Motion of Planetesimals in the Hill Sphere of the Star Proxima Centauri

Abstract

The motion of planetesimals initially located in the feeding zone of the planet Proxima Centauri c, at distances of 500 AU from the star to the star’s Hill sphere radius of 1200 AU was considered. In the analyzed non-gaseous model, the primary ejection of planetesimals from most of the feeding zone of an almost formed planet c to distances greater than 500 AU from the star occurred during the first 10 million years. Only for planetesimals originally located at the edges of the planet’s feeding zone, the fraction of planetesimals that first reached 500 AU over the time greater than 10 million years was more than half. Some planetesimals could reach the outer part of the star’s Hill sphere over hundreds of millions of years. Approximately 90% of the planetesimals that first reached 500 AU from Proxima Centauri first reached 1200 AU from the star in less than 1 million years, given the current mass of the planet c. No more than 2% of planetesimals with aphelion orbital distances between 500 and 1200 AU followed such orbits for more than 10 million years (but less than a few tens of millions of years). With a planet mass equal to half the mass of the planet c, approximately 70–80% of planetesimals increased their maximum distances from the star from 500 to 1200 AU in less than 1 million years. For planetesimals that first reached 500 AU from the star under the current mass of the planet c, the fraction of planetesimals with orbital eccentricities greater than 1 was 0.05 and 0.1 for the initial eccentricities of their orbits e_o = 0.02 and e_o = 0.15, respectively. Among the planetesimals that first reached 1200 AU from the star, this fraction was approximately 0.3 for both e_o values. The minimum eccentricity values for planetesimals that have reached 500 and 1200 AU from the star were 0.992 and 0.995, respectively. In the considered model, the disk of planetesimals in the outer part of the star’s Hill sphere was rather flat. Inclinations i of the orbits for more than 80% of the planetesimals that first reached 500 or 1200 AU from the star did not exceed 10°. With the current mass of the planet c, the percentage of such planetesimals with i > 20° did not exceed 1% in all calculation variants. The results may be of interest for understanding the motion of bodies in other exoplanetary systems, especially those with a single dominant planet. They can be used to provide the initial data for models of the evolution of the disk of bodies in the outer part of Proxima Centauri’s Hill sphere, which take into account gravitational interactions and collisions between bodies, as well as the influence of other stars. The strongly inclined orbits of bodies in the outer part of Proxima Centauri’s Hill sphere can primarily result from bodies that entered the Hill sphere from outside. The radius of Proxima Centauri’s Hill sphere is an order of magnitude smaller than the radius of the outer boundary of the Hills cloud in the Solar System and two orders of magnitude smaller than the radius of the Sun’s Hill sphere. Therefore, it is difficult to expect the existence of a similarly massive cloud around this star as the Oort cloud around the Sun.