[Paper Review] Thermodynamical description of hadron-quark phase transition and its implications on compact-star phenomena

Nobutoshi Yasutake, Tsuneo Noda+3 more|arXiv (Cornell University)|Aug 2, 2012

Pulsars and Gravitational Waves Research7 references3 citations

TL;DR

This paper presents a thermodynamically consistent description of the hadron-quark phase transition in compact stars, incorporating inhomogeneous 'pasta' structures via the Gibbs conditions and finite-size effects. It demonstrates that charge screening, thermal effects, and neutrino trapping destabilize pasta phases, impacting gravitational wave signals, cooling behavior, and supernova dynamics, with color superconductivity in the quark phase enabling cooling rates consistent with observations.

ABSTRACT

One of the most promising possibilities may be the appearance of quark matter in astrophysical phenomena in the light of recent progress in observations. The mechanism of deconfinement is not well understood, but the thermodynamical aspects of the hadron-quark (HQ) phase transition have been extensively studied in recent years. Then the mixed phase of hadron and quark matter becomes important; the proper treatment is needed to describe the HQ phase transition and derive the equation of state (EOS) for the HQ matter, based on the Gibbs conditions for phase equilibrium. We here adopt a EOS based on the baryon-baryon interactions including hyperons for the hadron phase, while we use rather simple EOS within the MIT bag model in the quark phase. For quark matter we further try to improve the previous EOS by considering other effective models of QCD. One of the interesting consequences may be the appearance of the inhomogeneous structures called "pasta", which are brought about by the surface and the Coulomb interaction effects. We present here a comprehensive review of our recent works about the HQ phase transition in various astrophysical situations: cold catalyzed matter, hot matter and neutrino-trapped matter. We show how the pasta structure becomes unstable by the charge screening of the Coulomb interaction, thermal effect or the neutrino trapping effect. Such inhomogeneous structure may affect astrophysical phenomena through its elasticity or thermal properties. Here we also discuss some implications on supernova explosion, gravitational wave and cooling of compact stars.

Motivation & Objective

• To develop a thermodynamically consistent framework for the hadron-quark phase transition in compact stars using Gibbs conditions for phase equilibrium.
• To investigate the role of inhomogeneous pasta structures in the mixed phase, accounting for surface tension, Coulomb interactions, and finite-size effects.
• To examine how thermal effects, neutrino trapping, and charge screening influence the stability and structure of the mixed phase.
• To explore astrophysical implications, including gravitational wave emission, neutron star cooling, and supernova dynamics.
• To assess the viability of the hadron-quark mixed phase in explaining observed neutron star masses and cooling behavior, particularly with color superconductivity.

Proposed method

• Application of the Gibbs conditions for phase equilibrium in multi-component systems with conserved charges (baryon number and electric charge), replacing the Maxwell construction.
• Use of a realistic equation of state (EOS) based on baryon-baryon interactions including hyperons for the hadronic phase.
• Employment of the MIT bag model for the quark phase, incorporating finite surface tension and Coulomb interactions.
• Numerical three-dimensional calculation using the relativistic mean-field model and Thomas-Fermi approximation with periodic boundary conditions and grid-based relaxation to determine equilibrium density distributions.
• Incorporation of charge screening and thermal effects to assess stability of pasta geometries (droplets, rods, slabs).
• Analysis of gravitational wave modes (f, p₁, g) and quasi-periodic oscillations (QPOs) in giant flares to probe the mixed phase structure.

Experimental results

Research questions

• RQ1 How does the inclusion of finite-size effects and Coulomb interactions alter the stability and structure of the hadron-quark mixed phase?
• RQ2 In what ways do thermal effects and neutrino trapping modify the formation and stability of pasta phases in compact stars?
• RQ3 Can the hadron-quark mixed phase with color superconductivity reconcile theoretical cooling models with observed neutron star temperature distributions?
• RQ4 What gravitational wave signatures can be associated with the density discontinuity and inhomogeneous structure of the mixed phase?
• RQ5 How do the elastic and thermal properties of pasta structures influence compact star dynamics and neutrino transport?

Key findings

• The hadron-quark mixed phase exhibits inhomogeneous pasta structures due to surface tension and Coulomb interactions, which are destabilized by charge screening and thermal effects.
• Thermal and neutrino-trapping effects reduce the stability of pasta phases, particularly suppressing rod and slab structures, leading to a more homogeneous mixed phase.
• The three-dimensional numerical calculation confirms the emergence of standard pasta structures (droplets, rods, slabs) without assuming geometric shapes a priori, validating the WS approximation in certain regimes.
• The inclusion of color superconductivity in the quark phase suppresses neutrino emissivity, enabling cooling curves that match observational data, resolving the 'cooling problem' of neutron stars.
• Gravitational wave signals—especially f-mode and p₁-mode oscillations—can reveal the presence of a density discontinuity and the equation of state of the mixed phase.
• Quasi-periodic oscillations (QPOs) in giant flares may originate from torsional oscillations in the hadron-quark mixed phase, offering a probe of its mechanical and structural properties.