Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: Inferences in the stochastic gravitational-wave background search (2110.13184v1)

Abstract: We present results from the search for a stochastic gravitational-wave background (GWB) as predicted by the theory of General Relativity using six radio millisecond pulsars from the Data Release 2 (DR2) of the European Pulsar Timing Array (EPTA) covering a timespan up to 24 years. A GWB manifests itself as a long-term low-frequency stochastic signal common to all pulsars, a common red signal (CRS), with the characteristic Hellings-Downs (HD) spatial correlation. Our analysis is performed with two independent pipelines, \eprise{} and \tn{}+\ftwo{}, which produce consistent results. A search for a CRS with simultaneous estimation of its spatial correlations yields spectral properties compatible with theoretical GWB predictions, but does not result in the required measurement of the HD correlation, as required for GWB detection. Further Bayesian model comparison between different types of CRSs, including a GWB, finds the most favoured model to be the common uncorrelated red noise described by a power-law with $A = 5.13_{-2.73}^{+4.20} \times 10^{-15}$ and $\gamma = 3.78_{-0.59}^{+0.69}$ (95\% credible regions). Fixing the spectral index to $\gamma=13/3$ as expected from the GWB by circular, inspiralling supermassive black-hole binaries results in an amplitude of $A =2.95_{-0.72}^{+0.89} \times 10^{-15}$. We implement three different models, BAYESEPHEM, LINIMOSS and EPHEMGP, to address possible Solar-system ephemeris (SSE) systematics and conclude that our results may only marginally depend on these effects. This work builds on the methods and models from the studies on the EPTA DR1. We show that under the same analysis framework the results remain consistent after the data set extension.

• The paper presents a 24-year high-precision analysis of pulsar timing data, revealing a common uncorrelated red noise signal as a key finding.
• It employs dual independent pipelines to compare spectral properties with theoretical expectations for a stochastic gravitational-wave background, though the Hellings-Downs correlation remains unresolved.
• The study minimizes solar-system ephemeris errors and benchmarks methods for refining gravitational-wave searches with expanded pulsar arrays and collaborative analyses.

Insights on the EPTA's 24-year Analysis of the Stochastic Gravitational-Wave Background

The subject of this paper is the detailed analysis of potential stochastic gravitational-wave backgrounds (GWB) using the 24-year high-precision timing data from the European Pulsar Timing Array (EPTA), which comprises observations from six radio millisecond pulsars. The research focuses on inferring the existence and properties of a GWB—a primary objective in the field of gravitational-wave astrophysics. These waves are long-term, low-frequency signals expected to manifest with a common red signal (CRS) and distinctive earth-pulsar correlated angular components defined by the Hellings-Downs curve.

The methodology involves two independent pipelines to ensure robust analysis and cross-verification of results. Throughout the paper, consistent results were achieved, showing spectral properties compatible with theoretical GWB expectations. Nevertheless, the essential detection of the Hellings-Downs correlation—crucial for confirming a GWB—remains unresolved. Instead, a common uncorrelated red noise (CURN) model, described by a power-law, emerged as the most favored interpretation of the data, with parameters $A = 5.13_{-2.73}^{+4.20} \times 10^{-15}$ and $\gamma = 3.78_{-0.59}^{+0.69}$.

The research implements models to address potential systematic errors originating from the Solar-system ephemeris (SSE), concluding that these effects are minimally impacting the results. Furthermore, consistency between this paper and prior data set analyses was affirmed under the same analytical framework, thereby boosting confidence in the methods and results.

Implications and Theoretical Insights

The strong CURN evidence compels consideration of intrinsic noise similarities among pulsars aside from gravitational waves. This has vital implications for GWB searches, as the differentiation between common astrophysical noise and GW-induced signals is critical. Moreover, measuring the Hellings-Downs curve with confidence remains an outstanding challenge—this would be a significant step forward for pulsar timing arrays as gravitational-wave detectors.

The constraints derived here provide both a benchmark and a challenge to theoretical models predicting the stochastic GWB from supermassive black hole binaries. The lack of definitive GWB detection suggests refinement in theoretical models is needed to explain this apparent signal strength and form.

Future Research Prospects

Future developments will likely involve extending the EPTA DR2 data set with more pulsars, an approach expected to enhance the precision of the results and reduce SSE-related errors. Expanding the array increases angular separation sampling, which is needed for a more reliable spatial correlation assessment. This broader dataset will shed more light on the overlapping contributions of GWB and CURN, potentially differentiating the two more distinctly.

Additionally, the consistency in analysis frameworks between the EPTA, NANOGrav, and other PTA collaborations highlights the benefit of collaborative approaches, such as the International Pulsar Timing Array (IPTA). In future investigations, methodologies could further blend, incorporating cross-correlation data and uniform analytical practices for a comprehensive understanding and detection capability for GR-predicted gravitational waves.

Continued upgrades in observing systems, improved noise mitigation strategies, and incorporation of new theoretical developments will all be essential as the search for stochastic GWBs progresses into more sensitive detection regimes.