标题： 在X射线观测中寻找共生X射线双星GX 1+4的轨道周期调制 显示英文标题

标题： Searching for orbital period modulation in X-ray observations of the symbiotic X-ray binary GX 1+4

摘要： 共生X射线双星GX 1+4具有一些自20世纪70年代初以来一直被研究的特殊特性。特别是，轨道周期多年来一直是争论的焦点，直到径向速度测量能够解决这一争议。到目前为止，这些径向速度结果尚未通过X射线数据得到确认，尽管在这些能量下多个因素会导致与轨道周期相同时间尺度的周期性变化。由于GX 1+4的轨道是偏心的且不是正面朝向的，视线方向上的吸积率和柱密度的变化可能导致自转频率测量、X射线光变曲线和源的硬度比出现周期性变化。此外，对于高倾角的轨道平面，中子星可能会被伴星遮挡，这将导致亮度的周期性下降。我们使用了来自多个不同X射线望远镜的数据，通过将Lomb-Scargle和相位折叠方法应用于源的长期光变曲线和自转频率测量数据，直接寻找周期性。我们通过折叠的光变曲线、硬度比和图像来支持我们的发现。我们发现我们的结果与径向速度结果一致，并形成了一个由折叠的硬度比和光变曲线支持的自洽模型。我们发现源在预测的掩食期间在X射线中被明确检测到。受该系统中缺乏掩食的启发，我们利用文献中提供的红巨星质量及表面重力的约束，将系统的倾角限制为$\sim 76^\circ-84^\circ$，并将系统中中子星的质量限制为$\sim1.23M_\odot - 1.45M_\odot$。此外，我们将红巨星的半径限制为$\sim 60R_\odot - 150R_\odot$。 显示英文摘要

摘要： 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 $\sim 60R_\odot - 150R_\odot$.