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Stochastic gravitational-wave background search using data from five pulsar timing arrays

Wang-Wei Yu, Bruce Allen

Abstract

Using public data from five pulsar timing arrays (PTAs), we search for a stationary, isotropic, and unpolarized nHz stochastic gravitational-wave background (SGWB). We use pulse time-of-arrival data from 121 pulsars, which is more informative than previous searches, carried out separately by the individual PTA collaborations using only their own data. For pulsars observed by more than one PTA, we employ a new "direct combination" method to merge their astrophysical models and data. This avoids the challenge of reconciling the different PTA timing models to obtain a single "best" model. A central result of our analysis is posterior probability distributions for the amplitude $A_{gw}$ and exponent $γ_{gw}$ of the putative SGWB energy-density spectrum, modeled as a power law in frequency. While these results are consistent with a nonzero SGWB amplitude $A_{gw}$, the statistical significance--assessed via a Bayesian odds ratio and through noise-marginalized false-alarm probabilities ($p$-values) for three different detection statistics--remains below the conventional $5σ$ threshold for a confident detection. We also reconstruct the inter-pulsar timing-residual correlation as a function of the angle $θ$ between the pulsar lines of sight. This is consistent with the curve predicted by Hellings and Downs (HD).

Stochastic gravitational-wave background search using data from five pulsar timing arrays

Abstract

Using public data from five pulsar timing arrays (PTAs), we search for a stationary, isotropic, and unpolarized nHz stochastic gravitational-wave background (SGWB). We use pulse time-of-arrival data from 121 pulsars, which is more informative than previous searches, carried out separately by the individual PTA collaborations using only their own data. For pulsars observed by more than one PTA, we employ a new "direct combination" method to merge their astrophysical models and data. This avoids the challenge of reconciling the different PTA timing models to obtain a single "best" model. A central result of our analysis is posterior probability distributions for the amplitude and exponent of the putative SGWB energy-density spectrum, modeled as a power law in frequency. While these results are consistent with a nonzero SGWB amplitude , the statistical significance--assessed via a Bayesian odds ratio and through noise-marginalized false-alarm probabilities (-values) for three different detection statistics--remains below the conventional threshold for a confident detection. We also reconstruct the inter-pulsar timing-residual correlation as a function of the angle between the pulsar lines of sight. This is consistent with the curve predicted by Hellings and Downs (HD).

Paper Structure

This paper contains 2 equations, 4 figures, 3 tables.

Figures (4)

  • Figure 1: A Mollweide projection showing sky locations of the 121 pulsars included in our analysis. Colors indicate how many PTAs contributed data for each pulsar.
  • Figure 2: The posteriors for the amplitude and exponent of the SGWB power spectrum, as defined in (\ref{['e:OmegaOfF']}).
  • Figure 3: Histograms of NPMV detection statistic $p$-values for the $20{}480$ CURN-hypothesis posterior samples. The left panel has $\gamma_{gw}$ free, and the right has $\gamma_{gw} = 13/3$. The upper horizontal axis is one-sided-Gaussian equivalent significance.
  • Figure 4: Reconstruction of the mean correlation between pulsar pairs as a function of angular separation, compared to the Hellings and Downs (HD) prediction (\ref{['e:HDmat']}). The vertical bars indicate the uncertainties in the estimates of the means.