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We argue that the full conversion of a hadronic star into a quark or a hybridstar occurs within two different regimes separated by a critical value of thedensity of the hadronic phase $\overline{n_h}$. The first stage, occurring for$n_h>\overline{n_h}$, is characterized by turbulent combustion and laststypically a few ms. During this short time-scale neutrino cooling is basicallyinactive 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 notactive anymore, and the conversion proceeds on a much longer time scale (of theorder of tens of seconds), with a velocity regulated by the diffusion and theproduction of strange quarks. At the same time, neutrino cooling is alsoactive. The interplay between the heating of the star due to the slowconversion 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 inthe neutrino luminosity which, if observed, would possibly represent a uniquesignature for the existence of quark matter inside compact stars. We willdiscuss the phenomenological implications of this scenario in particular inconnection with the time structure of long gamma-ray-bursts.

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