Covariant Energy Density Functionals for Neutron Star Matter Equation of State Modeling: Cross-Comparison Analysis Using \texttt{CompactObject}

Abstract

This study analyzes and contrasts different phenomenological methods used to model the nuclear equation of state (EOS) for neutron star matter based on covariant energy density functionals (CEDF). Using two complementary methodologies, we seek to capture a comprehensive picture of the potential behaviors of ultra-dense nucleonic matter and identify the most plausible models based on current observational and experimental constraints. Observational data from radio pulsar timing, gravitational wave detection of GW170817, and X-ray timing provide critical benchmarks for testing the models. We have derived the EOS posteriors for various CEDF models within the \texttt{CompactObject} package, utilizing recent observational data on neutron stars, state-of-the-art theoretical constraints from chiral effective field theory ($χ$EFT) calculations for pure neutron matter at low densities, and pQCD-derived constraints. Our analysis has demonstrated that while all considered CEDF models broadly reproduce current astrophysical and theoretical constraints, subtle yet important differences persist among them, with each framework exhibiting distinct characteristics at supra-nuclear density. This is in particular true for the proton fraction inside neutron stars, but also supported by the models' behavior with respect to the pure neutron matter EOS and the density dependence of the speed of sound. Our study highlights the sensitivity of dense matter predictions to the underlying EOS parameterizations and the priors considered.

Figures (12)

• Figure 1: Log-likelihood distributions of the posterior obtained for RMF-NL, DDH, DDB, and GDFMX models across six panels: (i) Contributions from nuclear saturation properties, $log(\mathcal{L}^{\rm NMP})$; (ii) MR constraints from NICER measurements of PSR J0030+0451 Riley:2019yda, $log(\mathcal{L}^{\rm J0030+0451})$; (iii) MR constraints for PSR J0740+6620 Riley:2021pdl, $log(\mathcal{L}^{\rm J0740+6620})$; (iv) MR constraints for PSR J0437+4715 Choudhury:2024xbk, $log(\mathcal{L}^{\rm J0437+4715})$; (v) Dimensionless tidal deformability constraints from GW170817 LIGOScientific:2018cki, $log(\mathcal{L}^{\rm GW170817})$; (vi) Total astrophysical contribution combining all NICER and GW170817 data, $log(\mathcal{L}^{\rm Astro})$. The vertical dashed lines, each in its respective color, signify the median of the distributions for each model.
• Figure 2: The 90% credible interval (CI) of binding energy (E/A - m, where m is nucleon mass) for pure neutron matter versus number density $\rho$ for phenomenological CEDF models in this study, compared with $\chi$EFT constraints from multiple sources (Ref. Huth:2021bsp). Density dependent models labeled 'model'$y$ include an extra parameter in the definition of the coupling $\Gamma_\varrho$ as defined in Eq. (\ref{['y']}).
• Figure 3: The 90% CI of pressure versus energy density for phenomenological CEDF models evaluated in this study. The grey contour encloses all the EOS that satisfy the $\chi$EFT at low densities as in Hebeler2013 and several astronomical constraints Annala:2021gom. The dashed grey line defines the region for which the PDF $\ge0.08$Altiparmak:2022bke, for the same set constraints. The light grey band defines the central baryonic density of the maximum mass configurations, above which no constraints have been imposed.
• Figure 4: The 90% credible interval (CI) posterior distribution of the neutron star's mass-radius $P (R|M )$ (left side) and mass-tidal deformability $P (\Lambda|M )$ (right side) is derived from different CEDF models. We also compare the 1, 2 and 3 $\sigma$ (full, dashed and dotted lines respectively) CI for the two-dimensional posterior distributions within the mass-radius parameter space of the millisecond pulsar PSR J0030+0451, shown with olive green lines Vinciguerra_2024 alongside with PSR J0740+6620, depicted with light blue lines salmi2024 and PSR J0437+4715 with red lines Choudhury:2024xbk, all derived from NICER X-ray observations. Additionally, the gray region represent the EOS independent MR posterior derived from GW170817 tidal deformability measurement LIGOScientific:2018cki
• Figure 5: The posterior distribution of the 90% CI for the proton fraction and multiple CEDF models as a function of the baryon density.