Observational features of the Bardeen–boson star with thin disk accretion

In this work, we construct spherically symmetric solutions of Bardeen–boson stars within the framework of the Einstein–Klein–Gordon theory coupled to nonlinear electrodynamics (NLED) by employing numerical methods. Considering a thin accretion disk in the equatorial plane as the light source, we systematically investigate the optical appearance of boson stars using the ray-tracing method and the stereographic projection technique. Particular attention is paid to the influence of the initial scalar field φ ₀ ϕ 0 , the magnetic charge G G , and the observation angle θ ₒ θ o , on the image structure. As compact horizonless objects, boson stars produce optical images dominated by direct emission, while their morphology undergoes significant distortions as θ ₒ θ o increases. Higher values of φ ₀ ϕ 0 and θ ₒ θ o can give rise to lensed images. For all the parameters, the image center exhibits a brightness depression similar to the inner shadow of black holes, which poses challenges for distinguishing between boson stars and black holes. To address this, we propose two possible approaches: (i) combining the analysis of lensing bands with the effective potential to determine the existence of photon rings; and (ii) examining the polarization effects under synchrotron emission mechanisms. These results provide theoretical support for future high-resolution imaging efforts aimed at discriminating boson stars from black holes.