The effect of hydrodynamical instabilities and of convection in the conversion of an hadronic star to a more compact object

We study the hydrodynamical transition from an hadronic star into a quark or a hybrid star. We discuss the possible mode of burning, using a fully relativistic formalism and realistic Equations of State in which hyperons can be present. We take into account the possibility that quarks form a diquark condensate. We find that the conversion process always corresponds to a deflagration and never to a detonation. Hydrodynamical instabilities can develop on the front but the increase in the conversion's velocity is not sufficient to transform the deflagration into a detonation. Concerning convection, it does not always develop. Instead, the process of conversion from ungapped quark matter to gapped quarks always allows the formation of a convective layer.