Can a dynamically robust bosonic star (BS) produce an (effective) shadow that mimics that of a black hole (BH)? We focus on models of spherical BSs with free scalar or vector fields, as well as with polynomial or axionic self-interacting fields. The BH shadow is linked to the existence of light rings (LRs). For free bosonic fields, yielding mini-BSs, it is known that these stars can become ultra-compact — i.e., possess LRs — but only for perturbatively unstable solutions. We show this remains the case even when different self-interactions are considered. However, an effective shadow can arise in a different way: if BSs reproduce the existence of an innermost stable circular orbit (ISCO) for timelike geodesics (located at r _ISCO = 6M for a Schwarzschild BH of mass M), the accretion flow morphology around BHs is mimicked and an effective shadow arises in an astrophysical environment. Even though spherical BSs may accommodate stable timelike circular orbits all the way down to their centre, we show the angular velocity Ω along such orbits may have a maximum away from the origin, at R _Ω; this scale was recently observed to mimic the BH's ISCO in some scenarios of accretion flow. Then: (i) for free scalar fields or with quartic self-interactions, R _Ω ≠ 0 only for perturbatively unstable BSs; (ii) for higher scalar self-interactions, e.g. axionic, R _Ω ≠ 0 is possible for perturbatively stable BSs, but no solution with R _Ω = 6M was found in the parameter space explored; (iii) but for free vector fields, yielding Proca stars, perturbatively stable solutions with R _Ω ≠ 0 exist, and indeed R _Ω = 6M for a particular solution. Thus, dynamically robust spherical Proca stars succeed in the imitation game: they can mimic the shadow of a (near-)equilibrium Schwarzschild BH with the same M, in an astrophysical environment, despite the absence of a LR, at least under some observation conditions, as we confirm by explicitly comparing the lensing of such Proca stars and Schwarzschild BHs.

动态强大的玻色子星 (BS)能否产生模拟黑洞 (BH) 的（有效）阴影？我们专注于具有自由标量或矢量场以及多项式或轴子自相互作用场的球形 BS 模型。BH 阴影与光环 (LR) 的存在有关。对于自由玻色场，产生迷你BS，众所周知，这些恒星可以变得超紧凑——即拥有 LR——但仅适用于微扰不稳定解。我们表明，即使考虑到不同的自我交互，情况仍然如此。然而，一个有效的阴影可以以不同的方式出现：如果 BS 为类时测地线（位于r _ISCO = 6 M对于质量为M的 Schwarzschild BH，模拟了 BH周围的吸积流形态，并且在天体物理环境中出现了有效阴影。尽管球形 BS 可以容纳一直向下到其中心的稳定的类时圆形轨道，但我们表明沿着这些轨道的角速度 Ω 可能在远离原点的R _Ω处具有最大值；最近观察到该比例在某些吸积流场景中模拟了 BH 的 ISCO。然后： (i) 对于自由标量场或四次自相互作用，R _Ω ≠ 0 仅适用于微扰不稳定 BS；(ii) 对于更高的标量自相互作用，例如 axionic，对于微扰稳定的 BS，R _Ω ≠ 0 是可能的，但没有解决方案 在探索的参数空间中发现R _Ω = 6 M；(iii) 但对于自由矢量场，产生 Proca 星，存在R _Ω ≠ 0 的微扰稳定解，对于特定解，确实R _Ω = 6 M。因此，动态稳健的球形 Proca 星在模仿游戏中取得成功：它们可以在天体物理环境中模拟具有相同M的（近）平衡 Schwarzschild BH 的阴影，尽管没有 LR，至少在某些观察条件下，正如我们通过明确比较这些 Proca 恒星和 Schwarzschild BHs 的透镜所确认的那样。