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Aims. A recent major high-angular-resolution imaging survey of 42 large main-belt asteroids (D > 100 km) with VLT/SPHERE has provided shape models of these bodies with an unprecedented accuracy. We ask whether the shapes of these bodies correspond to Maclaurin or Jacobi hydrostatic equilibrium figures. Methods. To address this question, we compared the aspect ratios and rotation rates of these asteroids with Maclaurin or Jacobi equilibrium figures. Results. The rotation rates and polar flattenings of the 42 asteroids globally do not match those of Maclaurin or Jacobi ellipsoids. Moreover, the equatorial axes of the asteroids are not compatible with an axial symmetry as for Maclaurin figures. Only a very few of them could be compatible with a known hydrostatic figure such as Maclaurin, Jacobi, or Clairaut ellipsoids.

Context. Cybele asteroids constitute an appealing reservoir of primitive material genetically linked to the outer Solar System, and the physical properties (size and shape) of the largest members can be readily accessed by large (8m class) telescopes. Aims. We took advantage of the bright apparition of the most iconic member of the Cybele population, (65) Cybele, in July and August 2021 to acquire high-angular-resolution images and optical light curves of the asteroid with which we aim to analyse its shape and bulk properties. Methods. Eight series of images were acquired with VLT/SPHERE+ZIMPOL, seven of which were combined with optical light curves to reconstruct the shape of the asteroid using the ADAM, MPCD, and SAGE algorithms. The origin of the shape was investigated by means of N-body simulations.Results. Cybele has a volume-equivalent diameter of 263± 3 km and a bulk density of 1.55 ± 0.19 g.cm −3 . Notably, its shape and rotation state are closely compatible with those of a Maclaurin equilibrium figure. The lack of a collisional family associated with Cybele and the higher bulk density of that body with respect to other large P-type asteroids suggest that it never experienced any large disruptive impact followed by rapid re-accumulation. This would imply that its present-day shape represents the original one. However, numerical integration of the long-term dynamical evolution of a hypothetical family of Cybele shows that it is dispersed by gravitational perturbations and chaotic diffusion over gigayears of evolution. Conclusions. The very close match between Cybele and an equilibrium figure opens up the possibility that D ≥ 260 km (M ≥ 1.5 × 10 19 kg) small bodies from the outer Solar System all formed at equilibrium. However, we cannot currently rule out an old impact as the origin of the equilibrium shape of Cybele. Cybele itself is found to be dynamically unstable, implying that it was 'recently' (<1 Gyr ago) placed on its current orbit either through slow diffusion from a relatively stable orbit in the Cybele region or, less likely, from an unstable, Jupiter-family-comet orbit in the planet-crossing region.Based on observations made with ESO Telescopes at the Paranal Observatory under programme ID 107.22QN.001 (PI: M. Marsset)Reduced and deconvolved images listed in Table A.