模仿游戏：可以模仿史瓦西阴影的Proca星
The imitation game: Proca stars that can mimic the Schwarzschild shadow
摘要：
一个动态健壮的玻色子星（BS）能产生一个模仿黑洞（BH）的（有效）阴影吗？BH阴影与光环（LR）的存在有关。对于自由玻色子场，产生迷你BS，已知这些恒星可以变得超紧凑-即，具有LRs -但仅限于扰动不稳定解。我们表明，即使考虑不同的自我相互作用，情况仍然如此。然而，一个有效的阴影可以出现在一个不同的方式：如果BS再现存在的最内层的稳定圆轨道（ISCO）的类时测地线（位于$r_{\rm ISCO}=6M$的史瓦西BH的质量M），吸积流形态周围的BH的模仿和有效的阴影出现在天体物理环境。即使球形BS可以容纳稳定的类时圆形轨道一路下降到他们的中心，我们显示沿这样的轨道的角速度可能有一个最大的远离原点，在$R_Ω$，这个规模最近观察到模仿BH的ISCO在某些情况下的吸积流。然后又道：（i）对于自由标量场或四次自相互作用，$R_Ω\neq 0$仅适用于微扰不稳定的BS;（ii）对于更高的标量自相互作用，例如轴子，$R_Ω\neq 0$对于微扰稳定的BS是可能的，但在所探索的参数空间中没有发现具有$R_Ω=6M$的解;（iii）但对于自由向量场，产生Proca星（PS），存在具有$R_Ω\neq 0$的微扰稳定解，并且确实对于特定解存在$R_Ω=6M$。因此，动态鲁棒的球形PS可以模仿阴影的（近）平衡史瓦西BH与相同的M，在天体物理环境中，尽管没有LR，至少在某些观测条件下，我们确认通过比较这种PS和史瓦西BH的透镜。
英文摘要：
Can a dynamically robust bosonic star (BS) produce an (effective) shadow that mimics that of a black hole (BH)? 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 $r_{\rm ISCO}=6M$ 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 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, $R_Ω\neq 0$ only for perturbatively unstable BSs; (ii) for higher scalar self-interactions, e.g. axionic, $R_Ω\neq 0$ 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 (PSs), perturbatively stable solutions with $R_Ω\neq 0$ exist, and indeed $R_Ω=6M$ for a particular solution. Thus, dynamically robust spherical PSs 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 comparing the lensing of such PSs and Schwarzschild BHs.
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