Probabilities of collisions of planetesimals with planets in the Proxima Centauri, Trappist-1 and Gliese 581 exoplanetary systems

Introduction. Migration of planetesimals to forming exoplanets from different distances from the central star was studied in the Proxima Centauri, TRAPPIST-1, and GLISSE 581 exoplanetary systems. The gravitational influence of the star and planets was taken into account. The symplectic algorithm RMVS3 from the SWIFT package was used to integrate the equations of motion. Planetesimals were excluded from integration when they collided with planets or the star or were ejected into hyperbolic orbits. The probabilities of collisions of planetesimals with planets and the star were calculated. Initially, the orbits of the planetesimals were near the orbit of one of the planets. The initial eccentricities of their orbits in different calculation options were e_o=0.02 or e_o=0.15, and their initial inclinations were e_o/2 rad.

Proxima Centauri. Migration of planetesimals in the Proxima Centauri exoplanetary system was studied in (Ipatov, 2023a,b,c, 2024a). According to the obtained estimates, the amount of water delivered by planetesimals to the inner planet Proxima Centauri b from the feeding zone of the outer, more massive planet Proxima Centauri c could exceed the mass of the Earth's oceans (Ipatov, 2023a). Although the initial orbits of the dust particles considered were close to the orbit of Proxima Centauri c, and planet c is more massive than planet b, for a ratio of the radiation pressure to the force of gravity β between 0.001 and 0.1 (for particle diameters of the order of 4-400 microns), more particles collided with the inner planet b than with the larger planet c (Ipatov, 2024a) With such values of β, the dust particles effectively deliver matter (including volatiles) to planet b.

TRAPPIST-1. Migration of planetesimals in the TRAPPIST-1 exoplanetary system was studied in (Ipatov, 2024b,c). In the TRAPPIST-1 exoplanetary system consisting of seven planets, the fraction of planetesimals that collided with the host planet (compared to collisions with all planets) generally decreased with increasing considered time interval. In each calculation variant, there was at least one planet for which the number of collisions with planetesimals exceeded 25% of the number of planetesimals’ collisions with the host planet. Planetesimals could have collided with all planets for disks near the orbits of planets from d to h. Therefore, the outer layers of neighboring planets in the TRAPPIST-1 system may include similar material if there were many planetesimals near their orbits at the late stages of planet accumulation.

Bodies from the outer zones of the TRAPPIST-1 exoplanetary system containing water could, in particular, fall onto planets d, e, and f, located in the habitable zone. For example, in the calculation variant with 1000 planetesimals initially located near the orbit of the outer planet h, with e_o=0.15 it was found that 47, 89 and 165 planetesimals fell onto planets d, e and f, respectively. This probability of collision is four orders of magnitude greater than the probability of a collision of a body from the zone of giant planets with the Earth. These data indicate the possibility of delivering a large amount of water to planets d, e and f in the TRAPPIST-1 system.

Gliese 581. Migration of planetesimals in the Gliese 581 exoplanetary system was studied in (Ipatov, 2023d, 2024c). In the calculations of the migration of planetesimals in the Gliese 581 exoplanetary system with three planets (b, c, and e), the evolution times of the disks of the planetesimals only slightly exceeded 1 million years. The fraction of planetesimals that collided with one of the neighboring planets (close to the host planet) for disks e, b, and c at e_o=0.02 was 0.50, 0.20, and 0.36, respectively. At e_o=0.15 this fraction was 0.52, 0.15, and 0.40, respectively. These results indicate that the outer layers of neighboring exoplanets in the Gliese 581 exoplanetary system may include similar material. The calculations of the migration of bodies in the Gliese 581 planetary system were also carried out with five planets (b, c, d, e, and g). At present, the existence of two outer planets (e and g) is not confirmed. The unconfirmed planet Gliese 581g (with a mass of about two Earth masses) would be in the habitable zone of its star. In calculations, about 5% of planetesimals from the orbital vicinity of the outer planet d (with a mass of 7 Earth masses) fell on planet g. Therefore, such planet g could have an influx of bodies containing water. Studies of migration of planetesimals in the considered exoplanetary systems were shortly summarized in (Marov, Ipatov, 2023; Ipatov 2024c).

Acknowledgments: The studies were carried out under government-financed research project for the Vernadsky Institute.

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