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 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 $\phi_0$, the magnetic charge $\mathcal{G}$, and the observation angle $\theta_o$, on the image structure. As compact horizonless objects, boson stars produce optical images dominated by direct emission, while their morphology undergoes significant distortions as $\theta_o$ increases. Higher values of $\phi_0$ and $\theta_o$ can give rise to lensing 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.