Abstract

The paper estimates the tidal distances \(|\xi_{c,1,2}|\) between the components of wide binary stars (BS) in the Pleiades. We used data on the parameters of the Pleiades cluster and wide BSs in the Pleiades, obtained earlier from the Gaia DR2 data. Two models of a cluster are considered in the form of a gravitating sphere, homogeneous and inhomogeneous in density. Using the integrals of angular momentum and energy of the motion of the centers of mass of the BSs, two elliptical orbits and two open ‘‘rosette-like’’ trajectories of the centers of mass of the BSs relative to the center of mass of the three-body system (the BS components and the cluster) are constructed. For three bodies in a coordinate system nonuniformly rotating relative to their center of mass with the origin at the center of mass of the BS the equations of motion are written. For the model of a homogeneous cluster, a formula is obtained for the value \(|\xi_{c,1,2}|\) for a BS moving along an elliptical orbit. The integrals of angular momentum and energy of motion of the components of the BS and three bodies of the system are obtained. The sizes of the area under the surface of zero velocities (SZV) of the BS components along the axes of the coordinate system with the origin in the center of mass of the BS are estimated. It is shown that in the model of a homogeneous cluster, the sizes of the area under the SZV of the BS components in the pericenters of the considered orbits are smaller than in the apocenters, and on the inner and outer parts of the BS orbits there are restrictions on the size of the area under the SZV of the BS components that differ in number and magnitude. For the model of an inhomogeneous cluster, an equation is obtained for the quantity \(|\xi_{c,1,2}|\) for the BS moving along the ‘‘rosette’’ trajectory relative to the center of mass of three bodies. The quantities \(|\xi_{c,1,2}|\) are numerically determined for the BS at different points of two such trajectories. With the help of the energy integral \(E_{1,2,3}\) of the motion of three bodies, the sizes of the area under the SZV of the BS components are determined. With an increase in the distance of the center of mass of the BS from the center of mass of three bodies in the model of an inhomogeneous cluster, an increase in the size of the area under the SZV of the BS components was noted, as well as the existence of more complex restrictions on the size of this area than in a homogeneous cluster. Mutual distances \(r_{i,j}\) between the components of wide BSs in the Pleiades are between the maximum and minimum values of \(|\xi_{c,1,2}|\) for BSs on ‘‘rosette’’ trajectories. The increase in \(r_{i,j}\) with the distances \(r_{i}\) of the BS components from the center of the cluster is mainly due to the motion of the BS along its trajectories in the Pleiades. Other applications of the integral \(E_{1,2,3}\) for estimating the BS parameters in the Pleiades are also considered.

中文翻译：

---

论昴宿星中宽双星组件之间的潮汐距离

摘要

该论文估计潮汐距离\(|\xi_{c,1,2}|\)昴星团中宽双星 (BS) 的成分之间。我们使用了先前从盖亚 DR2 数据中获得的关于昴宿星团和昴宿星团宽 BS 参数的数据。以引力球的形式考虑星团的两个模型，密度均匀和不均匀。利用 BS 质心运动的角动量和能量的积分，两个椭圆轨道和 BS 质心相对于构建了三体系统（BS组件和集群）。对于坐标系中的三个物体，它们相对于它们的质心非均匀旋转，原点在 BS 的质心处，写出运动方程。对于同构集群的模型，\(|\xi_{c,1,2}|\)对于沿椭圆轨道移动的 BS。获得了BS和系统三个物体的角动量和运动能量的积分。估计了 BS 分量沿坐标系轴的零速度表面 (SZV) 下区域的大小，原点位于 BS 的质心。结果表明，在同质星团模型中，所考虑轨道周心的 BS 分量的 SZV 下面积小于远心点，并且在 BS 轨道的内部和外部有是对数量和大小不同的 BS 组件的 SZV 下区域大小的限制。对于非均匀簇的模型，获得了数量的方程\(|\xi_{c,1,2}|\)对于 BS 沿着相对于三个物体的质心的“玫瑰花”轨迹移动。数量\(|\xi_{c,1,2}|\)是在两个这样的轨迹的不同点处为 BS 在数值上确定的。借助三体运动的能量积分\(E_{1,2,3}\) ，确定了BS分量的SZV下面积的大小。随着 BS 的质心与非均匀星团模型中三个物体的质心的距离增加，BS 组件的 SZV 下面积的大小也有所增加，因为对该区域的大小存在比同质集群更复杂的限制。相互距离\(r_{i,j}\)昴星团中宽 BS 的分量之间在“玫瑰花”轨迹上的 BS 的\(|\xi_{c,1,2}|\)的最大值和最小值之间。\(r_{i,j}\)随着BS 分量距星团中心的距离\(r_{i}\)的增加主要是由于 BS 沿其在昴星团中的轨迹运动。还考虑了积分\(E_{1,2,3}\)用于估计昴星团中 BS 参数的其他应用。