The optimal filters for the construction of the ensemble pulsar time

Abstract

The algorithm of the ensemble pulsar time based on the optimal Wiener filtration method has been constructed. This algorithm allows the separation of the contributions to the post-fit pulsar timing residuals of the atomic clock and pulsar itself. Filters were designed with the use of the cross- and autocovariance functions of the timing residuals. The method has been applied to the timing data of millisecond pulsars PSR B1855+09 and PSR B1937+21 and allowed the filtering out of the atomic scale component from the pulsar data. Direct comparison of the terrestrial time TT(BIPM06) and the ensemble pulsar time PT$_{\rm ens}$ revealed that fractional instability of TT(BIPM06)--PT$_{\rm ens}$ is equal to $\sigma_z=(0.8\pm 1.9)\cdot 10^{-15}$. Based on the $\sigma_z$ statistics of TT(BIPM06)--PT$_{\rm ens}$ a new limit of the energy density of the gravitational wave background was calculated to be equal to $\Omega_g h^2 \sim 3\cdot 10^{-9}$.