A light ray passing near a massive body bends around it, like a runner rounding the corner of a stadium. For a neutron star, this deflection angle is usually assumed to be the same as for a point mass. But if the star is wrapped in an invisible halo of dark matter, the picture changes: light passing through the halo is deflected less than the total mass would predict. This suppression is like a veil that slightly blurs the view, and its transparency tells you about what lies hidden.
The authors built a model of the star where ordinary matter and dark matter coexist as two fluids interacting only through gravity. For light dark matter particles, pressure puffs them into an extended halo beyond the visible surface of the star. They then computed the light deflection angle using a geometric theorem that relates the curvature of space to the mass inside a cylinder. They found that the deflection deficit is largest at the boundary of the visible surface and decreases toward the edge of the halo.
The shape of the deflection curve is not just a number; it is a map. In the plane of dark matter fraction versus halo radius, the contours of the deficit tilt and separate different equations of state for ordinary matter. A stiff core with a radius of 13 km and a standard one with a radius of 10 km leave different traces. This is a geometric way to tell dark matter apart from uncertainties in nuclear physics.
Previously, light deflection was computed for superimposed dark matter profiles without asking whether they are physically realizable. Here, the halo emerges as a solution to the stellar structure equations, and the lensing reflects the same microphysics as mass, radius, and tidal deformability. This is an independent cross-check for configurations derived from gravitational wave observations. The veil is no longer just an ornament; it becomes a measuring instrument.
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.