Combustion of a hadronic star into a quark star: the turbulent and the diffusive regimes

We argue that the full conversion of a hadronic star into a quark or a hybrid star occurs within two different regimes separated by a critical value of the density of the hadronic phase $\overline{n_h}$. The first stage, occurring for $n_h>\overline{n_h}$, is characterized by turbulent combustion and lasts typically a few ms. During this short time-scale neutrino cooling is basically inactive and the star heats up thanks to the heat released in the conversion. In the second stage, occurring for $n_h<\overline{n_h}$, turbulence is not active anymore, and the conversion proceeds on a much longer time scale (of the order of tens of seconds), with a velocity regulated by the diffusion and the production of strange quarks. At the same time, neutrino cooling is also active. The interplay between the heating of the star due to the slow conversion of its outer layers (with densities smaller than $\overline{n_h}$) and the neutrino cooling of the forming quark star leads to a quasi-plateau in the neutrino luminosity which, if observed, would possibly represent a unique signature for the existence of quark matter inside compact stars. We will discuss the phenomenological implications of this scenario in particular in connection with the time structure of long gamma-ray-bursts.