Neutron stars with Higgs-portal dark matter in Rastall gravity: From observable degeneracy to tidal Love-number probes

We study neutron stars (NSs) admixed with Higgs-portal fermionic dark matter (DM) in Rastall gravity, a one-parameter theory in which local energy–momentum conservation is relaxed as ∇ μ T μ ν = λ ∇ ν R . Using three density-dependent relativistic mean-field (DDRMF) functionals — DD2, DD-ME2 and DD-MEX — we solve the coupled mean-field, Rastall–Tolman–Oppenheimer–Volkoff and tidal equations for DM Fermi momentum k F DM = 10 –50 MeV and Rastall parameter η = 0 –0.01. The two parameters push the observables in opposite directions: DM softens the equation of state and shrinks the star, while a positive η weakens the effective self-gravity of the fluid and enlarges it. The response is strongly observable-dependent. Over η = 0 → 0.01 the maximum mass M max changes by only 0.3–0.4%, whereas the canonical radius R 1.4 changes by 15–20% and the tidal deformability Λ 1.4 by 7–16%. This creates a genuine degeneracy: a measured ( M max , R 1.4 ) pair can be reproduced by a softer matter sector or by a weaker effective gravity. We identify one quantity that does not follow this pattern. At fixed mass, the electric-type Love number k 2 E is suppressed by η , falling to 0.45–0.56 of its general-relativistic value at η = 0.01 , almost independently of the functional, while Λ nevertheless rises because the geometric factor ( R / M ) 5 grows faster than k 2 E falls. The tidal deformability therefore hides a compensation that the Love number itself exposes, and a joint measurement of the stellar compactness C and the gravitational-wave tidal deformability Λ from which k 2 E follows via the exact relation Λ = 2 3 k 2 E ( R / M ) 5 is a more promising route to separating geometry from dark matter than Λ alone.

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