Singh Jagadish, Haruna Sunusi
Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.
Basic Studies Department, School of General Studies, Kano State Polytechnic, Kano, Nigeria.
Sci Rep. 2020 Nov 2;10(1):18861. doi: 10.1038/s41598-020-75174-7.
The present paper studies the locations and linear stability of the triangular equilibrium points when both primaries are radiating and considered as heterogeneous spheroid with three layers of different densities. Additionally, we include the effects of small perturbations in the Coriolis and centrifugal forces and potential from a belt (circumbinary disc). It is observed that the positions of the triangular equilibrium points are substantially affected by all parameters (except a perturbation in Coriolis force) involved in the system.The stabilty of motion is found only when [Formula: see text], where [Formula: see text] is the critical mass value which depends on the combined effect of radiation pressures and heterogeneity of the primaries, small perturbations and the potential from a belt.It is also seen that the Coriolis force and the belt have stabilizing effect,while the centrifugal force, radiation and heterogeineity of the primaries have destabilizing behaviour.The net effect is that the size of the region of stability decreases when the value of these parameters increases where [Formula: see text] is the mass ratio and [Formula: see text] characterize heterogeneity of both primaries. A practical application of this model could be the study of motion of a dust grain near the heterogeneous and luminous binary stars surrounded by a belt.Finally, we carried out and discuss numerical experiments aiming at computing the positions of triangular points and critical masses of three binary systems: Archid, Xi Booties and Kruger 60.
本文研究了两颗主星均辐射且被视为具有三层不同密度的非均匀球体时三角平衡点的位置和线性稳定性。此外，我们考虑了科里奥利力和离心力中的小扰动以及来自一个环带（环绕双星盘）的势的影响。可以观察到，系统中涉及的所有参数（科里奥利力中的一个扰动除外）都会对三角平衡点的位置产生显著影响。仅当[公式：见原文]时运动才是稳定的，其中[公式：见原文]是临界质量值，它取决于辐射压力和主星非均匀性、小扰动以及环带势的综合影响。还可以看出，科里奥利力和环带具有稳定作用而已，主星的离心力、辐射和非均匀性具有破坏稳定的作用。净效应是当这些参数的值增加时（其中[公式：见原文]是质量比，[公式：见原文]表征两颗主星的非均匀性），稳定区域的大小会减小。该模型的一个实际应用可能是研究被环带环绕的非均匀发光双星附近尘埃颗粒的运动。最后，我们进行并讨论了旨在计算三个双星系统（大角星、牧夫座 Xi 和克鲁格 60）三角点位置和临界质量的数值实验。
