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Description
Using the software REBOUND [1] we explore the possible stable configurations for the 2/1, 1/2 and 1/1 retrograde mean motion resonances in planetary systems with arbitrary masses through a Monte Carlo method. The simulations were divided in two different cases: 1) varying mass of one planet; 2) varying masses for both planets. The upper limit for the masses was set to 0.012 Msun as this is near the transition between a planet and a brown dwarf [2]. The ratio of the semi-major axes and the orbital eccentricities of the planets were also varied in both simulations. We conclude that fixed point resonant families (identified by libration of all resonant angles [3]) exist for a wide range of values of the masses. Configurations with libration of a single resonant angle were also identified. Our results may be applied to identify resonant configurations amongst real extra-solar systems.
[1] Rein, Hanno e S-F Liu. “REBOUND: an open-source multi-purpose N-body code for collisional dynamics”. Astronomy & Astrophysics 537:A128, 2012.
[2] Spiegel, D. S., Burrows, A., & Milsom, J. A.,”The deuterium-burning mass limit for brown dwarfs and giant planets” The Astrophysical Journal, 727, 5, 2011.
[3] Caritá G. A., Signor A. C., Morais M. H. M., 2022, Monthly Notices of the Royal Astronomical Society, 515, 2280.
Acknowledgements: The authors acknowledge support from grants 2021/11982-5, 2022/08716-4, 2023/02528-4 & 2024/10557-7 of São Paulo Research Foundation (FAPESP).
