The optimal filters for the construction of the ensemble pulsar time

TL;DR

This paper develops an optimal Wiener filter algorithm for ensemble pulsar timing, enabling separation of atomic clock and pulsar contributions, and provides new limits on gravitational wave background energy density.

Contribution

The paper introduces a novel Wiener filtration method for ensemble pulsar timing, improving separation of clock and pulsar signals and setting new constraints on gravitational wave background.

Findings

Successfully filtered atomic clock signals from pulsar data.

Estimated fractional instability of terrestrial time relative to pulsar time.

Derived a new upper limit on gravitational wave background energy density.

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 $\Omega_g h^2 \sim 3\cdot 10^{-9}$.