The possible existence of cloud-like clusters of microparticles at the libration points of a binary star

The possible existence of clusters of microscopic gas-dust particles forming gigantic clouds is demonstrated in the framework of the photogravitational three-body problem. These clouds are pulsating formations representing heterogeneous ensembles of particles of various sizes, densities, and susceptibilities to the radiation pressure, with each of the particles moving along its own trajectory. The conditions for the existence of co-linear and triangular libration points are derived by analyzing the dynamical equations describing the motion of a test particle in the gravitational-repulsive field of two gravitating and radiating bodies moving in an elliptical orbit about their common center of mass. The stability of these libration points is studied for various eccentricities e, mass parameters µ, and reduction coefficients characterizing the action of the stellar radiation on particles, and the results generalized in diagrams. We demonstrate the formation of clouds of particles located at multiple stable libration points. The extent of these clouds and their distances from the binary components are estimated. Scenarios for the subdivision of the clouds based on variations of e and µ are presented. The results of computations for a binary star with characteristics similar to those for α Cen are presented.     

Instability of Libration Points and Resonance Phenomena in the Photogravitational Elliptic Restricted Three-Body Problem

The stability of collinear and triangular libration points is investigated in the photogravitational elliptic restricted three-body problem, in which two primary bodies emit light energy simultaneously. The conditions of stability of the collinear and triangular libration points are obtained based on a linearized set of equations of perturbed motion for various values of the eccentricity of the Keplerian orbits and the mass ratio of the primary bodies. The maximal numerical value is defined for the eccentricity at which a stable libration point can still exist. It is demonstrated how the parametric resonance causes an instability of collinear and triangular libration points; the evolution of the origination of the instability zones is traced. The minimal eccentricity value is found at which zones of instability of triangular libration points arise.