Large main-belt asteroids are generally not Maclaurin or Jacobi ellipsoids

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