Dynamical hadronization transition and hydrodynamical stability. II. Mixed phase.

Abstract

We extend our previous analysis of hydrodynamic stability of hadronization solutions to include solutions which produce hadrons via a region of mixed phase. We find that the transition from quark matter to mixed-phase matter must occur via a shock with supersonic velocities for both incoming and outgoing matter. The transition from mixed-phase matter to hadronic matter can occur either via a detonation solution or across a supersonic shock as in the quark--mixed-phase matter transition. Nucleation of both mixed-phase matter and hadronic matter is discussed using the criteria developed in our previous paper. We find that mixed-phase matter can nucleate in quark matter only when quark matter is at the transition temperature and that the region of nucleating solutions is a single point. Hadronic matter can nucleate in mixed-phase matter when the energy density of the mixed-phase matter reaches the hadronic transition energy density, and there is a region of possible nucleation solutions for any value of the mixed-phase energy density. We calculate entropy production and velocity boosts for the transitions from quark matter to mixed-phase matter and from mixed-phase matter to hadronic matter. We find that the expected entropy increase during hadronization is about 6.1% in the central rapidity region of a heavy-ion collision and about 4.2% in the early Universe in the absence of supercooling. If supercooling occurs, the entropy production will be increased by an amount which depends on the degree of supercooling. The expected velocity boost during hadronization is about 0.50c in heavy-ion collisions and about 0.33c in the early Universe, again assuming no supercooling. If supercooling occurs, the velocity boost will depend strongly on the degree of supercooling.