Motion of planetesimals and dust particles in the Proxima Centauri planetary system

Motion of planetesimals. The motion of planetesimals in the Proxima Centauri planetary system was studied at the late gas-less stage of formation of planets [1-3]. In the calculations of the motion of planetesimals, the gravitational influence of the star (with a mass equal to 0.122 of the solar mass) and two planets: b (a_b=0.04857 AU, e_b=0.11, m_b=1.17m_E, m_E is the mass of the Earth) and c (a_c=1.489 AU, e_c=0.04, m_c=7m_E) was taken into account. Initial orbits of planetesimals were in some vicinity of the orbit of planet c. Initial eccentricities e_o of their orbits equaled to 0.02 or 0.15. Initial inclinations of their orbits were equal to e_o/2 rad. The symplectic code from the SWIFT integration package [4] was used for integration of the motion equations. The planetesimals or particles were excluded from integration when they collided with the star or planets or reached 1200 AU from the star. The considered time interval was up to 1000 Myr.

It was concluded in [1] that the total mass of planetesimals ejected into hyperbolic orbits were about (3.5-7)m_E, the total mass of planetesimals in the feeding zone of planet c could exceed 10m_E and 15m_E at e_o=0.2 and e_o=0.15, respectively, and the semi-major axis of the orbit of planet c could decrease by a factor not less than 1.5 during accumulation of this planet. The probability of a collision of a planetesimal initially located in the feeding zone of planet c with planet b , which can be in the habitable zone, was obtained to be about 2·10^-4 and 10^-3 at e_o equal to 0.02 or 0.15, respectively. The above values of the probabilities were greater than the probability of a collision with the Earth of a planetesimal migrated from the zone of the giant planets in the Solar System, which was typically less than 10^-5 [5]. The probability of collisions of planetesimals with planet d (a_d=0.029 AU, e_d=0, m_c=0.29m_E) was calculated based on the arrays of orbital elements of migrated planetesimals to be about twice less than that with planet b. A lot of icy material and volatiles could be delivered to planets b and d.

The size of the feeding zone of Proxima Centauri c is discussed in [2]. After hundreds of millions of years, some planetesimals could still move in elliptical resonant orbits (e.g. at the resonances 1:1, 5:4, and 3:4 with this planet) inside the feeding zone of planet c that had been mainly cleared from planetesimals. The strongly inclined orbits of bodies in the outer part of the Hill sphere of the star Proxima Centauri can only be mainly due to the bodies that came into the Hill sphere from outside. The inclinations of orbits of 80% of the planetesimals that moved between 500 or 1200 AU from the star did not exceed 10^o. About 90% of the planetesimals that first reached 500 AU from the star, for the first time reached 1200 AU from the star in less than 1 Myr [3]. It is difficult to expect the existence of such a massive analogue of the Oort cloud near the star Proxima Centauri as near the Sun.

Motion of dust: Migration of dust from initial orbits close to the orbit of planet Proxima Centauri c with initial eccentricities e_o equal to 0.02 or 0.15 was studied with the use of the Bulirsh-Stoer code from the SWIFT package [4]. The relative error per integration step was taken to be less than 10^-8. The gravitational influence of the star and planets b and c, the Poynting-Robertson drag, radiation pressure, and star wind drag were taken into account similar to [6]. The ratio of star wind drag to Poynting-Robertson drag was considered to be 0.35. In different variants [7], the ratio β between the radiation pressure force and the gravitational force varied from 0.0002 to 1. For the silicate particles in the Solar System, such values of β correspond to particle diameters d between 2000 and 0.4 microns; d is proportional to 1/β.

Though initial orbits of dust particles were close to the orbit of planet c, and planet c is more massive than planet b, at 0.001≤β≤0.1 more particles collided with inner planet b than with a greater planet c. In the Solar System, silicate particles with 0.001≤β≤0.1 correspond to diameters from 4 to 400 microns. At such values of β, dust particles are effective in delivery of matter (including volatiles) to planet b. The probabilities of collisions of particles with planet b for e_o=0.02 were about 0.15-0.2, 0.1, 0.06-0.08, and 0.016-0.03 at 0.001≤β≤0.004, β=0.01, β=0.02, and 0.04≤β≤0.1, respectively. For e_o=0.15, such probabilities were about 0.07-0.15, 0.04, and 0.01-0.03 at 0.001≤β≤0.01, β=0.02, and 0.04≤β≤0.1, respectively. For e_o=0.02, the probabilities of collisions of particles with planet c were about 0.016-0.05, 0.02, and 0.01-0.02 at 0.001≤β≤0.004, β=0.01, and 0.02≤β≤0.1. For e_o=0.15, such probabilities were not more than 0.03 for all considered variants. At β≥0.4 (for diameters less than a micron) the fraction of particles collided with planets was small or zero, and most of particles were ejected into hyperbolic orbits. At 0.004≤β≤0.2, most of particles collided with the star, with maximum probability at β=0.04. The times of evolution of considered dust disks were mainly smaller for greater β. They were 300 years at β=1 and were a few million years at 0.004≤β≤0.04.

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

References: [1] Ipatov S.I. Meteoritics and Planetary Science. 2023. 58: 752-774. https://doi.org/10.1111/maps.13985, https://arxiv.org/abs/2309.00695. [2] Ipatov S.I. Solar System Research. 2023. 57: 236-248. https://doi.org/10.1134/S0038094623030036. https://arxiv.org/abs/2309.00492. [3] Ipatov S.I. Solar System Research. 2023. 57: 612-628. https://doi.org/10.1134/S0038094623060047. [4] Levison H.F. and Duncan M.J. Icarus. 1994. 108: 18–36. [5] Marov M.Ya. and Ipatov S.I. Physics–Uspekhi. 2023. 66: 2-31. https://doi.org/10.3367/UFNe.2021.08.039044. https://arxiv.org/abs/2309.00716. [6] Ipatov S.I. Proceedings of IAU Symposium S263 "Icy bodies in the Solar System". Cambridge University Press. 2010. pp. 41-44. https://doi.org/10.1017/S174392131000147X, http://arxiv.org/abs/0910.3017. [7] Ipatov S.I. Meteoritics and Planetary Science. 2023. V. 58. Issue S1. P. A131. https://www.hou.usra.edu/meetings/metsoc2023/pdf/6078.pdf.