Probabilities of collisions of planetesimals with exoplanets in the Proxima Centauri planetary system
Authors: Ipatov Sergei 
Published: October 2020

&#160;&#160; Schwarz et al. [1] studied migration of exocomets in the Proxima Centauri system. Besides the exoplanet with a semi-major axis a1=0.0485 AU located in a habitable zone, they also considered the second exoplanet with a semi-major axis a2 from 0.06 to up to 0.3 AU (for test calculations up to 0.7 AU). Now it is considered [2,3] that the semi-major axis of the second planet equals to 1.489&#177;0.049 AU.&#160;&#160; In the first series of calculations, according to [2], I considered a star with a mass equal to 0.122 of the solar mass, and two exoplanets with the following semi-major axes and masses: a1=0.0485 AU, a2=1.489 AU, m1=1.27mE and m2=12mE, where mE is the mass of the Earth. For the first exoplanet, the initial eccentricity e1 and initial inclination i1 were considered to be equal to 0, and the initial eccentricity e2 of the second exoplanet was considered to be equal to 0 or to 0.1. The calculations were made for initial inclination of the second exoplanet i2=e2/2=0.05 rad and for e2=i2=0. For interest, I also considered i2=152o, such calculations characterize the case when orbits of planetesimals were inclined to the orbit of the planet. In the second series of calculations, according to [3], I considered a1=0.04857 AU, e1=0.11, m1=1.17mE, a2=1.489 AU, e2=0.04, m1=7mE. I supposed i1=i2=0. In both series of calculations, the density of the first and second exoplanets were considered to be equal to densities of the Earth and Uranus, respectively.&#160;&#160; In different calculation variants, initial semi-major axes ab of planetesimals were in the range from amin to amax=amin+0.1 AU, with amin from 1.2 to 1.7 AU with a step of 0.1 AU. Initial eccentricities eb of planetesimals were equal to 0 or to 0.15 for the first series of calculations, and eb=0.02 for the second series of calculations. Initial inclinations ib of the planetesimals equaled to eb/2 rad. 250 planetesimals were considered in each calculation variant. The motion of planetesimals and exoplanets was calculated with the use of the symplectic code from [4]. Based on the obtained arrays of orbital elements of migrated planetesimals and exoplanets stored with a step of 100 yr, I calculated the probabilities of collisions of planetesimals with the exoplanets. The calculations were made similar to those in [5-7], which had been made for the planets of the solar system, but for different masses and radii of a star and exoplanets.&#160;&#160; The probability p1 of a collision of one planetesimal, initially located near the second exoplanet, with the first exoplanet was 0 in most calculations for both series. For the second series, p1 about 0.01-0.02 at amin=1.2 and amin=1.3 AU. For the first series, only&#160;at i2=e2/2=0.05 rad and eb=0.15 the values of p1 were considerable and could exceed 0.1 at time T=10 Myr, i.e. they were much greater than the fraction (less than 10-5)&#160;of planetesimals from the zone of the giant planets collided with the Earth [8].&#160;&#160; For i2=e2=0 and eb=0.15, the values of the probability p2 of a collision of one planetesimal, initially located near the second exoplanet, with this exoplanet were about 0.06-0.1. For i2=e2/2=0.05 and eb=0.15, p2 was about 0.02-0.04, i.e. it was less than p1. For the second series of calculations, p2 was about 0.1-0.2 at T=5 Myr, exclusive for p2=0.5 at amin=1.7 AU and&#160;for amin=1.4 AU when p2 exceeded 1 already at T=1 Myr. The fraction of ejected planetesimals for the second series at T=5 Myr was between 0.6 and 0.8 at 1.5&#8804;amin&#8804;1.6 AU.&#160;&#160; For both series of calculations, the ratio of planetesimals ejected into hyperbolic orbits usually exceeded the number of planetesimals collided with the planets by at least a factor of 4 if the number of planetesimals decreased by a factor of several. Only at amin=1.4 AU this ratio was less than 1. In some calculations a few planetesimals could be left in elliptical orbits after 100 Myr. For i2=152o, e2=0, and T=10 Myr, the values p2 were about 0.02 at eb=0 and about 0.02-0.05 (the range is for different values of amin) at eb=0.15. There was a small growth of p2 after 10 Myr. For i2=152o, e2=0.1, T=10 Myr, the values of p2 were very small at eb=0 and were about 0.01-0.05 (the range is for different values of amin) at eb=0.15.&#160;&#160; The work was carried out as a part of the state assignments of the Vernadsky Institute of RAS and was supported by the grant on exoplanets of the Russian Ministry of Education and Science.&#160;&#160; References&#160;&#160; [1] Schwarz R., Bazso A., Georgakarakos N., et al. Exocomets in the Proxima Centauri system and their importance for water transport // MNRAS, 2018, v. 480, p. 3595-3608.&#160;&#160; [2] Kervella P., Arenou F., Schneider J. Orbital inclination and mass of the exoplanet candidate Proxima c // Astronomy &amp; Astrophysics, 2020, v. 635: L14.&#160;&#160; [3] Benedict G.F., McArthur B.E. A Moving Target&#8212;Revising the Mass of Proxima Centauri c // Research Notes of the AAS, 2020, V. 4, N 6, ID 86. doi:10.3847/2515-5172/ab9ca9.&#160;&#160; [4] Levison H.F., Duncan M.J. The long-term dynamical behavior of short-period comets // Icarus, 1994, v. 108, p. 18-36&#160;&#160; [5] Ipatov S.I., Mather J.C. Migration of Jupiter-family comets and resonant asteroids to near-Earth space // Annals of the New York Academy of Sciences, 2004, v. 1017, p. 46-65. http://arXiv.org/format/astro-ph/0308448&#160;&#160;&#160;&#160; [6] Ipatov S.I., Mather J.C. Comet and asteroid hazard to the terrestrial planets // Advances in Space Research, 2004, v. 33, p. 1524-1533. http://arXiv.org/format/astro-ph/0212177.&#160;&#160; [7] Ipatov S.I., Probabilities of collisions of planetesimals from different regions of the feeding zone of the terrestrial planets with the forming planets and the Moon // Solar System Research, 2019, v. 53, N 5, p. 332-361. http://arxiv.org/abs/2003.11301&#160;&#160; [8] Ipatov S.I. Migration of planetesimals to the Earth and the Moon from different distances from the Sun // 50th LPSC, 2019, #2594. https://www.hou.usra.edu/meetings/lpsc2019/pdf/2594.pdf