Rotational properties of MB family asteroids, Hildas, and Trojans, based on K2 and TESS observations

Our understanding of Solar System family asteroids has been significantly widened by space surveys primarily targeted to exoplanet detections. In K2 and TESS fields, many asteroids passed through, being a basis of continuous sateroid photometry covering several basis. This enabled the proof
of the high fraction of slow rotators (period>30 hours) in asteroid families (30%), non-family MB asteroids (35%), the Hilda group (39%) and the Trojan swarms (25%). High ratio of extremely slow rotators (P > 100 hr) in the Hilda group is (18%) is unique in the Solar System. 

We found a family-specific amplitude and/or period distribution only in some asteroid families (Hungaria, Maria, Juno, Eos, Eucharis, and Alauda). Older families tend to contain a larger fraction of more spheroidal, low-amplitude asteroids. The rotation period distributions are different in the cores and outskirts of the Flora and Maria families, while the Vesta, Eos, and Eunomia families lack this feature. We also confirm that very fast spinning 
asteroids are close to spherical (or spinning top shapes), and minor planets rotating slower than ≈11 h are also more spherical than asteroids in the 4-8 h period range and this group is expected to contain the most elongated bodies. 

Despite a previously suggested mixed origin of Hildas from the MB and the Trojan swarms, we revealed no differences in the photometric properties between the taxonomically different R and LR Hildas: the entire Hilda group highly resembles the Trojans for rotational properties.