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The symbiotic X-ray binary GX 1+4 possesses a number of peculiar properties that have been studied since the early 1970s. In particular, the orbital period has been a point of debate for many years, until radial velocity measurements were able to settle the debate. These radial velocity findings have so far not been confirmed using X-ray data, even though multiple factors would cause a periodic variation on the same timescale as the orbital period at these energies. Because the orbit of GX 1+4 is eccentric and not seen face-on, changes in the accretion rate and column density along the line of sight could cause a periodic variation in the spin-frequency measurements, X-ray light curves, and hardness ratios of the source. Furthermore, for a high inclination of the orbital plane, the neutron star could be eclipsed by the companion, which would lead to periodic decreases in brightness. We used data from a number of different X-ray telescopes to search directly for periodicity by applying the Lomb-Scargle and epoch-folding approaches to long-term light-curve and spin-frequency measurement data of the source. We support our findings using folded light curves, hardness ratios, and images. We find that our results agree with the radial velocity findings, and we form a self-consistent model that is supported by folded hardness-ratios and light curves. We find that the source is clearly detected in X-rays during the predicted eclipse. Motivated by this absence of an eclipse in the system, we constrain the inclination of the system to $\sim 76^\circ-84^\circ$ and the mass of the neutron star in the system to $\sim1.23M_\odot - 1.45M_\odot$ using the constraints on the red giant mass and surface gravity provided in the literature. Furthermore, we constrain the radius of the red giant to $\sim 60R_\odot - 150R_\odot$., Comment: 8 pages, 8 figures, to be published in A&A

Cen X-3 is the first X-ray pulsar discovered 50 years ago. Radiation from such objects is expected to be highly polarized due to birefringence of plasma and vacuum associated with propagation of photons in presence of the strong magnetic field. Here we present results of the observations of Cen X-3 performed with the Imaging X-ray Polarimetry Explorer. The source exhibited significant flux variability and was observed in two states different by a factor of ~20 in flux. In the low-luminosity state no significant polarization was found either in pulse phase-averaged (with the 3$\sigma$ upper limit of 12%) or phase-resolved data (the 3$\sigma$ upper limits are 20-30%). In the bright state the polarization degree of 5.8$\pm$0.3% and polarization angle of $49.6\deg\pm1.5\deg$ with significance of about 20$\sigma$ was measured from the spectro-polarimetric analysis of the phase-averaged data. The phase-resolved analysis showed a significant anti-correlation between the flux and the polarization degree as well as strong variations of the polarization angle. The fit with the rotating vector model indicates a position angle of the pulsar spin axis of about 49$\deg$ and a magnetic obliquity of 17$\deg$. The detected relatively low polarization can be explained if the upper layers of the neutron star surface are overheated by the accreted matter and the conversion of the polarization modes occurs within the transition region between the upper hot layer and a cooler underlying atmosphere. A fraction of polarization signal can also be produced by reflection of radiation from the neutron star surface and the accretion curtain., Comment: Submitted to ApJL. 18 pages, 12 figures