Spin states of X-complex asteroids in the inner main belt -- I. Investigating the Athor and Zita collisional families

The aim of our study is to characterise the spin states of the members of the Athor and Zita collisional families and test whether these members have a spin distribution consistent with a common origin from the break up of their respective family parent asteroids. Our method is based on the asteroid family evolution, which indicates that there should be a statistical predominance of retrograde-rotating asteroids on the inward side of family's V-shape, and prograde-rotating asteroids on the outward side. We used photometric data from our campaign and the literature in order to reveal the spin states of the asteroids belonging to these families. We combined dense and sparse photometric data in order to construct lightcurves; we performed the lightcurve inversion method to estimate the sidereal period, spin axis and convex shape of several family members. We obtained 34 new asteroid models for Athor family members and 17 for Zita family members. Along with the literature and revised models, the Athor family contains 60% of retrograde asteroids on the inward side and, 76% of prograde asteroids on the outward side. We also found that the Zita family exhibits 80% of retrograde asteroids on the inward side and an equal amount of prograde and retrograde rotators on the outward side. However, when we applied Kernel density estimation, we also found a clear peak for prograde asteroids on the outward side, as expected from the theory. The spin states of these asteroids validate the existence of both families, with the Athor family exhibiting a stronger signature for the presence of retrograde-rotating and prograde-rotating asteroids on the inner and outer side of the family, respectively. Our work provides an independent confirmation and characterisation of these very old families, whose presence and characteristics offer constraints for theories and models of the Solar System's evolution.