Quark deconfinement in the proto-magnetar model of long gamma-ray bursts

We investigate the possible implications of quark deconfinement on the phenomenology of long gamma-ray bursts focusing, in particular, on the possibility to describe multiple prompt emission phases in the context of the proto-magnetar model. Starting from numerical models of rotating Hadron Stars and Quark Stars in full general relativity we track the electromagnetic spin-down evolution in both the hadronic and quark phase, linking the two families through conservation of baryon number and angular momentum. We give estimates of the time-scales and the energetics involved in the spin-down process deriving, in the relevant spin range, the relation between the initial and the final masses and rotational energies, whenever hadron- quark conversion is possible. We show how the results can be used in relevant astrophysical cases such as the double burst GRB 110709B.