Investigating ultra-long gravitational waves with measurements of pulsars rotational parameters

TL;DR

This paper proposes a method to detect ultra-low frequency gravitational waves by analyzing pulsars' rotational parameters, providing new limits on gravitational wave background energy density and a potential detection approach.

Contribution

It introduces a novel technique using pulsar rotational derivatives to explore gravitational waves in the ultra-low frequency range, extending current detection methods.

Findings

Limit on GWB energy density: _{gw}<2^{-6}

Method for cross-correlating pulsar frequency time series

Potential for GWB detection in ultra-low frequency range

Abstract

A method is suggested to explore the gravitational wave background (GWB) in the frequency range from $10^{-12}$ to \hbox{$10^{-8}$ Hz}. That method is based on the precise measurements of pulsars' rotational parameters: the influence of the gravitational waves (GW) in the range will affect them and therefore some conclusions about energy density of the GWB can be made using analysis of the derivatives of pulsars' rotational frequency. The calculated values of the second derivative from a number of pulsars limit the density of GWB $\Omega_{gw}$ as follows: $\Omega_{gw}<2\times10^{-6}$. Also, the time series of the frequency $\nu$ of different pulsars in pulsar array can be cross-correlated pairwise in the same manner as in anomalous residuals analysis thus providing the possibility of GWB detection in ultra-low frequency range.