Inner main belt asteroids in Slivan states?

Context. The spin state of ten asteroids in the Koronis family has previously been determined. Surprisingly, all four asteroids with prograde rotation were shown to have spin axes nearly parallel in the inertial space. All asteroids with retrograde rotation had large obliquities and rotation periods that were either short or long. The Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect has been demonstrated to be able to explain all these peculiar facts. In particular, the effect causes the spin axes of the prograde rotators to be captured in a secular spin-orbit resonance known as Cassini state 2, a configuration dubbed “Slivan state”. Aims. It has been proposed based on an analysis of a sample of asteroids in the Flora family that Slivan states might also exist in this region of the main belt. This is surprising because convergence of the proper frequency s and the planetary frequency s6 was assumed to prevent Slivan states in this zone. We therefore investigated the possibility of a long-term stable capture in the Slivan state in the inner part of the main belt and among the asteroids previously observed. Methods. We used the swift integrator to determine the orbital evolution of selected asteroids in the inner part of the main belt. We also implemented our own secular spin propagator into the swift code to efficiently analyze their spin evolution. Results. Our experiments show that the previously suggested Slivan states of the Flora-region asteroids are marginally stable for only a small range of the flattening parameter Δ. Either the observed spins are close to the Slivan state by chance, or additional dynamical effects that were so far not taken into account change their evolution. We find that only the asteroids with very low-inclination orbits (lower than ≃4°, for instance) could follow a similar evolution path as the Koronis members and be captured in their spin state into the Slivan state. A greater number of asteroids in the inner main-belt Massalia family, which are at a slightly larger heliocentric distance and at lower inclination orbits than in the Flora region, may have their spin in the Slivan state