Identification of asteroid groups in the z1 and z2 nonlinear secular resonances through genetic algorithms

Linear secular resonances are observed when there is a ratio between the precession period of the longitudes of pericenter or nodes of a minor body and a planet. Nonlinear secular resonances occur for higher-order combinations of frequencies. They can change the shape of asteroid families in the (a, e, sin(i)) proper elements space. Identifying asteroids in secular resonances requires performing numerical simulations, and then visually inspecting if the resonant argument is librating, which is generally a time-consuming procedure. Here, we use machine learning genetic algorithms to select the most optimal model and training set to best-fit asteroids likely to be in librating states of the z1 and z2 secular resonances. We then identify groups in domains of librating asteroids, as predicted by our algorithms, and verified whether these clusters belong to known collisional families. Using this approach, we retrieved all the asteroid families known to interact with the two resonances and identified 5 fairly robust previously unknown groups.