[Paper Review] Pasta structures in compact stars

Toshiki Maruyama, Toshitaka Tatsumi+2 more|arXiv (Cornell University)|May 29, 2006

High-pressure geophysics and materialsEarth and Planetary Sciences2 references3 citations

TL;DR

This paper investigates pasta structures in compact stars arising from first-order phase transitions in dense nuclear matter, focusing on three distinct transitions: liquid-gas, kaon condensation, and hadron-quark deconfinement. Using a relativistic mean-field approach with chiral symmetry realization, it demonstrates that the Coulomb interaction stabilizes geometrically symmetric mixed phases (e.g., droplets, rods, slabs, tubes, bubbles), and shows that charge screening effectively recovers the Maxwell construction, significantly altering the density regime of pasta phases.

ABSTRACT

We review our recent works about ``pasta'' structures following the first-order phase transition in dense matter, which correspond to the structured mixed phases with geometrical symmetries. Three kinds of phase transitions at different density ranges are examined as the stages of pasta structures: liquid-gas phase transition at subnuclear density, kaon condensation and hadron-quark phase transition at high density. Charge density as well as particle density is non-uniform there. A consistent treatment of the Coulomb potential and the particle densities is presented and a peculiar role of the Coulomb potential is elucidated: the physical picture of the Maxwell construction will be effectively recovered. It largely influences the density regime of pasta structures by the charge screening effect.

Motivation & Objective

• To understand the formation of non-uniform, geometrically symmetric mixed phases (pasta structures) in dense nuclear matter under extreme conditions.
• To examine the role of the Coulomb interaction and charge screening in stabilizing specific pasta phases during first-order phase transitions.
• To extend the Maxwell construction concept to multi-component, charged systems by incorporating Coulomb and surface energy balance.
• To investigate three distinct phase transitions: liquid-gas, kaon condensation, and hadron-quark deconfinement, each with unique structural and thermodynamic implications.
• To develop a consistent theoretical framework using relativistic mean-field theory with chiral symmetry to describe these phases and their transitions.

Proposed method

• Formulates a thermodynamic potential including contributions from nucleons, kaons, electrons, and vector mesons (σ, ω, ρ), with non-linear self-interactions and mean-field approximations.
• Derives equations of motion for scalar, vector, and kaon fields using variational principles applied to the total thermodynamic potential.
• Incorporates the Coulomb potential via the electrostatic potential V, with charge density ρ^ch derived from proton, kaon, and electron densities.
• Linearizes the kaon field equations in θ for small fluctuations and includes non-linear terms (X₀²θ², σ²θ²) to capture self-interactions and medium effects.
• Imposes chiral symmetry constraints on coupling constants (e.g., gσNgσK/mσ² = ΣKN/(2mKf²)) to reproduce known kaon-nucleon interactions.
• Solves the coupled system of partial differential equations numerically to determine stable configurations of pasta phases across varying densities and compositions.

Experimental results

Research questions

• RQ1 How do geometrically symmetric mixed phases (pasta structures) emerge in dense nuclear matter due to the interplay between surface tension and Coulomb interactions?
• RQ2 To what extent does the Coulomb potential modify the phase transition regime, particularly through charge screening, and how does this affect the validity of the Maxwell construction?
• RQ3 What is the role of kaon condensation in inducing a first-order phase transition and stabilizing specific pasta phases at high densities?
• RQ4 How does the inclusion of vector mesons (ω, ρ) and scalar fields (σ) in a relativistic mean-field framework influence the stability and structure of pasta phases?
• RQ5 Can the thermodynamic treatment of multi-component, charged systems recover the physical picture of the Maxwell construction despite the absence of uniform chemical potential conditions?

Key findings

• The Coulomb interaction plays a decisive role in stabilizing structured mixed phases, favoring geometries that minimize total energy, including surface and Coulomb contributions.
• Charge screening effectively recovers the Maxwell construction for multi-component systems, significantly altering the density range over which pasta phases exist.
• Pasta structures emerge across a sequence of phase transitions: from droplets to rods, slabs, tubes, and bubbles, depending on density and composition.
• Kaon condensation induces a first-order phase transition that softens the equation of state and stabilizes exotic pasta phases at high densities.
• The model reproduces known kaon-nucleon interactions via chiral symmetry constraints, validating its consistency with established effective field theories.
• The inclusion of non-linear terms in the kaon potential (X₀²θ², σ²θ²) is essential for capturing medium effects and self-consistent phase structure.