Hydrodynamical study on the conversion of hadronic matter to quark matter. II. Diffusion-induced conversion

Abstract

We study transitions of hadronic matter (HM) to three-flavor quark matter (3QM), regarding the conversion processes as combustion and describing them hydrodynamically. 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, we consider in this paper the conversion induced by diffusions of the seed 3QM. This is a sequel to our previous paper, in which the shock-induced conversion was studied in the same framework. We not only pay attention to 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. We employ for HM Shen's equation of state (EOS), which is based on the relativistic mean field theory, and the bag model-based EOS for quark matter just as in the previous paper. We demonstrated in that paper that in this combination of EOSs, the combustion will occur for a wide range of the bag constant and strong coupling constant in the so-called endothermic regime, in which the Hugoniot curve for combustion runs below the initial state. Elucidating the essential features of the diffusion-induced conversion both in the exothermic and endothermic regimes first by a toy model, we then analyze more realistic models. We find that weak deflagration nearly always occurs and that weak detonation is possible only when the diffusion constant is (unrealistically) large and the critical strange fraction is small. The velocities of the conversion front are $\ensuremath{\sim}{10}^{3}--{10}^{7}\text{ }\text{ }\mathrm{cm}/\mathrm{s}$ depending on the initial temperature and density as well as the parameters in the quark matter EOS and become particularly small when the final state is in the mixed phase. Finally we study linear stability of the laminar weak-deflagration front and find that it is unstable in the exothermic regime (Darrius-Landau instability) but stable in the endothermic regime, which is quite contrary to the ordinary combustions.