Asteroids in the 2:1 resonance with Jupiter:: dynamics and size distribution

The 2 : 1 mean motion resonance with Jupiter in the main asteroid belt is associated to one of the largest Kirkwood gaps: the so-called Hecuba gap. Centred at about 3.3 au, the Hecuba gap is characterized by a very small number of asteroids when compared to its neighbourhoods. Long-term instabilities caused by resonant planetary perturbations are thought to be responsible for the almost lack of bodies in the gap. However, current observations suggest a significant population of asteroids in the 2 : 1 resonance. The origin of these bodies is puzzling. Do we observe the few lucky survivors of a much larger population formed in the resonance in primordial times? Do the resonant orbits of the observed asteroids have a more recent origin? To understand these issues, we performed numerical simulations of the orbital evolution of both real and fictitious asteroids in the 2 : 1 resonance. Our models include gravitational perturbations by the major planets. Based on the dynamical lifetimes, we classify the observed resonant asteroids into three groups: (i) the Zhongguos, which seems to be stable over the age of the Solar system; (ii) the Griquas, with typical lifetimes in the resonance of the order of some 100 Myr; and (iii) the strongly unstable asteroids, which escape from the resonance in a few 10 Myr or less. Our simulations confirm that the Zhongguos may be primordial asteroids, located in the 2 : 1 resonance since the formation of the Solar system. The dynamics of the Zhongguos constitute a typical example of slow chaotic evolution confined to a small region of the resonance. On the other hand, an analysis of the size distribution of the Zhongguos reveals a rather steep distribution. Such a distribution would not be compatible with a long collisional history, rather suggesting that the Zhongguos are likely to be the outcomes of a recent breakup event. Thus, while dynamics points toward a primordial resonant origin, the size distribution rather points to a recent origin. A possible explanation is that the Zhongguos formed by the cratering/fragmentation of a large resonant or near-resonant asteroid.