Neutron stars are natural laboratories for studying superdense matter and dark matter. Two lines of research developed almost independently: the structure and cooling of the star on one hand, and gravitational lensing of light in its field on the other. This work unites them by asking what imprint dark matter leaves on weak light deflection. There are already studies on lensing by superimposed dark matter halos, but they do not account for the self-consistent structure of the star. Our work sits alongside research on dark matter in neutron stars and gravitational lensing, but differs in that the halo emerges as a solution to the structure equations rather than being inserted by hand.
The star is modeled as two perfect fluids: baryonic and dark, interacting only through gravity. The coupled Tolman-Oppenheimer-Volkoff (TOV) equations are integrated for a realistic baryonic equation of state (SLy4 or APR4) and self-interacting dark matter. For light dark matter particles (mass less than 0.2 GeV), pressure supports an extended halo beyond the baryonic surface. The light deflection angle is computed using the Gibbons-Werner method, where the deflection equals the integral of the Gaussian curvature of the optical metric over the region bounded by the ray. In the weak field, the deflection is determined by the cylindrical mass: the mass enclosed within a cylinder of radius equal to the impact parameter.
The main result: for rays passing through the halo (impact parameter less than the halo radius), the deflection is suppressed compared to a point mass of the same total mass. This suppression is described by the cylindrical mass, which is less than the total mass because part of the halo lies outside the cylinder. The deflection deficit is maximal at the baryonic surface and decreases monotonically to zero at the halo boundary. For a typical star with a dark matter fraction of 0.35 and a halo radius of 30 km, the deficit at the inner edge reaches 0.35. Deficit maps in the (dark matter fraction, halo radius) plane show that the contours tilt and separate different baryonic equations of state (standard core radius 10 km and stiff core radius 13 km).
This work differs from neighboring studies by linking lensing to a self-consistent two-fluid model of the star. Previously, light deflection was computed for superimposed dark matter profiles without asking whether they are physically realizable. Here, the halo is an output of the TOV equations, and lensing reflects the same microphysics as mass, radius, and tidal deformability. This provides an independent geometric cross-check for dark matter configurations inferred from gravitational wave observations. The shape of the deficit, rather than its normalization, may help distinguish dark matter from nuclear equation of state uncertainty.
The topic could develop toward including neutron star rotation. For rapidly rotating millisecond pulsars, frame dragging and the quadrupole moment introduce corrections to light deflection. Extending the optical metric to the axisymmetric Hartle-Thorne geometry would allow separating the contributions of rotation and the dark halo. Also promising is the application of the finite-distance version of the Gauss-Bonnet theorem for sources and observers at finite distances, which is relevant for galactic neutron stars.
The results will impact the astrophysics of compact objects and cosmology: they offer a new way to test for the presence of dark matter in neutron stars through gravitational lensing. This will also strengthen the connection between stellar structure modeling and gravitational wave observations.
The next step is to include rotation in the two-fluid model and compute light deflection in the Hartle-Thorne metric. Another step is to assess the observability of the effect in astrometric microlensing events with Gaia precision.
This work is directly related to the unresolved degeneracy between dark matter and the equation of state of dense nuclear matter in neutron stars. The proposed geometric diagnostic, the shape of the deflection curve, may help break this degeneracy, which limits the interpretation of mass, radius, and tidal deformability data.
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors constructed a self-consistent two-fluid model of a neutron star with baryonic and dark matter interacting through gravity, and computed the light deflection angle using the Gibbons–Werner method. They showed that for rays passing through the dark halo, the deflection is suppressed compared to a point mass, and the deficit depends on the dark matter fraction and the halo radius. The deficit maps show sensitivity to the stiffness of the baryonic equation of state.
Where its strength is
Linking gravitational lensing to the self-consistent two-fluid structure of the star is a rare move that turns the shape of the deflection deficit into an independent geometric test of microphysics. This opens a path to cross-checking dark matter configurations derived from gravitational wave observations.
Where it could go next
Worth trying
Why this may matter
If the geometric signal of the dark halo can be isolated in future lensing observations, it would provide a way to probe neutron star composition and dark matter properties that is independent of electromagnetic and gravitational wave methods.
Nearby works in our archive
The closest work in the archive sits at 0.62 by meaning — the usual level for our corpus.
The light deflection angle of a neutron star with a dark halo at an impact parameter equal to the halo radius is about 16 degrees, which is much larger than the Sun's deflection of 1.75 arcseconds.