Reading signatures of supermassive binary black holes in pulsar timing array observations

TL;DR

This paper re-evaluates the European Pulsar Timing Array DR2 results for the nanohertz gravitational-wave background by implementing a hierarchical, data-driven noise model that marginalises pulsar-noise priors. The analysis yields lower background amplitude $A$ and a steeper spectral index $\gamma$ closer to the canonical $\gamma=13/3$ when Hellings-Downs correlations are included, reducing tensions with SMBHB population predictions. Under the GW-driven, circular SMBHB framework, the background scales as $h_c^2(f) \propto f^{-4/3}$ with $h_c(f) \propto f^{-2/3}$, and the inferred $A$ maps to SMBH number density $\rho_{\mathrm{BH}}$ and mass scale $M_*$, bringing observations into better agreement with theoretical expectations and disfavoring strong environmental or eccentric evolution. The work underscores the critical role of accurate noise modelling in PTA analyses and provides a framework for integrating astrophysical priors with hierarchical noise inference to better constrain the SMBHB population.

Abstract

We find the inferred properties of the putative gravitational wave background in the second data release of the European Pulsar Timing Array to be in better agreement with theoretical expectations under the improved noise model. In particular, our improved noise models show consistency of the background's strain spectral index with the value of -2/3, favoring the population of supermassive black hole binaries as the origin of the background. Our results further suggest that the observed gravitational wave emission is the dominant source of the binary energy loss, with no evidence of environmental effects or eccentric orbits. At the reference gravitational wave frequency of yr$^{-1}$, we also find a lower power-law strain amplitude of the background than in previous data analyses. This mitigates some of the tensions of the strain amplitude with the expected number density and mass scale of binaries discussed in the literature. However, we show that it is mostly affected by strong covariance of the amplitude and the strain spectral index at yr$^{-1}$, whereas the strain amplitude at 0.1 yr$^{-1}$ and the strain amplitude at yr$^{-1}$ assuming a fixed spectral index of -2/3 remains unaffected. Our results highlight the importance of accurate noise models for correctly inferring properties of the gravitational wave background.

Figures (4)

• Figure 1: Posterior distributions for the power-law amplitude $A$ and spectral index $\gamma$ of the putative gravitational wave background in the European Pulsar Timing Array (EPTA) data. The results of a fit to Hellings-Downs correlations are shown in the left panel (full 25-year data) and the middle panel (the 10-year subset of the data described in ref. EPTA_DR2_GW). The results of a fit of only temporal correlations to the 10-year data are shown in the right panel. Dashed red contours correspond to the result using the standard pulsar noise priors, and the blue contours correspond to our improved model. The horizontal dashed line corresponds to the background from supermassive binary black holes inspiralling entirely due to gravitational wave emission (subject to cosmic variance). Our improved model results in a lower median-aposteriori strain amplitude of the background and mitigates tensions with $\gamma=13/3$.
• Figure 2: Consistency of the inferred strain amplitude of the gravitational wave background with theoretical expectations. Bottom panels show the predicted log-10 strain amplitude $\lg A$ from $26$ studies. Top panels show posteriors on $\lg A$ marginalised over $\gamma$. Red lines correspond to the original EPTA noise model, blue lines correspond to our revised model. Solid lines correspond to the 10-year data, dashed lines correspond to the 25-year data. Blue bands correspond to $1\sigma$ credible levels for 10-year data and our improved noise model. The left panel shows the characteristic strain amplitude at $\text{yr}^{-1}$, $\lg A$. The right panel shows the strain amplitude at the frequency of $(10~\text{yr})^{-1}$, $\lg A_{10\text{yr}}$.
• Figure 3: Posterior of the population parameters for supermassive black hole binaries with the 10-year EPTA data. Effectively, the constraints are provided solely by the inferred characteristic strain amplitude of the gravitational wave background, assuming the strain power law index of $-2/3$. Hellings-Downs correlations are included in the model.
• Figure 4: Posterior on inter-pulsar correlations of the common stochastic process in the 10-year EPTA data, assuming our improved noise model, as a function of angular separation between the observed pulsar pairs. Hellings-Downs function of the gravitational wave background is shown as the dashed line.