Asteroid spin-states of a 4 Gyr collisional family

Context. Families of asteroids generated by the collisional fragmentation of a common parent body have been identified using clustering methods of asteroids in their proper orbital element space. However, there is growing evidence that some of the real families are larger than the corresponding cluster of objects in orbital elements, and there are families that escaped identification by clustering methods. An alternative method has been developed in order to identify collisional families from the correlation between the asteroid fragment sizes and their proper semi-major axis distance from the family centre (V-shape). This method has been shown to be effective in the cases of the very diffuse families that formed billions of years ago. Aims. Here we use multiple techniques for observing asteroids to provide corroborating evidence that one of the groups of asteroids identified as a family from the correlation between size and proper semi-major axis of asteroids are real fragments of a common parent body, and thus form a collisional family. Methods. We obtained photometric observations of asteroids in order to construct their rotational light curves; we combine them with the literature light curves and sparse-in-time photometry; we input these data in the light curve inversion methods, which allow us to determine a convex approximation to the 3D shape of the asteroids and their orientation in space, from which we extract the latitude (or obliquity) of the spin pole in order to assess whether an object is prograde or retrograde. We included in the analysis spin pole solutions already published in the literature aiming to increase the statistical significance of our results. The ultimate goal is to assess whether we find an excess of retrograde asteroids on the inward side of the V-shape of a 4 Gyr asteroid family identified via the V-shape method. This excess of retrograde rotators is predicted by the theory of asteroid family evolution. Results. We obtained the latitude of the spin poles for 55 asteroids claimed to belong to a 4 Gyr collisional family of the inner main belt that consists of low-albedo asteroids. After re-evaluating the albedo and spectroscopic information, we found that nine of these asteroids are interlopers in the 4 Gyr family. Of the 46 remaining asteroids, 31 are found to be retrograde and 15 prograde. We also found that these retrograde rotators have a very low probability (1.29%) of being due to random sampling from an underlying uniform distribution of spin poles. Conclusions. Our results constitute corroborating evidence that the asteroids identified as members of a 4 Gyr collisional family have a common origin, thus strengthening their family membership.