  Dynamical models of Solar System evolution have suggested that P-/D-type
volatile-rich asteroids formed in the outer Solar System and may be genetically
related to the Jupiter Trojans, the comets and small KBOs. Indeed, their
spectral properties resemble that of anhydrous cometary dust.
High-angular-resolution images of P-type asteroid (87) Sylvia with VLT/SPHERE
were used to reconstruct its 3D shape, and to study the dynamics of its two
satellites. We also model Sylvia's thermal evolution. The shape of Sylvia
appears flattened and elongated. We derive a volume-equivalent diameter of 271
+/- 5 km, and a low density of 1378 +/- 45 kg.m-3. The two satellites orbit
Sylvia on circular, equatorial orbits. The oblateness of Sylvia should imply a
detectable nodal precession which contrasts with the fully-Keplerian dynamics
of the satellites. This reveals an inhomogeneous internal structure, suggesting
that Sylvia is differentiated. Sylvia's low density and differentiated interior
can be explained by partial melting and mass redistribution through water
percolation. The outer shell would be composed of material similar to
interplanetary dust particles (IDPs) and the core similar to aqueously altered
IDPs or carbonaceous chondrite meteorites such as the Tagish Lake meteorite.
Numerical simulations of the thermal evolution of Sylvia show that for a body
of such size, partial melting was unavoidable due to the decay of long-lived
radionuclides. In addition, we show that bodies as small as 130-150 km in
diameter should have followed a similar thermal evolution, while smaller
objects, such as comets and the KBO Arrokoth, must have remained pristine, in
agreement with in situ observations of these bodies. NASA Lucy mission target
(617) Patroclus (diameter~140 km) may, however, be differentiated.
