[Paper Review] A new class of hybrid EoS with multiple critical endpoints for simulations of supernovae, neutron stars and their mergers

O. Ivanytskyi, D. Blaschke|arXiv (Cornell University)|May 6, 2022

Pulsars and Gravitational Waves Research44 references24 citations

TL;DR

This paper introduces a new two-zone interpolation scheme (TZIS) for hybrid equations of state (EoS) in neutron stars, incorporating finite-temperature effects and color superconductivity in quark matter. By modeling both crossover and first-order quark-hadron transitions, it demonstrates that color superconductivity enhances temperature evolution during supernova collapse, enabling access to QCD phase diagram regions relevant to neutron star mergers and heavy-ion collisions.

ABSTRACT

We introduce a family of equations of state (EoS) for hybrid neutron star (NS) matter that is obtained by a two-zone parabolic interpolation between a soft hadronic EoS at low densities and a stiff quark matter EoS with color superconductivity at high densities within a finite region of baryonic chemical potentials $\mu_B^h < \mu_B < \mu_B^q$. We consider two scenarios corresponding to a cross-over and a strong first-order transition between quark and hadron phases considered at finite and zero temperatures. This allows us to analyze the effects of finite entropy on the EoS and mass-radius relation of NS. We demonstrate that the formation of a color superconducting state of quark matter drives the evolution of matter in supernovae explosions under the condition of entropy conservation to higher temperatures than in the case of deconfinement to normal quark matter. Within the presented hybrid EoS scenario, regions of the QCD phase diagram may be accessible to supernovae and NS mergers that can be reached also in terrestrial experiments with relativistic heavy ion collisions.

Motivation & Objective

• To develop a finite-temperature extension of the two-zone interpolation scheme (TZIS) for hybrid neutron star matter.
• To investigate the impact of color superconductivity on the quark-hadron phase transition in protoneutron stars.
• To analyze how finite entropy per baryon affects the mass-radius relation of protoneutron stars.
• To assess whether supernova and merger environments can access QCD phase diagram regions accessible in relativistic heavy-ion collisions.

Proposed method

• A two-zone parabolic interpolation is used to connect soft hadronic EoS at low densities to stiff quark matter EoS with color superconductivity at high densities.
• The transition is modeled as either a crossover (continuous density) or first-order (discontinuous density) via a tunable function ∆n[µc(T)] along the matching line µc(T).
• The quark matter EoS is based on a confining density functional approach with scalar diquark pairing, enabling the 2SC phase and color superconductivity.
• The model incorporates finite entropy per baryon (s/nB) and is applied to solve the Tolman-Oppenheimer-Volkoff (TOV) equations for protoneutron stars.
• The Maxwell construction is used as a benchmark to compare with the TZIS results.
• The phase diagram is analyzed for multiple critical endpoints (CEPs), including one at high temperature and a second at low temperature due to competition between chiral symmetry breaking and diquark condensation.

Experimental results

Research questions

• RQ1 How does finite temperature affect the quark-hadron phase transition in hybrid neutron star matter?
• RQ2 What role does color superconductivity play in shaping the mixed phase boundary and transition temperature?
• RQ3 How do entropy per baryon and temperature influence the mass-radius relation of protoneutron stars?
• RQ4 Can supernova and binary neutron star merger environments access QCD phase diagram regions relevant to heavy-ion collisions?
• RQ5 What is the impact of a two-zone interpolation scheme on the location and nature of critical endpoints in the QCD phase diagram?

Key findings

• Color superconductivity in quark matter increases the temperature of the quark-hadron transition compared to normal quark matter, driving protoneutron star evolution toward higher-temperature regions of the QCD phase diagram.
• The TZIS with a first-order transition produces a more pronounced softening of the EoS in the mixed phase than the Maxwell construction, due to a larger volume fraction of quark matter.
• At s/nB = 0.5, all observational constraints on neutron star masses and radii (including R1.4 ≤13.6 km and R1.6 ≥10.68 km) are satisfied for both TZIS and Maxwell construction.
• At s/nB = 1.0, only the Maxwell construction with a first-order transition satisfies constraints, while TZIS with n* = 0.15 fm−3 shows marginal agreement.
• For s/nB = 1.5, protoneutron star radii increase significantly to R1.4 ≃16–17 km, indicating strong entropy-driven softening at low densities.
• The model reveals a second critical endpoint at low temperatures due to the competition between chiral symmetry breaking and diquark condensation, enabling a richer QCD phase diagram structure than previously modeled.