A Hydrodynamical Study on the Conversion of Hadronic Matter to Quark Matter: II. Diffusion-Induced Conversion

TL;DR

This paper investigates the hydrodynamic process of hadronic matter converting to quark matter via diffusion, analyzing the front structure, velocity, and stability, with implications for neutron star physics.

Contribution

It introduces a detailed hydrodynamic model of diffusion-induced hadronic to quark matter conversion, including front structure and stability analysis, extending previous shock-induced studies.

Findings

Weak deflagration is the dominant conversion mode.

Conversion front velocities range from 10^3 to 10^7 cm/s.

The laminar deflagration front is unstable in the exothermic regime.

Abstract

We study transitions of hadronic matter (HM) to 3-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 2-flavor quark matter (2QM), we consider in this paper the conversion induced by diffusions of seed 3QM. This is a sequel to our previous paper, in which the shock-induced conversion was studied in the same frame work. 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 the Shen's EOS, which is based on the relativistic mean field theory, and the bag model-based EOS for QM just as in the previous paper. We demonstrated in that paper that in this combination of EOS's 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. 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 ~ $10^3-10^7$ cm/s depending on the initial temperature and density as well as the parameters in the QM 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.