Perturbation of the Earth’s rotation by monochromatic gravitational waves from astrophysical sources

Gravitational waves (GWs) of astrophysical origin were detected for the first time in 2015 through strain deformation measured at the Earth's surface. The inertia tensor of the deformable Earth is also disturbed resulting in the perturbation of its rotation vector and excitation of the rotational normal modes. Using a linearized theory of gravitation and the linearized equations of conservation of the angular momentum, we compute the equatorial polar motion and length of day changes generated by GWs. We show that GWs of strain amplitude ${h}_{0}$ and frequency ${f}_{g}$ give rise to perturbations of the inertia tensor of the Earth with an amplitude of ${10}^{14}{h}_{0}{f}_{g}^{2}$, resulting in relative perturbation of the Earth's rotation rate and equatorial polar motion respectively of the order ${10}^{6}{h}_{0}{f}_{g}^{2}$ and ${10}^{14}{h}_{0}{f}_{g}^{2}$. The amplitude of the rotational effect is much smaller than the geophysically induced rotational perturbation even if a resonance with the Earth's rotational normal modes would be possible. The amplitude of this rotational effect increases with the frequency but is several orders of magnitude below the theoretical sensitivity level of current geodetic instruments. The centrifugal deformation associated with the GW-induced polar motion would be $\ensuremath{\sim}{10}^{6}{f}_{g}^{2}{h}_{0}\ensuremath{\sim}{10}^{\ensuremath{-}17}/\sqrt{\mathrm{Hz}}$ for ${f}_{g}={10}^{\ensuremath{-}4}\text{ }\text{ }\mathrm{Hz}$ and ${h}_{0}={10}^{\ensuremath{-}16}$. The strain amplitudes of such centrifugal deformation are beyond the detectability of current laser strainmeters used to detect GWs. In the future, improvement in the sensitivities of geophysical instruments to measure Earth's rotation fluctuations, particularly at subdaily periods, and the development of the Laser Interferometer Space Antenna would make the present quantifications worth considering.