[Paper Review] Gravitational wave sources for Pulsar Timing Arrays

Ligong Bian, Shuailiang Ge+4 more|arXiv (Cornell University)|Jun 30, 2023

Pulsars and Gravitational Waves ResearchPhysics and Astronomy13 citations

TL;DR

The paper performs Bayesian model comparisons of SGWB sources for PTA data (SMBHBs, FOPT, cosmic strings, domain walls, scalar-induced GWs) using NANOGrav, PPTA, and EPTA datasets, finding no strong preference for any single model given current data.

ABSTRACT

Very recently, several pulsar timing array collaborations, including CPTA, EPTA, and NANOGrav, reported their results from searches for an isotropic stochastic gravitational wave background (SGWB), with each finding positive evidence for SGWB. In this work, we assessed the credibility of interpreting the Hellings-Downs correlated free-spectrum process of EPTA, PPTA, and NANOGrav as either the result of supermassive black hole binary mergers or various stochastic SGWB sources that originated in the early Universe, including first-order phase transitions, cosmic strings, domain walls, and large-amplitude curvature perturbations. Our observations show that the current new datasets do not display a strong preference for any specific SGWB source based on Bayesian analysis.

Motivation & Objective

• Assess the credibility of various SGWB sources as explanations for the Hellings-Downs correlated signal in PTA data.
• Compare SMBHB and cosmological SGWB models using Bayesian model selection across recent PTA datasets.
• Constrain the parameter spaces of SMBHBs, first-order phase transitions, cosmic strings, domain walls, and curvature perturbations.
• Provide implications for related beyond-Standard-Model physics and guide future PTA analyses.

Proposed method

• Model five SGWB sources: SMBHBs, first-order phase transitions (FOPT), cosmic strings, domain walls, and scalar-induced GWs.
• Use Bayesian fitting of the HD free-spectrum data from PPTA, EPTA, and NANOGrav, focusing on the first five low-frequency bins.
• Estimate posterior distributions and Bayes factors among models; interpret via Bayes factors as model evidence.
• Present constraints on model parameters such as A for SMBHBs, α_PT, β/H*, T*, v_b for FOPT, Gμ and α_CS for cosmic strings, σ and ΔV for domain walls, and PR0 and m for curvature perturbations.

Figure 1: Constraints on the SMBHB parameter $\log_{10}A$ from the Bayesian model fitting.

Experimental results

Research questions

• RQ1 Does the combined PTA data show a strong preference for SMBHBs or any cosmological SGWB source over others?
• RQ2 What are the credible ranges for the key parameters of SMBHBs, FOPT, cosmic strings, domain walls, and curvature perturbations given the data?
• RQ3 How do Bayes factors between models compare across PPTA, EPTA, and NANOGrav datasets?
• RQ4 Can current PTA observations distinguish among SGWB models that produce the HD correlation?

Key findings

• Current datasets do not display a strong preference for any specific SGWB source based on Bayesian analysis.
• NANOGrav and PPTA show more inclination toward FOPT than other sources, while EPTA favors cosmic strings.
• All cosmological SGWB models can reproduce the HD signal, with no model uniquely favored over SMBHBs given the data.
• Constraints imply moderate-strength slow phase transitions around 1 MeV are possible but restricted by BBN/CMB considerations.
• Cosmic strings imply a U(1) symmetry-breaking scale η ~ 10^{13-14} GeV; domain walls constrain symmetry-breaking scales below ~10^4 TeV; PBHs from curvature perturbations are severely constrained.

Figure 2: The constraints on parameters of FOPT from Bayesian model fitting. Contours contain 68% and 95% of the probability.