Polarization perspectives on Hercules X-1: further constraining the geometry

We conduct a comprehensive analysis of the accreting X-ray pulsar, Hercules X-1, utilizing data from Imaging X-ray Polarimetry Explorer (IXPE) and Nuclear Spectroscopic Telescope Array. IXPE performed five observations of Her X-1, consisting of three in the Main-on state and two in the Short-on state. Our time-resolved analysis uncovers the linear correlations between the flux and polarization degree as well as the pulse fraction and polarization degree. Geometry parameters are rigorously constrained by fitting the phase-resolved modulations of Cyclotron Resonance Scattering Feature and polarization angle with a simple dipole model and Rotating Vector Model, respectively, yielding roughly consistent results. The changes of χ_p (the position angle of the pulsar's spin axis on the plane of the sky) between different Main-on observations suggest the possible forced precession of the neutron star crust. Furthermore, a linear association between the energy of Cyclotron Resonance Scattering Feature and polarization angle implies the prevalence of a dominant dipole magnetic field, and their phase-resolved modulations likely arise from viewing angle effects.