Many-body effects on dense matter with hyperons at finite temperature

In this work, we present the first extension of the Many-Body Forces (MBF) Model to finite temperature. The MBF Model describes nuclear matter in a relativistic quantum hadrodynamics formalism that takes many-body forces into account through a field dependence of the nuclear interaction coupling constants. Assuming nuclear matter to be charge neutral, beta-equilibrated, and populated by the baryon octet, electrons, and muons, we explore the parameters of the model, three different hyperon coupling schemes (also introduced here for the first time in MBF), and temperature effects to describe basic properties of nuclear matter, including the speed of sound, compressibility, and adiabatic index. We also investigate the mass-radius relation of compact stars by solving the Tolman-Oppenheimer-Volkoff equations at zero and finite temperature, including scenarios with fixed entropy per baryon. Our original results at finite temperature open the path to a new description of proto-neutron stars.

💡 Research Summary

In this work the authors present the first finite‑temperature extension of the Many‑Body Forces (MBF) model, a relativistic quantum hadrodynamics framework that incorporates many‑body correlations through density‑dependent couplings of the scalar σ and vector ω, ρ mesons. Assuming charge neutrality, β‑equilibrium, and a composition of the full baryon octet together with electrons and muons, they explore three distinct hyperon coupling schemes: (i) the conventional SU(6) symmetry‑based ratios, (ii) a phenomenological set calibrated to Λ‑hypernuclear binding energies and to experimental Σ and Ξ potentials, and (iii) a new “stiffening” scheme tuned to reproduce a desired compressibility and maximum neutron‑star mass.

The formalism is generalized to finite temperature by adding the thermal contribution to the grand‑canonical potential, allowing calculations at fixed temperature (T = 0, 20, 30 MeV) and at fixed entropy per baryon (s = 0, 1 k_B). The authors solve the mean‑field equations self‑consistently, obtaining temperature‑dependent effective masses, meson fields, and chemical potentials. They find that increasing temperature lowers the density at which hyperons appear by roughly 0.1–0.3 n₀, because thermal excitations make the creation of strange baryons energetically favorable earlier than in the cold case. Consequently, the equation of state (EoS) softens modestly at a given baryon density, but the sound speed c_s² remains causal (≤ 1) and never exceeds the conformal limit 1/3 at the highest densities considered.

Thermodynamic quantities are examined in detail. The incompressibility K decreases by about 5–10 % when temperature rises to 30 MeV, while the adiabatic index Γ grows from the low‑density value ≈ 4/3 up to ≈ 1.7–1.8 in the hot, dense regime, reflecting the increasing importance of thermal pressure. The three hyperon coupling schemes produce markedly different high‑density behavior: the SU(6) case yields the softest EoS and a maximum mass M_max ≈ 2.0 M_⊙, the phenomenological set gives M_max ≈ 2.2 M_⊙, and the stiffening scheme can reach M_max ≈ 2.3 M_⊙, all compatible with current pulsar mass measurements.

Using these finite‑temperature EoS, the Tolman‑Oppenheimer‑Volkoff equations are solved to obtain mass‑radius (M‑R) relations for both cold neutron stars and hot proto‑neutron stars (PNS). At fixed temperature, the stellar radius expands by roughly 0.5–1 km compared with the cold case, while the maximum mass is only slightly reduced. For the fixed‑entropy sequence (s = 1 k_B per baryon), the central temperature adjusts self‑consistently with density, leading to an early hyperon population that temporarily stiffens the pressure support and yields a modest increase in the maximum mass relative to the isothermal sequence.

Overall, the paper demonstrates that (1) many‑body forces modeled via density‑dependent couplings can be consistently extended to finite temperature, (2) hyperon onset is strongly temperature‑dependent, (3) the choice of hyperon couplings critically influences compressibility, sound speed, and the maximum mass of compact stars, and (4) proto‑neutron‑star structure—mass, radius, and stability—can be substantially altered by thermal effects and entropy content. These results provide a more realistic microphysical input for simulations of core‑collapse supernovae, neutron‑star mergers, and the thermal evolution of young neutron stars, and they open the way for future studies that couple the MBF model to neutrino transport and magnetic‑field effects.