Dirac vs. Majorana Dark Matter Imprints on Neutron Star Observables

TL;DR

This work addresses whether the fermionic dark matter is Dirac or Majorana by studying its imprints on neutron star observables. It develops DM-extended equations of state within an RMF framework coupled to a scalar Higgs-like portal and a quarkyonic matter description, then solves the Tolman–Oppenheimer–Volkoff equations to obtain mass-radius relations and tidal deformabilities. The key finding is that Dirac DM, with more internal degrees of freedom, softens the EoS more than Majorana DM for identical DM parameters, leading to smaller radii and lower maximum masses; notably, Majorana DM with $M_\chi \sim 400$ GeV and $k_f^{DM} \sim 0.03$–$0.04$ GeV can satisfy NICER and GW constraints while predicting reduced tidal deformabilities by about 20–40%. These results imply that precision neutron star measurements from NICER and gravitational-wave observations could indirectly probe the Dirac/Majorana nature of dark matter, complementing terrestrial searches.

Abstract

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.

Figures (4)

• Figure 1: Equation of state for dark matter–admixed quarkonic star having transition density $\rm n_{\rm t} = 0.3\,\,\hbox{fm}^{-3}$, QCD confinement scale $\Lambda_{\rm cs} = 800\,$ MeV and DM Fermi momentum $\rm k_{\rm f}^{\rm DM}=$ 0.03 GeV (red) and 0.04 GeV (blue) with the G3 and IOPB-I forces. The solid and dashed lines represent the Majorana and Dirac nature, respectively.
• Figure 2: Mass–radius relation of dark matter–admixed quarkonic stars obtained using the G3 and IOPB-I parameter sets with $\rm n_{\rm t} = 0.3\,\,\hbox{fm}^{-3}$. The solid (dashed) curve corresponds to Majorana (Dirac) dark matter contribution to $M-R$ relation. The horizontal shaded regions represent observational constraints from recent pulsar Miller2019Miller2021 and gravitational wave data GW170817Riley2019.
• Figure 3: M-R relations for the Majorona type EoSs having $\rm n_{\rm t} = 0.3\, {\rm fm}^{-3}$, QCD confinement scale $\Lambda_{\rm cs} = 800$ MeV and DM Fermi momentum $\rm k_{\rm f}^{\rm DM}$ = 0.03 GeV (solid) and 0.04 GeV (dashed) at different DM masses M$_{\chi}$ = 100, 200, 300, 400 GeV, for the G3 and IOPB-I forces, along with the observational data GW170817Miller2019Miller2021Riley2019.
• Figure 4: $\Lambda$ - M relations for the Majorona type EoSs having $\rm n_{\rm t} = 0.3\, {\rm fm}^{-3}$, QCD confinement scale $\Lambda_{\rm cs} =$ 800 MeV and DM Fermi momentum $\rm k_{\rm f}^{\rm DM}=$ 0.03 GeV (solid) and 0.04 GeV (dashed) at different DM masses M$_{\chi}$ = 100, 200, 300, 400 GeV, for the G3 and IOPB-I forces, along with the observational data GW170817Riley2019.