[Paper Review] Posterior samples: Reading signatures of supermassive binary black holes in pulsar timing array observations

B. Goncharov, Shubhit Sardana+11 more|arXiv (Cornell University)|Sep 5, 2024

Pulsars and Gravitational Waves Research4 citations

TL;DR

This study reanalyzes the European Pulsar Timing Array (EPTA) second data release using a hierarchical Bayesian framework that models pulsar noise priors dynamically via hyperparameters, reducing systematic errors and improving consistency with theoretical expectations for supermassive binary black hole signals. The updated analysis increases Bayesian odds for Hellings-Downs correlations by ~10% and brings the inferred strain spectrum closer to predictions from gravitational wave-driven binary evolution.

ABSTRACT

This directory contains posterior samples to reproduce all figures in the paper "Reading signatures of supermassive binary black holes in pulsar timing array observations" (arXiv:2409.03627): Files posterior_*.txt contain posterior samples as rows, and parameters as columns. Characters in place of * indicate the corresponding figure from the paper. Posterior samples for Figure 2, left, are the same as for Figure 1b. Files parameters_*.txt contain parameter names in the same order as in posterior_*.txt. Files *.pdf are figures produced from the posterior samples in this data repository.

Motivation & Objective

• To address systematic errors in pulsar timing array (PTA) analyses caused by static, observationally uncalibrated noise priors.
• To improve the consistency of inferred gravitational wave background properties with theoretical expectations for supermassive binary black hole populations.
• To quantify the impact of dynamic noise prior modeling on Bayesian evidence for Hellings-Downs correlations and strain spectrum parameters.
• To assess whether residual tensions in spectral index and amplitude can be mitigated through improved hierarchical modeling of pulsar-specific noise.
• To provide a foundation for future PTA analyses by introducing a new marginalization procedure over hyperparameters that describe noise prior distributions.

Proposed method

• Applies hierarchical Bayesian inference to model the distribution of pulsar-specific noise parameters across the array using hyperparameters.
• Introduces a new numerical marginalization procedure over hyperparameters to account for uncertainty in noise prior distributions.
• Uses a power-law model for the characteristic strain spectrum: $ h_c(f) = A (f~{}\text{yr}^{-1})^{-\alpha} $, with $ \alpha = 2/3 $ corresponding to gravitational wave-driven binary inspirals.
• Reanalyzes EPTA's 10-year data using the new noise prior model, comparing results with standard static prior approaches.
• Computes Bayesian evidence and Bayes factors to evaluate model selection, particularly for Hellings-Downs correlations.
• Performs frequency-resolved comparison of the inferred strain spectrum against black hole population synthesis models to identify potential systematic sources.

Experimental results

Research questions

• RQ1 Can dynamic modeling of pulsar noise priors reduce systematic errors in PTA measurements of the gravitational wave background?
• RQ2 To what extent does the revised noise model improve agreement between observed strain spectra and theoretical predictions for supermassive binary black hole populations?
• RQ3 Does the improved analysis increase Bayesian support for Hellings-Downs correlations in EPTA data?
• RQ4 Are the observed tensions in the spectral index $ \gamma $ and strain amplitude $ A $ with the $ \gamma = 13/3 $ prediction for gravitational wave-driven binaries reduced by the new modeling approach?
• RQ5 What frequency bins show persistent deviations from theory, and could they point to unmodeled noise systematics?

Key findings

• The revised noise prior model reduces systematic errors in the strain spectrum measurement by approximately 1σ, improving consistency with theoretical expectations.
• Bayesian odds for Hellings-Downs correlations increase by approximately 10% compared to previous analyses with static noise priors.
• The best-fit strain spectrum parameters $ (\lg A, \gamma) $ from the 10-year EPTA data now align more closely with those from a 25-year dataset that lacks Hellings-Downs correlations, suggesting reduced bias.
• The analysis shows that inter-pulsar correlations in the 10-year data still provide strong constraints on $ (\lg A, \gamma) $, even when temporal correlations alone are modeled.
• Residual tension in the spectral index $ \gamma $ persists, with excess noise observed in two frequency bins at ~10⁻⁸ Hz and ~3×10⁻⁸ Hz, suggesting unmodeled systematics may remain.
• The study identifies potential sources of remaining systematics, including mismodeled radio-frequency-dependent noise and nearby binary systems, which may require improved correlation models in future work.