We study photon rings of constant scalar hairy black holes with mass m, charge Q, and scalar hair S obtained from the Einstein-Maxwell-conformally coupled scalar theory. These black holes are classified as scalar hairy Reissner-Nordström (SHRN) black hole, scalar hairy charged black hole with \(S> -Q^2\), and mutated-RN black hole. The first two respect both dominant and strong energy conditions and have positive ADM mass and entropy, while the last does not respect two energy conditions and has negative ADM mass and entropy. We find that all of these black holes respect the lower bound (\(r_\gamma \ge 1.2 r_+\)) of photon rings. We obtain all real bounds of photon rings for these black holes and discuss physical and observational properties of real bounds. It is shown that the observationally favored region based on the shadow radius includes SHRN black hole, scalar hairy charged black hole, and mutated-RN black hole.

我们研究由爱因斯坦-麦克斯韦共形耦合标量理论获得的质量为m、电荷Q和标量毛S的恒定标量毛状黑洞的光子环。这些黑洞被分类为标量毛状赖斯纳-诺德斯特伦 (SHRN) 黑洞、标量毛状带电黑洞\(S> -Q^2\)和突变 RN 黑洞。前两个同时考虑主导和强能量条件，并具有正 ADM 质量和熵，而最后一个不考虑两种能量条件，并具有负 ADM 质量和熵。我们发现所有这些黑洞都遵循光子环的下界（\(r_\gamma \ge 1.2 r_+\) ）。我们获得了这些黑洞的光子环的所有实界，并讨论了实界的物理和观测特性。结果表明，基于阴影半径的观测有利区域包括SHRN黑洞、标量毛状带电黑洞和突变RN黑洞。