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

Abstract

We study transitions of hadronic matter (HM) to 3-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 (EOS's) 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 2-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 2, 3QM's are approximated by the MIT bag model. We demonstrate for a wide range of bag constant and strong coupling constant in this combination of EOS's 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 p − V plane, and which has no terrestrial counter part. 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 (QM) 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 QM 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. * Electronic address: furusawa@cfca.jp 2

The Structure of the Hadron-Quark Combustion Zone

“…However, we agree with Furusawa et al [7] that Coll's condition is not justified under rigorous physical and thermodynamic grounds, and instead is postulated as an apriori hypothesis [4]. This is because the question of the possibility of combustion can be solved with thermodynamics, without the use of some aprioristic condition like Coll's: combustion simply appears when the conversion between hadronic to quark matter is energetically favourable, which is a question of comparing the helmholtz free energy per baryon of both the hadronic state and the quark state, without having to appeal to the internal energy at a specific pressure and dynamical volume (where the pressure and dynamical volume are assumed to be equal at both sides, since both sides of the inequality (2) share the same pressure P ).…”

“…In the realistic scenario, the conversion of hadronic to quark matter must appear if it is energetically favourable, in other words if it decreases the free energy of the system. However in order to track the free energy of the reaction zone, the resolution of the study must be fine enough to take into account weak interaction terms and heat transfer across the reaction zone [7]. Given that most studies approximate the reaction zone as a discontinuity and consequently do not track this free energy, an approximation must be used.…”

“…2), there is no need for Coll's condition, since the second law of thermodynamics allows combustion for all fuel densities -all we need to assume is that the hypothesis of absolutely stable quark matter is true. Furthermore, Coll's condition is merely a hypothesis assumed apriori (see [7]) with little physical justification. Combustion is allowed (or not) depending on the behavior of the free energy, not the energy density.…”

Strange quark matter and quark stars with the Dyson-Schwinger quark model

“…As a last application, we consider the formation of a SQS from a pure metastable NS, which might occur once and if an initial seed of SQM has been formed in one of several hypothetical ways [11,88,89,90], for example in a two-step phase transition of nuclear matter to 2QM to SQM [91,92], or in the combustion of hot nuclear matter [93,94,95,96,97,98]. This transition is accompanied by a huge energy release, which could be associated with the long gammaray bursts [99,100,101] or the two-neutrino-burst scenario supernovas [102].…”

A systematic analysis of transverse momentum spectra of $J/ψ$ mesons in high energy collisions

“…As the basic theory of strong interactions of parti-cles [1][2][3][4][5][6], QCD predicts that the hadronic matter can be heated to a very high temperature when it experiences very strong interactions. Then, the system will go through a phase transition from the hadron matter to quark-gluon plasma (QGP) in the process [21][22][23]. The experiment of relativistic heavy ion collisions is the only way of achieving a QCD phase transition in laboratory conditions [24][25][26].…”