pulsar timing data over more than a decade, expanding the understanding of potential gravitational-wave signals emanating from supermassive black hole binaries (SMBHBs) and primordial GWs.

Key Contributions and Findings

1. Analysis Methodology: The paper leverages improved methods to detect GWs by modeling them as a red-spectrum process across pulsars. The analysis includes Bayesian inference for managing complex parameter spaces and systematic error modeling due to the Solar System ephemeris (SSE). A notable contribution is the recognition that SSE errors can mimic GWB signals.
2. Robust Limit Setting: An emphasis is placed on the GWB arising from inspiraling SMBHBs and its characterization, revealing an upper limit on the GW strain amplitude of $1.45 \times 10^{-15}$ at the frequency of 1-year$^{-1}$, marking an improvement over previous datasets. This process involves employing powerful statistical tools to ensure SSE-related systematic errors do not bias the GW constraints.
3. Solar System Ephemeris (SSE) Impact: The paper uncovers that differences in SSE models can lead to spurious signals interpreted as GWs, prompting a reevaluation of prior results. A new Bayesian method, BayesEphem, is introduced to handle these uncertainties, enhancing the reliability of current and future PTA constraints.
4. Astrophysical and Cosmological Implications: The paper discusses constraints on cosmic string tensions and the energy density of a primordial GWB, offering critical insights into the early Universe and foundational cosmological theories. The refined upper limit on cosmic string tension is demonstrated to be $G\mu < 5.3 \times 10^{-11}$, which constitutes a significant improvement and constrains theoretical models involving cosmic string formations.
5. Astrophysical Scenarios: The paper explores SMBHB interactions with galactic environments through sophisticated simulations, incorporating potential deviations from standard inspiral behavior that may affect the GWB spectrum. These novel approaches contribute to a deeper understanding of SMBH-galactic bulge scaling relationships and highlight the intention to tighten constraints on cosmic-string tension using recent simulations.

Future Prospects and Theoretical Developments

The implications of this research for the field of gravitational-wave astronomy are profound. The increasing sensitivity and analysis sophistication of PTAs, demonstrated by NANOGrav's 11-year dataset, push us closer to the thresholds required for direct GW detection. The methods and results presented significantly enhance the potential to delineate the astrophysical phenomena that govern GW sources, such as SMBHBs, and to offer evidence that could potentially validate theories of cosmic string networks and the early Universe's conditions.

Continued improvements in pulsar timing data, along with methodological advancements like BayesEphem, forecast promising developments in gravitational-wave detection within the nanohertz frequency range. These advances will enable further insights into the intricacies of galactic dynamics and provide additional constraints on cosmological models involving scenarios such as primordial GW backgrounds. The consistent refinement of these methods underscores the role of NANOGrav and similar collaborations in charting the future course of gravitational-wave astronomy.