Examination of the transportation abilities of the 3:1 MMR with Jupiter

Resonances in the main asteroid belt play a significant role in dynamical evolution of small bodies in the Solar system. They are capable of driving objects into near-Earth object (NEO) region as well.Last year we presented our results for the 5:2 mean motion resonance (MMR) with Jupiter [1, 2]. This work examines the transportation abilities of the 3:1 MMR. The 5:2 MMR is located in the outer part of the main belt and therefore it is believed to be not very efficient in delivering objects to the NEO region [3]. However, it has a non-negligible contribution to NEO population at larger sizes. On the other hand, the 3:1 MMR and the secular resonance  in the inner main belt are considered to be the largest contributors to the steady-state NEO population regardless of the size [4].We used analogous method as in the case of the 5:2 MMR. Firstly, short-term FLI (fast Lyapunov indicator [5]) maps of the 3:1 MMR were computed in order to distinguish between stable and unstable orbits. Then over 10 000 unstable particles were selected and integrated for a longer period of time, up to 10 Myr, to reveal the transportation abilities of the resonance. All our calculations were made using the MERCURIUS integrator from REBOUND package [6, 7]. We are interested in transportation to the NEO region and final state of these particles. Moreover, we also search for the orbits of potentially hazardous asteroids (PHAs), close encounters with planets and migration closer to the Sun. However, these results might be distorted because we were not taking collisions with planets or the Sun into account, just because we wanted to obtain results comparable to the papers on 5:2 MMR [1, 2, 8]. This means that our test particles survived arbitrarily close encounters. But we actually tracked the close encounters in such a way that we can later tell if there would have been a collision; however, this data is still being processed.According to our current results, 98.58% of test particles became NEOs at some point during the integration, which is slightly less than in the case of the 5:2 MMR. However, we obtained considerably larger amount of particles reaching a < 1 au (20.71%) and we also registered extremely large number (~ 71.76%) of Sun-grazing particles, i.e. particles that reached perihelion distance q < 0.016 au. In our simulation, the vast majority (96.82%) of test particles entered the Hill sphere of the Earth, which is a little more compared to the 5:2 MMR. The amount of particles that got as close to the orbit of Earth as PHAs was, of course, even larger (97.80%), which is almost the same amount as in the case of the 5:2 MMR. We confronted the results of our simulations with the list of all known PHAs, i.e. we searched for the orbits of PHAs in our simulation. The list was downloaded from JPL SBD (Jet Propulsion Laboratory Small-Body Database) [9]. According to our simulation, the orbits of 49 known PHAs were recovered by at least 70% of the test particles at some point. Orbits of only 7 of these PHAs were also recovered by more than 20% of test particles from simulation dedicated to the 5:2 MMR. The highest percentage was 25.24%. The final distribution of test particles in our simulation revealed that ejections to hyperbolic orbits or to orbits with a > 100 au were predominantly caused by Jupiter, as was expected. We did not find any other value of perihelion distance (other than perihelion distance of Jupiter) that would be significantly associated with elimination of the test particles. The same result we also obtained for 5:2 MMR. The elimination along q ≃ 0.26 au [8] was not confirmed in the case of the 5:2 MMR. Acknowledgement:The development and testing of the method, the examination of the 5:2 MMR, as well as participation in EPSC-DPS2025 were supported by the VEGA - Slovak Scientific Grant Agency, grant no. 2/0009/22. The 3:1 MMR examination itself was supported by the PostdokGrant APD0093. References:[1] Kováčová M., 2024, A&A, 686, A107[2] Kováčová M., 2024, Re-examination of the transportation abilities of the 5:2 MMR with Jupiter. In Interactive Conference of Young Scientists 2024. Občianske združenie Preveda, ISBN: 978-80-974608-1-5[3]Bottke W.F., Morbidelli A., Jedicke R., et al., 2002, Icarus, 156, 399[4] Granvik M.,  Morbidelli A., Jedicke R., et al., 2018, Icarus, 312, 181.[5] Skokos C., Gottwald G. & Laskar J., 2016, Chaos detection and predictability (Chapter 2).[6] Rein H., Hernandez D., Tamayo D., et al., 2019, MNRAS, 485, 5490[7] REBOUND (https://rebound.readthedocs.io/en/latest/)[8] Todorović N., 2017, MNRAS, 465, 4441[9] JPL SBD (https://ssd.jpl.nasa.gov/tools/sbdb_query.html)