Scattering V-type asteroids during the giant planet instability: a step for Jupiter, a leap for basalt

V-type asteroids are a taxonomic class whose surface is associated with a basaltic composition. The only known source of V-type asteroids in the Main Asteroid Belt is (4) Vesta, which is located in the inner part of the Main Belt. However, many V-type asteroids cannot be dynamically linked to Vesta, in particular, those asteroids located in the middle and outer parts of the Main Belt. Previous works have failed to find mechanisms to transport V-type asteroids from the inner to the middle and outer belts. In this work, we propose a dynamical mechanism that could have acted on primordial asteroid families. We consider a model of the giant planet migration known as the jumping Jupiter model with five planets. Our study is focused on the period of 10 Myr that encompasses the instability phase of the giant planets. We show that, for different hypothetical Vesta-like paleo-families in the inner belt, the perturbations caused by the ice giant that is scattered into the asteroid belt before being ejected from the Solar system are able to scatter V-type asteroids to the middle and outer belts. Based on the orbital distribution of V-type candidates identified from the Sloan Digital Sky Survey and the VISTA Survey colours, we show that this mechanism is efficient enough provided that the hypothetical paleo-family originated from a 100 to 500 km crater excavated on the surface of (4) Vesta. This mechanism is able to explain the currently observed V-type asteroids in the middle and outer belts, with the exception of (1459) Magnya.