Thermodynamic Consistent Description of Compact Stars of Two Interacting Fluids: The Case of Neutron Stars with Higgs Portal Dark Matter

We consider a thermodynamically consistent approach for the computation of the masses, radii, and tidal deformabilities of compact stars consisting of two interacting fluids with separately conserved quantum numbers. We apply this interacting fluid approach to the case of compact stars of neutron star matter with the Higgs portal fermionic dark matter model for the first time in a thermodynamically consistent manner. The patterns for the mass-radius curves and the tidal deformability depend on the dark matter particle mass and are different from former studies. Compared to ordinary neutron star properties, we obtain smaller masses and radii for dark matter particle masses similar to the nucleon mass and, hence, smaller tidal deformabilities as a result of the softening of the equation of state due to the presence of dark matter. For dark matter particle masses below the nucleon mass and sizable chemical potentials with respect to the dark matter particle mass, there will be a dark halo instead of dark core. Our investigation provides the basis for studying mergers of compact stars where the two fluids of neutron star matter and dark matter are coupled kinetically to each other and are described by one combined energy-momentum tensor of the two interacting fluids but are chemically different with two separately conserved number currents.

💡 Research Summary

The paper presents a thermodynamically consistent framework for modeling compact stars composed of two interacting fluids: ordinary neutron‑star matter and fermionic dark matter (DM) coupled via the Higgs portal. The authors emphasize that each fluid carries its own conserved number current (baryon number for nucleons, particle number for DM) while the total energy‑momentum tensor is conserved, leading to a single set of structure equations with kinetic coupling but chemical separation.

Starting from Klein’s law (µ e^ν = const) they derive the radial evolution of the chemical potentials, dµ/dr = ‑µ dν/dr, for both fluids. Together with the generalized Tolman‑Oppenheimer‑Volkoff (TOV) equations for the metric function ν(r), the enclosed mass M(r), and the total energy density ε(r), they obtain a closed system of four coupled ordinary differential equations. These equations are rendered dimensionless using Landau mass and radius scales, facilitating numerical integration from the stellar centre where the central chemical potentials µ_N,c and µ_DM,c are prescribed. Integration stops when each chemical potential reaches the corresponding particle mass, defining the surface of each component.

For the microphysics, the nucleonic sector is described by a relativistic mean‑field (RMF) model with σ, ω, and ρ mesons, including nonlinear scalar self‑interactions to reproduce nuclear saturation properties. The dark sector introduces a Dirac fermion χ interacting with the Standard Model through a scalar Higgs field h (the Higgs portal). The Lagrangian contains the usual kinetic and mass terms for χ and h, a Yukawa coupling y h χ̄χ, and a scalar coupling f M_N ψ̄ h ψ that mediates DM‑nucleon interactions. Solving the mean‑field equations yields the equation of state (EoS) for the combined system as a function of the two chemical potentials.

Numerical results show two distinct regimes depending on the DM particle mass m_χ relative to the nucleon mass M_N. When m_χ ≈ M_N (or slightly larger), DM accumulates in the core, forming a “dark core”. The additional component softens the total EoS, reducing the maximum gravitational mass to ≲ 1.5 M_⊙ and shrinking radii to ≲ 10 km. Consequently, the tidal deformability Λ is significantly lowered, comfortably satisfying the LIGO‑Virgo constraint Λ < 800 from GW170817.

Conversely, for lighter DM (m_χ < M_N) and sufficiently large DM chemical potential, the DM forms an extended halo surrounding the nucleonic core. In this configuration the nucleonic interior remains almost unchanged, but the outer halo contributes to the gravitational field, leading to even smaller Λ values (≈ 300–400) while preserving typical neutron‑star masses and radii. The authors point out that previous studies often assumed a fixed Fermi momentum for DM, which violates the thermodynamic relation dµ/dr = ‑µ dν/dr and thus yields inconsistent results. Their interacting‑fluid approach (IF‑A) resolves this by allowing the chemical potentials to vary self‑consistently with the metric.

The paper also discusses implications for binary mergers. Since the two fluids share a single energy‑momentum tensor but retain separate number currents, merger simulations would need to track both the kinetic coupling (affecting the spacetime dynamics) and the chemical decoupling (affecting the distribution of DM after coalescence). The presence of a dark halo or core could imprint characteristic signatures on the gravitational‑wave waveform, offering a novel avenue to probe Higgs‑portal dark matter with future GW observations.

In summary, the work provides a rigorous, thermodynamically sound method to incorporate Higgs‑portal fermionic dark matter into neutron‑star structure calculations, demonstrates how the DM mass controls whether a dark core or halo forms, and shows that these configurations lead to observable reductions in mass, radius, and tidal deformability, thereby opening new possibilities for constraining dark‑matter physics through multimessenger astrophysics.