[Paper Review] A new relativistic model of hybrid star with interactive quark matter and dense baryonic matter

Koushik Chakraborty, Farook Rahaman+1 more|arXiv (Cornell University)|Oct 8, 2014

Pulsars and Gravitational Waves Research1 references3 citations

TL;DR

This paper proposes a relativistic model of hybrid stars using conformal symmetry and an interacting two-fluid approach, treating quark matter (MIT bag model) and baryonic matter as distinct fluids. It finds that a repulsive interaction (Q > 0) between the two phases best matches observational mass-radius data, with the equation of state for baryonic matter consistent with the Walecka model at high density.

ABSTRACT

We propose a relativistic model of hybrid star admitting conformal symmetry considering quark matter and baryonic matter as two different fluids. We define interaction equations between the normal baryonic matter and the quark matter and study the physical situations for repulsive, attractive and zero interaction between the constituent matters. From the interaction equations we find out the value of the equation of state (EOS) parameter for normal baryonic matter which is found to be consistent with the value obtained from the Walecka model for nucleonic matter at high density. The measured value of the Bag constant is used to explore the space time geometry inside the star. The theoretical mass-radius values are compared with the available observational data of the compact objects. From the nature of the match with the observational data, we predict the nature of interaction that must be present inside the hybrid stars

Motivation & Objective

• To develop a relativistic model of hybrid stars incorporating conformal symmetry and two interacting fluids: quark matter and baryonic matter.
• To investigate the physical nature of interactions—repulsive, attractive, or zero—between quark and baryonic matter inside hybrid stars.
• To test the model against observational data for compact stars, particularly mass-radius relationships.
• To determine the role of the Bag constant in shaping spacetime geometry and equation of state within the star.
• To assess consistency with the Walecka model and Buchdahl’s condition for stellar stability.

Proposed method

• Adopts a static, spherically symmetric spacetime metric in geometrical units (G = c = 1) with conformal symmetry.
• Applies Einstein field equations to derive the system of differential equations governing the metric functions ν(r) and λ(r).
• Models quark matter using the MIT bag model equation of state with a measured Bag constant value.
• Introduces interaction equations between the two fluids via conservation laws, leading to a parameter Q representing interaction strength.
• Solves the resulting system of equations numerically for two equations of state of baryonic matter, yielding mass-radius profiles.
• Compares theoretical mass-radius predictions with observational data from pulsars like PSR J1614-2230 and J0348+0432.

Experimental results

Research questions

• RQ1 Does the spacetime geometry of a hybrid star admit conformal symmetry?
• RQ2 What is the nature of interaction (repulsive, attractive, or none) between quark matter and baryonic matter that best fits observational data?
• RQ3 How does the equation of state of baryonic matter in this model compare with the Walecka model at high densities?
• RQ4 Can the model satisfy the Buchdahl’s condition for stellar stability?
• RQ5 How does the Bag constant influence the spacetime geometry and mass-radius relation in hybrid stars?

Key findings

• The model confirms that the spacetime of hybrid stars admits conformal symmetry, suggesting an intrinsic geometric-matter relationship.
• A repulsive interaction (Q > 0) between quark and baryonic matter provides the best fit to observational mass-radius data, especially for higher-mass stars.
• The equation of state for baryonic matter yields a sound speed c_s = 1, consistent with predictions from the Walecka model at high densities.
• Theoretical mass and radius values satisfy the Buchdahl’s condition, supporting the physical viability of the model.
• The Bag constant is linked to spacetime geometry through the constant C₃², which determines the proportionality between e^λ and the scalar field ψ.
• Theoretical mass predictions closely match those from Alford et al. for Q > 0, reinforcing the model’s consistency with high-mass neutron star observations.