On Equilibrium Figures of Particle Clouds around the Sun and Stars

[摘要] Equilibrium figures of cold gas-dust (or cometary) clouds are studied in a more general setting than the classical Roche problem. The cloud is considered to be under the influence of gravitational attraction of the central star and the tidal field of the Galaxy. Our analysis also takes into account the centrifugal forces due to the rotation of the cloud, which moves around the center of the stellar system together with the star. The limit equilibrium figure is found to have three planes of symmetry and to be shaped like a “lemon” with lateral swellings and two singular points. The shape of this figure and its cusp angles in the planes of two main sections are calculated. The average density inside the equilibrium figure is shown to be almost exactly equal to the average density of matter in the Galaxy. This coincidence cannot be accidental and means that equilibrium figures with the critical level of the total surface potential fill the entire volume of the Galaxy. A possible consequence is that the cometary clouds of neighboring stars in the Galaxy may touch each other (or even intersect because of the presence of dark matter). Hence stars may exchange comets and part of the comets in the Solar System may belong to other stars.

[关键词] celestial mechanics;Galaxy solar neighborhood