Can large icy moons accrete undifferentiated?

The apparent moments of inertia of Callisto and Titan inferred from gravity data suggest incomplete differentiation of their interior, commonly attributed to slow and cold accretion. To understand whether such large icy moons can really avoid global melting and subsequent differentiation during their accretion, we have developed a 3D numerical model that characterizes the thermal evolution of a satellite growing by multi-impacts, simulating the satellite growth and thermal evolution for a body radius ranging from 100 to 2000 km. The effects of individual impacts (energy deposition, excavation) are simulated and integrated for impactor sizes ranging from a few kilometers to one hundred kilometers, while for smaller impactors, a simplified approach with successive thin uniform layers spreading all over the satellite is considered. Our simulations show that the accretion rate plays only a minor role and that extending the duration of accretion does not significantly limit the increase of the internal temperature. The mass fraction brought by large impactors plays a more crucial role. Our results indicate that a satellite exceeding 2000 km in radius may accrete without experiencing significant melting only if its accretion is dominated by small impactors (