Dirac vs. Majorana Dark Matter Imprints on Neutron Star Observables

The fundamental character of a fermionic dark matter, whether it is a Dirac or Majorana particle remains a key unresolved issue whose answer would profoundly affect dark-sector phenomenology and detection strategies thereby motivates complementary probes across particle and astrophysical experiments. Compact stars, particularly neutron stars, offer unique astrophysical laboratories for probing such fundamental properties under extreme densities. The presence of a fermionic DM admixed with nuclear matter can modify the equation of state, thereby affecting observable quantities such as the mass-radius (M-R) relation and tidal deformability. In this work, we investigate how the intrinsic particle nature of fermionic DM influences neutron star structure. Within a relativistic mean-field framework extended by a scalar (or Higgs like) portal coupling between DM and nucleons, we construct self-consistent equation of states for both Dirac and Majorana cases and solve the Tolman-Oppenheimer-Volkoff equations to obtain stellar configurations. Owing to the difference in internal degrees of freedom, Dirac DM (four degrees of freedom) generally softens the equation of state more strongly than Majorana DM (two degrees of freedom), leading to smaller radii and lower maximum masses. We identify the parameter space consistent with current NICER and gravitational-wave constraints, highlighting the potential of compact-star observations to discriminate between Dirac and Majorana dark matter.

💡 Research Summary

The paper investigates whether the intrinsic particle nature of fermionic dark matter—specifically, whether it is a Dirac or a Majorana particle—leaves observable imprints on neutron‑star (NS) structure. The authors work within a relativistic mean‑field (RMF) description of dense nuclear matter, employing two well‑tested parameter sets (G3 and IOPB‑I) that include nonlinear σ, ω, ρ, δ meson self‑ and cross‑couplings. To capture possible deconfinement at supranuclear densities, they embed a quark‑yonic model in which low‑momentum quark states coexist with nucleons near the Fermi surface, smoothly transitioning at a chosen density n_t with a confinement scale Λ_cs.

The dark sector is introduced as a fermionic field χ that couples to a scalar mediator h (interpreted as the Standard Model Higgs or a Higgs‑like particle). The interaction Lagrangian differs for Dirac and Majorana cases: for Dirac χ the term is (\bar\chi(i!\not!\partial-M_\chi)+y_\chi h\bar\chi\chi); for Majorana the kinetic term carries an extra factor ½, reflecting the self‑conjugate nature. In the mean‑field approximation the scalar acquires a vacuum expectation value h₀, which shifts the effective masses of nucleons and dark matter: (M_i^=M_i-g_\sigma\sigma_0-f_{Mi}h_0) and (M_\chi^=M_\chi-y_\chi h_0).

Crucially, the degeneracy factor g_χ equals 4 for Dirac fermions (particle + antiparticle, two spin states) and 2 for Majorana fermions (only spin states). Consequently, the dark‑matter contributions to the total energy density and pressure scale linearly with g_χ. The authors write the dark‑matter energy density and pressure as integrals over the Fermi sea, adding the scalar‑mediator mass term. Because Dirac DM carries twice as many degrees of freedom, it softens the overall equation of state (EoS) more strongly than Majorana DM for identical mass M_χ, coupling y_χ, and Fermi momentum k_F^χ.

The total EoS is the sum of nuclear, quark‑yonic, and dark‑matter pieces. Using this composite EoS, the Tolman‑Oppenheimer‑Volkoff (TOV) equations are solved for a range of central pressures, yielding mass‑radius (M‑R) curves, maximum masses, and tidal deformabilities. The study explores two representative dark‑matter Fermi momenta (k_F^χ = 0.03 GeV and 0.04 GeV) while fixing n_t = 0.3 fm⁻³ and Λ_cs = 800 MeV.

Results show a clear hierarchy: for the same dark‑matter parameters, the Majorana‑DM‑admixed stars are stiffer, producing larger radii (by ≈0.5 km) and higher maximum masses (≈0.1–0.2 M_⊙) than the Dirac‑DM counterparts. With k_F^χ = 0.03 GeV, the Majorana models comfortably satisfy NICER constraints on PSR J0030+0451 and PSR J0740+6620, as well as the tidal‑deformability bounds from GW170817. The Dirac models, however, tend to predict radii that are too small and sometimes fail to reach the ≈2 M_⊙ lower bound set by massive pulsars. Raising k_F^χ to 0.04 GeV over‑softens both cases, pushing the configurations outside observational limits, which indicates that only modest dark‑matter fractions are allowed.

The authors conclude that the internal degrees of freedom of fermionic dark matter imprint measurable differences on neutron‑star observables. Current astrophysical data already favor a Majorana‑type dark sector if a scalar portal is operative. They also note that the scalar portal reduces nucleon effective masses, amplifying the softening effect; therefore, exploring alternative mediators (vector or pseudoscalar) would be a valuable extension. Finally, they argue that future, more precise measurements of NS masses, radii, and tidal deformabilities could provide a novel, astrophysical avenue to discriminate between Dirac and Majorana dark matter, complementing terrestrial direct‑detection and collider searches.