Light passing through an extended dark-matter halo around a neutron star is deflected less, in the model, than it would be by a point lens with the same total mass. The difference appears for rays with impact parameter below the halo radius, the case in which the rays sample the two-fluid shell rather than the vacuum Schwarzschild region.
The preprint examines how a neutron star's structure imprints itself on weak light deflection. It is reported as arXiv:2608.25587v1, an arXiv preprint whose header is dated 26 August 2026 and whose document date is 27 August 2026.
Building the star in a computer
To build the star, the authors integrate coupled two-fluid Tolman-Oppenheimer-Volkoff equations. One fluid represents baryonic matter and the other dark matter, with the two components interacting through gravity; the calculation then computes the deflection angle using the Gibbons-Werner Gauss-Bonnet construction.
The modeled baryonic core has a mass of 1.4 solar masses. The calculation uses two tabulated baryonic equations of state, or descriptions of how that matter is modeled: SLy4 and APR4.
The explored dark-matter fraction runs from 0.05 to 0.40 in steps of 0.012. Halo radii range from 15 to 50 kilometers, particle masses from 0.10 to 0.20 GeV, and the interaction scale from 10 to 30 GeV^-1. The numerical integration uses a 1-meter step, and the paper reports four numerical runs plus a separate ray-tracing experiment.
Where the lensing difference shows up
The comparison is made with the vacuum Schwarzschild prediction and with a point-mass prediction carrying the same total mass. Rays with an impact parameter greater than the halo radius remain in the vacuum Schwarzschild region; rays with an impact parameter below it sample the non-Schwarzschild two-fluid shell.
For the inner-ray case, the modeled deflection is below the equal-total-mass point-mass prediction, while the mass inside the ray's cylinder is less than the total mass. The leading analytic expression uses the mass encircled by the ray rather than the total mass, with the pressure contribution treated as subdominant for a dilute, non-relativistic halo.
The size and shape of the shortfall vary across the model. The fractional deficit is largest at the baryonic surface and decreases toward the halo edge. It also becomes stronger as the ray moves inward and as the dark-matter fraction and halo radius grow.
A separate case is a dark-matter core confined inside the baryonic surface. There, exterior lensing is not distinguishable from lensing by an ordinary star with the corresponding total mass and compactness.
A profile, not just a mass
The calculations map the deficit at the baryonic surface across halo radius and the two baryonic equation-of-state cases. The contours tilt with halo radius and separate the modeled SLy4 and APR4 cases.
In a separate ray-tracing illustration, the total mass and source are held fixed. The admixed model shows a counter-image, or secondary image, that is displaced outward and stretched tangentially relative to the vacuum case.
A signal too small for direct imaging
At a modeled distance of 100 parsecs, the paper gives the halo-boundary angle as about 2.01 nanoarcseconds. In an example with an inner-edge fractional deficit of 0.35, the predicted displacement on the sky is about 0.23 nanoarcseconds. The paper describes both scales as below current direct-imaging resolution.
The angular estimates are model-based and have no reported uncertainty propagation. The ray-tracing image is illustrative and does not provide a statistical measurement uncertainty.
An idealised view of a rotating star
The main calculation assumes a spherically symmetric spacetime, while real neutron stars rotate and break spherical symmetry.
The calculations use selected baryonic and dark-sector parameter ranges, and no statistical uncertainty is reported for the modeled results.
Paper data and sources
Original title: Weak gravitational lensing by a dark-matter-admixed neutron star: a self-consistent two-fluid halo and the Gauss--Bonnet deflection angle
Authors: Yashmitha Kumaran, Ilídio Lopes
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text