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

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: ${\Omega }_{gw}<2\times 10^{-6}$. 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.

5 pages, submitted to MNRAS; changes of content in Section 3, reference added for section 1; changes in content in Section 3, refernce added, generally matches MNRAS version

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• Imprints of Relic Gravitational Waves in Cosmic Microwave Background Radiation
• Limits on the speed of gravitational waves from pulsar timing