Understanding and analysing time-correlated stochastic signals in pulsar timing

TL;DR

This paper develops a Bayesian framework for analyzing pulsar timing data with time-correlated stochastic signals, improving parameter estimation accuracy and computational efficiency, and provides new expressions for gravitational-wave background effects.

Contribution

It introduces a Bayesian method for pulsar timing analysis that accounts for time-correlated noise, along with closed-form expressions and efficient techniques for large datasets.

Findings

Derived closed-form expressions for post-fit signals with TCSSs.

Developed a Bayesian approach for parameter estimation in correlated noise.

Provided a new method for analyzing multiple datasets simultaneously.

Abstract

Although it is widely understood that pulsar timing observations generally contain time-correlated stochastic signals (TCSSs; red timing noise is of this type), most data analysis techniques that have been developed make an assumption that the stochastic uncertainties in the data are uncorrelated, i.e. "white". Recent work has pointed out that this can introduce severe bias in determination of timing-model parameters, and that better analysis methods should be used. This paper presents a detailed investigation of timing-model fitting in the presence of TCSSs, and gives closed expressions for the post-fit signals in the data. This results in a Bayesian technique to obtain timing-model parameter estimates in the presence of TCSSs, as well as computationally more efficient expressions of their marginalised posterior distribution. A new method to analyse hundreds of mock dataset realisations simultaneously without significant computational overhead is presented, as well as a statistically rigorous method to check the internal consistency of the results. As a by-product of the analysis, closed expressions of the rms introduced by a stochastic background of gravitational-waves in timing-residuals are obtained. Using $T$ as the length of the dataset, and $h_c(1\rm{yr}^{-1})$ as the characteristic strain, this is: $\sigma_{\rm GWB}^2 = h_{c}(1\rm{yr}^{-1})^2 (9\sqrt[3]{2\pi^4}\Gamma(-10/3) / 8008) \rm{yr}^{-4/3} T^{10/3}$.