The asteroid population in g-type non-linear secular resonances

Non-linear secular resonances of g-type, i.e. involving the frequency of precession g of the asteroid pericentre, can affect the proper eccentricities of asteroids in resonant or near-resonant configurations. We first identified objects that could potentially be affected by non-linear secular resonances of this type. We then numerically integrated these objects and checked for their resonant argument. We identified a population of 1517 asteroids in g -2g(6) + g(5) librating states, and of 128 objects in g -3g(6) + 2g(5) resonant configurations. While secular resonances are rather extended structures and many objects from different and unrelated parts of the main belt could be encountered within, we found that g-2g(6) + g(5) librators are predominantly of the S taxonomical type (56 per cent of the total), but with a significant fraction of other spectral types. No spectral type dominates in the population of g -3g(6) + 2g(5) resonators. Several asteroid families are affected by the g -2g(6) + g(5) secular resonance. The Astraea group is cut into two by this resonance, while the Tirela and Brasilia groups are on the resonance centre and on the left side, respectively. The g -2g(6) + g(5) secular can significantly affect the shape of families inside the resonance, such as Astraea. It can also increase the flux of asteroids to nearby powerful mean-motion resonances, such as the 5J:-2A and the 2J:-1A. As expected, the long-term effect of g-type resonances on inclinations is essentially negligible.