The NANOGrav 15-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries (2306.16222v1)

Abstract: Evidence for a low-frequency stochastic gravitational wave background has recently been reported based on analyses of pulsar timing array data. The most likely source of such a background is a population of supermassive black hole binaries, the loudest of which may be individually detected in these datasets. Here we present the search for individual supermassive black hole binaries in the NANOGrav 15-year dataset. We introduce several new techniques, which enhance the efficiency and modeling accuracy of the analysis. The search uncovered weak evidence for two candidate signals, one with a gravitational-wave frequency of $\sim$4 nHz, and another at $\sim$170 nHz. The significance of the low-frequency candidate was greatly diminished when Hellings-Downs correlations were included in the background model. The high-frequency candidate was discounted due to the lack of a plausible host galaxy, the unlikely astrophysical prior odds of finding such a source, and since most of its support comes from a single pulsar with a commensurate binary period. Finding no compelling evidence for signals from individual binary systems, we place upper limits on the strain amplitude of gravitational waves emitted by such systems.

• The paper introduces a Bayesian search employing the QuickCW algorithm to efficiently analyze pulsar timing data for SMBHB gravitational wave signals.
• It establishes a sky-averaged 95% strain amplitude upper limit of 8×10⁻¹⁵ at 6 nHz, constraining models of supermassive black hole binaries.
• The research integrates comprehensive noise modeling and advanced MCMC techniques to refine pulsar timing methods for future gravitational wave detection.

Overview of "The NANOGrav 15-Year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries"

The paper "The NANOGrav 15-Year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries" represents a comprehensive effort by the NANOGrav Collaboration to advance the understanding of gravitational waves generated by supermassive black hole binaries (SMBHBs) through a detailed analysis of pulsar timing array data. The research leverages Bayesian methodologies to establish upper limits on gravitational wave emissions, thus providing insights into the possible presence of individual SMBHB sources within the dataset.

Methodological Advances

The paper employs a sophisticated Bayesian search protocol for identifying traces of gravitational waves from individual SMBHB systems in the NANOGrav 15-year dataset, which consists of timing data from 67 millisecond pulsars over a 16.03-year observational period. The authors introduce several innovative techniques that enhance both the efficiency and accuracy of the analysis. Particularly notable is the application of QuickCW, a novel algorithm that significantly expedites the computation process by optimizing the likelihood evaluation and the Markov Chain Monte Carlo (MCMC) sampling. This optimization leads to enhanced speed without compromising the integrity of the search results.

Key methodological improvements include:

• Implementation of QuickCW, leading to substantial accelerations in parameter sampling and likelihood calculations.
• Search for SMBHBs across the full prior range of gravitational wave frequencies rather than using a discrete grid.
• Marginalization over parameters of common red noise processes to address potential covariances between detected signals and the stochastic gravitational-wave background (GWB).

Results and Discussion

The research identifies weak evidence for potential candidate signals at gravitational-wave frequencies of approximately 4 nHz and 170 nHz. However, further analysis incorporating Hellings-Downs correlations within the background model significantly reduces the confidence in these detections. The high-frequency candidate is particularly discounted due to several factors, including a lack of plausible host galaxies, unlikely prior odds for such a high-frequency source, and dependence on data from a single pulsar with similar period characteristics.

No compelling evidence of individual SMBHB signals is found, leading the authors to establish upper limits on the strain amplitude of gravitational waves emitted by SMBHB systems. The analysis places a sky-averaged 95% upper limit on the strain amplitude of $8\times10^{-15}$ at the most sensitive frequency of 6 nHz. Additionally, the authors compute exclusion volumes and corresponding effective radii which help delineate regions where the presence of SMBHBs can be ruled out based on frequency emissions.

Implications and Future Directions

The implications of this research are twofold:

1. Practical Constraints: Establishes practical strain amplitude limits that are integral to refining models of SMBHB populations and their contributions to the GWB.
2. Methodological Innovations: Demonstrates the viability of integrating complex noise models and advanced sampling techniques into pulsar timing data analysis, paving the way for refined future searches as datasets expand.

Looking forward, the methodology and findings of this paper will serve as a benchmark for future gravitational-wave detection efforts, particularly as larger datasets become available and computational techniques continue to evolve. The theoretical implications include enhancing the understanding of galaxy mergers and SMBHB formation processes, while practically, enabling more sensitive detection of gravitational-wave signals amid complex cosmic noise backgrounds.

Overall, this paper represents a significant advancement in both the methods and understanding of gravitational-wave data analysis, providing a solid foundation for the next generation of SMBHB research.