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From $χ$EFT to Multi-Region Modeling: Neutron star structure with a polytropic extension of $χ$EFT and MUSES Calculation Engine multi-layer modeling

Federico Nola

TL;DR

This work addresses how NS structure depends on high-density EoS extrapolations. It compares a $β$-stabilized $χ$EFT EoS extended with a polytropic/SoS tail against the MUSES Calculation Engine's multi-layer EoS that couples crust, inner crust, and core physics. The authors show that both strategies agree where microscopic input is reliable but diverge at supranuclear densities, producing different maximum masses and radii, thus bracketing the allowed stiffness of dense matter. They conclude that polytropic extrapolations are useful diagnostics while MUSES CE offers a physically grounded core treatment, and that multi-messenger constraints will be essential to discriminate high-density models.

Abstract

Neutron stars provide a unique environment to probe the properties of dense nuclear matter. In this work, we present a comparative study between two approaches to modeling the neutron star structure: a Chiral Effective Field Theory based approach and the MUSES Calculation Engine framework, which uses three different approaches for the three density regions. We analyze the resulting mass-radius relations, discussing the respective advantages and limitations of the two methods.

From $χ$EFT to Multi-Region Modeling: Neutron star structure with a polytropic extension of $χ$EFT and MUSES Calculation Engine multi-layer modeling

TL;DR

This work addresses how NS structure depends on high-density EoS extrapolations. It compares a -stabilized EFT EoS extended with a polytropic/SoS tail against the MUSES Calculation Engine's multi-layer EoS that couples crust, inner crust, and core physics. The authors show that both strategies agree where microscopic input is reliable but diverge at supranuclear densities, producing different maximum masses and radii, thus bracketing the allowed stiffness of dense matter. They conclude that polytropic extrapolations are useful diagnostics while MUSES CE offers a physically grounded core treatment, and that multi-messenger constraints will be essential to discriminate high-density models.

Abstract

Neutron stars provide a unique environment to probe the properties of dense nuclear matter. In this work, we present a comparative study between two approaches to modeling the neutron star structure: a Chiral Effective Field Theory based approach and the MUSES Calculation Engine framework, which uses three different approaches for the three density regions. We analyze the resulting mass-radius relations, discussing the respective advantages and limitations of the two methods.
Paper Structure (12 sections, 19 equations, 6 figures, 3 tables)

This paper contains 12 sections, 19 equations, 6 figures, 3 tables.

Table of Contents

  1. INTRODUCTION
  2. modeling methods
  3. $\beta$-stabilized $\chi$EFT Equation of State & piecewise polytropic extension
  4. MUSES Calculation Engine Nuclear Equation of State
  5. RESULTS and conclusions
  6. Sensitivity of the high-density extension to the polytropic and speed-of-sound parameters
  7. Overall stiffness ordering.
  8. Where parameter sensitivity becomes visible.
  9. Interpretation in terms of parameters.
  10. Maximum mass and high-density stiffness.
  11. Radii at canonical masses.
  12. Stable vs. unstable branch.

Figures (6)

  • Figure 1: Hierarchy of chiral nuclear interactions up to fourth order (or N3LO) in the chiral expansion. Nucleons (pions) are represented by solid (dashed) lines. The circled numbers indicate the number of short-range contact low-energy constants. Note that there is a finite number of diagrams at each order in the chiral power counting expansion.
  • Figure 2: Example of neutron star slice obtained with MUSES CE PhysRevD.111.103037. The different colors indicate the different models used, as shown in the legend. The proportions of the layers depend on the mass of the star.
  • Figure 3: EoS from P$\chi$EFT-$npe\mu$ and MUSES-$npe\mu$MusesCalculationEngine. Solid lines represent the results obtained from the analyses performed in this paper, with the two different approaches. The dashed line represent the results in bombaci2018equation, obtained with a $\chi$EFT+$\Delta(1232)$ approach.
  • Figure 4: $M-R$ relation from P$\chi$EFT-$npe\mu$ and MUSES-$npe\mu$MusesCalculationEngine. Solid lines represent the results obtained from the analyses performed in this paper, with the two different approaches. Dashed lines represent the results for two other different microscopic approaches bombaci2018equationdavis2025crust. In light (dark) grey the 50% (90%) confidence region for neutron star $M-R$ relation shown in miller2021radius.
  • Figure 5: Sensitivity of the pressure--energy-density relation $P(\varepsilon)$ to the high-density extension parameters. The three curves correspond to the parameter sets in Table \ref{['tab:param_sets_ABC']}. In the displayed range, Set A (red) is systematically stiffer than Set B (blue), which is stiffer than Set C (green).
  • ...and 1 more figures