This paper uses observations of neutron stars to constrain a particular kind of dark matter made of repulsively interacting bosons. The dark matter is modeled as a complex scalar field that feels normal matter only through gravity. In that setup the dark component can sit in the star’s center as a ‘‘dark core’’ or form an extended ‘‘dark halo.’’ The work asks which combinations of dark-matter properties are consistent with current astrophysical data.

The authors scanned three dark-sector parameters — the boson mass mχ, the self-interaction strength λ, and an effective coupling Fχ — while also sampling uncertainties in the nuclear physics that controls how ordinary matter behaves at very high density. To represent nuclear uncertainty they used 27 equations of state (EOS) based on a DDME2 covariant density-functional family, varying two EOS-related parameters called L_sym and Q_sat across ranges given in the study. They compared all model variants to two recent NICER mass–radius analyses (the Amsterdam and the Maryland/Illinois results) and to the GW170817 gravitational-wave constraint on tidal deformability. The comparison was done in a Bayesian framework and the final numbers were averaged (evidence-weighted) over the EOS ensemble.

After this analysis the EOS-relevant dark-sector scale μχ ≡ mχ/λ1/4 is localized near 250 MeV for both NICER data sets. If one looks at mχ and λ separately, the marginalized posterior for the boson mass peaks around 300–330 MeV while λ remains broadly distributed. The authors stress that the bosonic equation of state depends on mχ and λ only through μχ, so the separate mχ and λ results depend on the prior assumptions used in the scan.

The inferred fraction of dark matter inside neutron stars depends on which NICER analysis is used. The posterior mode for the dark fraction is near 4% for the Maryland/Illinois data and near 12% for the Amsterdam data. The presence of bosonic dark matter also shifts the most likely values of Q_sat from negative toward intermediate and positive values, while the response of L_sym is weaker. The authors interpret this as a trade-off between the compactifying effect of dark matter and the high-density stiffness of ordinary nuclear matter: different combinations can give similar observable radii and tidal deformabilities.