European Pulsar Timing Array Limits On An Isotropic Stochastic Gravitational-Wave Background (1504.03692v3)

Abstract: We present new limits on an isotropic stochastic gravitational-wave background (GWB) using a six pulsar dataset spanning 18 yr of observations from the 2015 European Pulsar Timing Array data release. Performing a Bayesian analysis, we fit simultaneously for the intrinsic noise parameters for each pulsar, along with common correlated signals including clock, and Solar System ephemeris errors, obtaining a robust 95$\%$ upper limit on the dimensionless strain amplitude $A$ of the background of $A<3.0\times 10^{-15}$ at a reference frequency of $1\mathrm{yr^{-1}}$ and a spectral index of $13/3$, corresponding to a background from inspiralling super-massive black hole binaries, constraining the GW energy density to $\Omega_\mathrm{gw}(f)h^2 < 1.1\times10^{-9}$ at 2.8 nHz. We also present limits on the correlated power spectrum at a series of discrete frequencies, and show that our sensitivity to a fiducial isotropic GWB is highest at a frequency of $\sim 5\times10^{-9}$~Hz. Finally we discuss the implications of our analysis for the astrophysics of supermassive black hole binaries, and present 95$\%$ upper limits on the string tension, $G\mu/c^2$, characterising a background produced by a cosmic string network for a set of possible scenarios, and for a stochastic relic GWB. For a Nambu-Goto field theory cosmic string network, we set a limit $G\mu/c^2<1.3\times10^{-7}$, identical to that set by the {\it Planck} Collaboration, when combining {\it Planck} and high-$\ell$ Cosmic Microwave Background data from other experiments. For a stochastic relic background we set a limit of $\Omega^\mathrm{relic}_\mathrm{gw}(f)h^2<1.2 \times10^{-9}$, a factor of 9 improvement over the most stringent limits previously set by a pulsar timing array.

• The paper establishes a 95% upper limit on the gravitational-wave strain amplitude (A < 3.0×10⁻¹⁵) using 18 years of pulsar timing observations.
• The Bayesian methodology effectively disentangles intrinsic pulsar noise from potential gravitational-wave signals to ensure robust results.
• The derived limits refine constraints on supermassive black hole binaries and cosmic string models, guiding future astrophysical research.

Overview of the European Pulsar Timing Array Limits on a Stochastic Gravitational-Wave Background

The paper by Lentati et al. presents a paper on the limits of a stochastic gravitational-wave background (GWB) using the European Pulsar Timing Array (EPTA). The analysis uses an extensive dataset spanning 18 years, incorporating observations from six pulsars. The primary goal is to establish stringent upper limits on the GWB, characterizing it as isotropic and low-frequency, originating from sources such as merging supermassive black hole binaries (SMBHBs) and possible contributions from cosmic phenomena like cosmic strings or relics from the primordial universe.

The research uses advanced statistical techniques, specifically a Bayesian approach, to modulate the noise intrinsic to the pulsar data while simultaneously searching for signals consistent with a GWB. Key results from this analysis yield a 95% upper limit on the dimensionless strain amplitude $A$ of the background of $A < 3.0 \times 10^{-15}$, with a reference frequency of $1\rm{yr^{-1}}$. This equates to a gravitational-wave energy density constrained to $\Omega_{\mathrm{gw}}(f)h^2 < 1.1 \times 10^{-9}$ at a frequency of 2.8 nHz. These constraints offer significant insights into the expected GWB from various cosmological models, providing data to influence theories on key astronomical phenomena.

Implications for Astrophysical Models

The limits derived in this work have notable implications for our understanding of SMBHBs. Although the set limits do not strongly constrain contemporary theoretical predictions for the cosmic SMBHB population, they do narrow parameter space and suggest directions for future paper. The work concludes that only a small fraction of current theoretical distributions is invalidated, indicating a necessary refinement in existing models to adapt to these observations.

Furthermore, the paper explores implications for cosmic strings—a theoretical framework positing high-energy cosmic phenomena in the early universe. The research sets an upper limit on the string tension, $G\mu/c^2$, of $G\mu/c^2 < 1.3 \times 10^{-7}$ under certain network assumptions, a noteworthy constraint in line with limits from cosmological observations such as the Planck satellite measurements.

Speculation on Future Developments

The current paper establishes a methodological framework that can be applied to larger datasets, like those anticipated from the Square Kilometer Array (SKA). This infrastructure may offer the sensitivity required to place even more stringent constraints on models of cosmic evolution, approaching theoretical thresholds for detecting a primordial relic GWB as hypothesized in some early universe cosmology models.

Practical and Theoretical Considerations

Practically, no direct detection of a GWB is observed within this paper's sensitivity limits. However, the methods employed highlight the challenges of isolating GW signals from intrinsic pulsar noise and common noise sources such as a potential error in the Solar System ephemeris. A robust analytical framework to distinguish these noises from true GWB signals will be critical as more sensitive pulsar timing datasets become available.

Theoretical advancements may lie in refining the understanding of noise sources intrinsic to the instrumentation and further modeling the detailed astrophysical processes contributing to the GWB. Such improvements will likely enhance the precision of future analyses and the potential for new astrophysical discoveries.

In conclusion, this essay outlines the significant contributions made by Lentati et al. in the research of gravitational waves using the EPTA. While not detecting GWB directly, the results lay crucial groundwork in the astrophysical community's ongoing efforts to explore the cosmos through gravitational radiation. Future advancements will continue to build upon the methodologies and insights presented in this paper.