Modeling the Gravitational Wave Signal from the X-ray Pulsar Her X-1

The paper is devoted to modeling the gravitational waves from the X-ray pulsar Her X-1. The neutron star is considered as a freely precessing ellipsoid. The gravitational wave signal is calculated in the quadrupole approximation. The $h_{\times }$ and $h_{+}$ polarization profiles are constructed for the precession parameters of the neutron star in Her X-1 measured in up-to-date works. The possibility of signal detection with the DECIGO telescope is assessed. The formulas for the semi-analytical modeling of the gravitational wave signal from precessing neutron stars by the method of perturbations in the small neutron star ellipticity parameter are deduced.