[Paper Review] A new quark-hadron hybrid equation of state for astrophysics - I. High-mass twin compact stars

Sanjin Benić, D. Blaschke+3 more|Repository of the Faculty of Science, University of Zagreb|Nov 11, 2014

Pulsars and Gravitational Waves Research58 references19 citations

TL;DR

This paper presents a new quark-hadron hybrid equation of state (EoS) that incorporates excluded volume effects in the hadronic phase and higher-order repulsive quark interactions, enabling a strong first-order phase transition with large latent heat. This leads to the formation of a disconnected third family of compact stars—high-mass twin stars—where two stars of the same mass (≈2 M⊙) can have radii differing by up to 1 km, offering a unique observational signature of a first-order quark-hadron transition.

ABSTRACT

Aims: We present a new microscopic hadron-quark hybrid equation of state model for astrophysical applications, from which compact hybrid star configurations are constructed. These are composed of a quark core and a hadronic shell with a first-order phase transition at their interface. The resulting mass-radius relations are in accordance with the latest astrophysical constraints. Methods: The quark matter description is based on a quantum chromodynamics (QCD) motivated chiral approach with higher-order quark interactions in the Dirac scalar and vector coupling channels. For hadronic matter we select a relativistic mean-field equation of state with density-dependent couplings. Since the nucleons are treated in the quasi-particle framework, an excluded volume correction has been included for the nuclear equation of state at suprasaturation density which takes into account the finite size of the nucleons. Results: These novel aspects, excluded volume in the hadronic phase and the higher-order repulsive interactions in the quark phase, lead to a strong first-order phase transition with large latent heat, i.e. the energy-density jump at the phase transition, which fulfils a criterion for a disconnected third-family branch of compact stars in the mass-radius relationship. These twin stars appear at high masses ($\sim$ 2 M$_\odot$) that are relevant for current observations of high-mass pulsars. Conclusions: This analysis offers a unique possibility by radius observations of compact stars to probe the QCD phase diagram at zero temperature and large chemical potential and even to support the existence of a critical point in the QCD phase diagram.

Motivation & Objective

• To construct a microscopic, QCD-motivated hybrid equation of state that supports stable compact star configurations with masses up to 2 M⊙.
• To address the 'masquerade problem' by ensuring a first-order phase transition that distinguishes quark-hadron hybrid stars from neutron stars.
• To incorporate excluded volume effects in the hadronic phase and higher-order quark interactions to generate a large latent heat, enabling a disconnected third family of stars.
• To produce mass-radius relations consistent with current astrophysical constraints, including high-mass pulsars and canonical star radii.
• To provide a testable prediction: high-mass twin stars with identical mass but significantly different radii, observable via future X-ray missions.

Proposed method

• Uses a chiral quark-meson model with higher-order self-interactions in the scalar and vector channels to describe quark matter, enhancing repulsion at high density.
• Employs a relativistic mean-field EoS with density-dependent couplings for hadronic matter, modified by an excluded volume correction to account for finite nucleon size at suprasaturation densities.
• Applies Tolman-Oppenheimer-Volkoff (TOV) equations to compute stellar structure and mass-radius relations from the hybrid EoS.
• Varying the strength of higher-order quark interactions allows exploration of different phase transition characteristics and their impact on compact star sequences.
• Ensures causality and stability by verifying that the speed of sound remains within physical bounds across all phases.
• Compares the resulting EoS with observational constraints from high-mass pulsars (e.g., PSR J0348+0432) and canonical stars (M ≈ 1.7 M⊙) with radii ≈14–17 km.

Experimental results

Research questions

• RQ1 Can a first-order quark-hadron phase transition in dense matter lead to a disconnected third family of compact stars, even at high masses (~2 M⊙)?
• RQ2 Does the inclusion of excluded volume effects in the hadronic phase and higher-order repulsive interactions in the quark phase generate a sufficiently large latent heat to stabilize such a third family?
• RQ3 Are the resulting mass-radius relations consistent with current astrophysical observations, including high-mass pulsars and canonical neutron star radii?
• RQ4 Can the twin star phenomenon—two stars of the same mass but different radii—be observed at high masses, and what would be its observational signature?
• RQ5 Can future X-ray missions like NICER, SKA, or NUSTAR resolve the twin star phenomenon, and what would it imply for the QCD phase diagram?

Key findings

• The inclusion of excluded volume effects in the hadronic phase results in larger radii for intermediate-mass neutron stars, improving agreement with observational constraints.
• The hybrid EoS produces a strong first-order phase transition with a large latent heat, enabling the formation of a disconnected third family of compact stars.
• Stable hybrid stars emerge with a tiny quark core, followed by an unstable branch, which then re-stabilizes due to strong repulsive higher-order quark interactions.
• All configurations satisfy causality, and the maximum masses of the stable hybrid branch exceed 2 M⊙, consistent with observed high-mass pulsars.
• High-mass twin stars with masses ≈2 M⊙ can have radius differences of up to approximately 1 km, providing a unique observational signature.
• The model provides a viable pathway to probe the QCD phase diagram at zero temperature and large baryon density, potentially supporting the existence of a critical point.