Generalized Three-Cornered Hat Method and Its Application for the Construction of an Ensemble Pulsar Time Scale

Abstract

Based on a pairwise comparison of the behavior of individual pulsar time scales, we have developed a method to calculate the rating of pulsars that are used to construct an ensemble pulsar time scale (generalized three-cornered hat method). The method is applied to the observational pulsar timing data from the NANOGrav project. The behavior of the constructed ensemble pulsar time scale coincides with the behavior of the TT(BIPM2017) time scale within the error $\sigma_{\textrm{ept}}=0.077$ $\mu$s; the fractional instability over an interval of 12 years is $\sigma_{z}=\left({1.0\pm 0.9}\right)\times 10^{-16}$. Based on the fractional instability, we have obtained an upper limit on the fractional energy density of the stochastic gravitational-wave background that arose in the early Universe at a level of $\Omega_{g}h^{2}=10^{-13}$ at a frequency of $2.6\times 10^{-10}$ Hz. The upper limit of the amplitude of variations in the variable gravitational potential is estimated to be $\Psi_{c}\sim 10^{-16}$ at the same frequency.