重心恒星运动的严格处理：天体测量和径向速度数据中的透视和光时效应
Rigorous treatment of barycentric stellar motion: Perspective and light-time effects in astrometric and radial velocity data
摘要：
高精度的天体测量和径向速度观测需要对恒星运动进行精确建模，以便推断长时间间隔的测量结果，并检测由看不见的伴星等造成的匀速运动偏差。我们的目标是探索最简单的恒星运动的运动学模型，即相对于太阳系重心的均匀直线运动，在可观察到的量，包括误差传播。一致的直线运动的表观路径方程解析求解的经典（特殊相对论）的框架，导致严格的表达式（表观）天体测量参数和径向速度的（真实）运动学参数的恒星在重心参考系。我们提出了严格的和明确的公式转换恒星的位置，松弛，自行车，径向速度从一个时代到另一个，假设均匀的直线运动，并考虑到光时间的影响。还给出了变换的雅可比矩阵，允许在任意时间间隔内准确和可逆地传播误差。光时效应通常很小，但依巴谷星表中至少有33颗恒星在100年内超过0.1质量或0.1米/秒。对于距离太阳几十秒差距内的高速恒星，光时效应通常比它们在银河势中的轨道曲率效应更重要。
英文摘要：
High-precision astrometric and radial-velocity observations require accurate modelling of stellar motions in order to extrapolate measurements over long time intervals, and to detect deviations from uniform motion caused for example by unseen companions. We aim to explore the simplest possible kinematic model of stellar motions, namely that of uniform rectilinear motion relative to the Solar System Barycentre, in terms of observable quantities including error propagation. The apparent path equation for uniform rectilinear motion is solved analytically in a classical (special-relativistic) framework, leading to rigorous expressions which relate the (apparent) astrometric parameters and radial velocity to the (true) kinematic parameters of the star in the barycentric reference system. We present rigorous and explicit formulae for the transformation of stellar positions, parallaxes, proper motions, and radial velocities from one epoch to another, assuming uniform rectilinear motion and taking into account light-time effects. The Jacobian matrix of the transformation is also given, allowing accurate and reversible propagation of errors over arbitrary time intervals. The light-time effects are generally very small but exceeds 0.1 mas or 0.1 m/s over 100 yr for at least 33 stars in the Hipparcos Catalogue. For high-velocity stars within a few tens of pc from the Sun light-time effects are generally more important than the effects of the curvature of their orbits in the Galactic potential.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
