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

TL;DR

This work investigates the optical and polarized appearance of horizonless Bardeen-boson stars by solving the Einstein-Klein-Gordon system with nonlinear electrodynamics to obtain self-consistent, regular spacetimes, then modeling thin-disk illumination and light propagation via ray-tracing. The authors fit the numerically obtained metric with analytic expressions for $g_{tt}$ and $g_{rr}$ and analyze eight configurations spanning different $φ_0$ and $𝒢$, studying how these parameters and the viewing angle $θ_o$ affect direct and lensing images. They find a central brightness depression akin to an inner shadow across all cases, with no photon rings for the explored regimes, though lensing images emerge at larger $θ_o$ and/or $φ_0$, and polarization signatures show strong interior effects absent in black holes. The results provide theoretical guidance for discriminating boson stars from black holes in future high-resolution imaging, highlighting the value of combining lensing-band signatures with polarization analyses and suggesting further work with varied potentials and more realistic accretion models.

Abstract

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 $φ_0$, the magnetic charge $\mathcal{G}$, and the observation angle $θ_o$, on the image structure. As compact horizonless objects, boson stars produce optical images dominated by direct emission, while their morphology undergoes significant distortions as $θ_o$ increases. Higher values of $φ_0$ and $θ_o$ 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.

Figures (11)

• Figure 1: Relationship between the mass and the frequency $\omega$, radius $R$, and scalar field $\phi$. The red, green, blue, and orange lines correspond to $\mathcal{G}=0.01, 0.07, 0.1,$ and $0.15$, respectively. The fixed parameters are $\mathcal{S}=0.2$ and $\phi_0=0.6$.
• Figure 2: Scalar field and numerical metric of BS1--BS4. The red, green, blue, and orange lines correspond to $\phi_0=0.3,0.35,0.55,0.6$, respectively. The fixed parameters are $\mathcal{S}=0.8,\mathcal{G}=0.35$.
• Figure 3: Scalar field and numerical metric of BS5--BS8. The red, green, blue, and orange lines correspond to $\mathcal{G}=0.01,0.07,0.1,0.15$, respectively. The fixed parameters are $\mathcal{S}=0.2,\phi_0=0.6$.
• Figure 4: Fitting results for BS1--BS4. The solid lines represent the fitting functions, and the dashed lines represent the numerical metrics. The red, green, blue, and orange lines correspond to $\phi_0=0.3,0.35,0.55,0.6$, respectively. The fixed parameters are $\mathcal{S}=0.8,\mathcal{G}=0.35$.
• Figure 5: Fitting results for BS5--BS8. The solid lines represent the fitting functions, and the dashed lines represent the numerical metrics. The red, green, blue, and orange lines correspond to $\mathcal{G}=0.01,0.07,0.1,0.15$, respectively. The fixed parameters are $\mathcal{S}=0.2,\phi_0=0.6$.