Hydrodynamical study on the conversion of hadronic matter to quark matter: I. Shock-induced conversion

We study transitions of hadronic matter (HM) to three-flavor quark matter (3QM) locally, regarding the conversion processes as combustion and describing them hydrodynamically. Not only the jump condition on both sides of the conversion front but the structures inside the front are also considered by taking into account what happens during the conversion processes on the time scale of weak interactions as well as equations of state (EOSs) in the mixed phase. Under the assumption that HM is metastable with their free energies being larger than those of 3QM but smaller than those of two-flavor quark matter (2QM), we consider the transition via 2QM triggered by a rapid density rise in a shock wave. Based on the results, we discuss which combustion modes (strong/weak detonation) may be realized. HM is described by an EOS based on the relativistic mean field theory, and 2QMs and 3QMs are approximated by the MIT bag model. We demonstrate for a wide range of the bag constant and strong coupling constant in this combination of EOSs that the combustion may occur in the so-called endothermic regime, in which the Hugoniot curve for combustion runs below the one for the shock wave in the p-V plane and which has no terrestrial counterpart. Elucidating the essential features in this scenario first by a toy model, we then analyze more realistic models. We find that strong detonation always occurs. Depending on the EOS of quark matter as well as the density of HM and the Mach number of the detonation front, deconfinement from HM to 2QM is either completed or not completed in the shock wave. In the latter case, which is more likely if the EOS of quark matter ensures that deconfinement occurs above the nuclear saturation density and that the maximum mass of cold quark stars is larger than 2M, the conversion continues further via the mixing state of HM and 3QM on the time scale of weak interactions.