We study numerically the nonlinear stability of excited fermion–boson stars in spherical symmetry. Such compound hypothetical stars, composed by fermions and bosons, are gravitationally bound, regular, and static configurations described within the coupled Einstein–Klein–Gordon–Euler theoretical framework. The excited configurations are characterized by the presence in the radial profile of the (complex, massive) scalar field—the bosonic piece—of at least one node across the star. The dynamical emergence of one such configuration from the accretion of a cloud of scalar field onto an already-formed neutron star, was numerically revealed in our previous investigation. Prompted by that finding we construct here equilibrium configurations of excited fermion–boson stars and study their stability properties using numerical-relativity simulations. In addition, we also analyze their dynamical formation from generic, constraint-satisfying initial data. Contrary to purely boson stars in the excited state, which are known to be generically unstable, our study reveals the appearance of a cooperative stabilization mechanism between the fermionic and bosonic constituents of those excited-state mixed stars. While similar examples of stabilization mechanisms have been recently discussed in the context of ℓ-boson stars and multi-field, multi-frequency boson stars, our results seem to indicate that the stabilization mechanism is a purely gravitational effect and does not depend on the type of matter of the companion star.

我们数值研究了激发态的非线性稳定性球对称的费米子-玻色子星。这种由费米子和玻色子组成的复合假想星是在爱因斯坦-克莱因-戈登-欧拉耦合理论框架内描述的引力束缚、规则和静态配置。激发配置的特点是在（复杂的、大质量的）标量场——玻色子部分——的径向剖面中存在至少一个跨越恒星的节点。在我们之前的研究中，从数字上揭示了从标量场云吸积到已经形成的中子星上的这种配置的动态出现。受这一发现的启发，我们在这里构建了受激费米子-玻色子星的平衡构型，并使用数值相对论模拟研究了它们的稳定性。此外，我们还从通用的、满足约束的初始数据中分析了它们的动态形成。与已知一般不稳定的激发态纯玻色子星相反，我们的研究揭示了这些激发态混合星的费米子和玻色子成分之间的协同稳定机制的出现。虽然最近在以下方面讨论了类似的稳定机制例子ℓ -玻色子星和多场、多频率的玻色子星，我们的结果似乎表明稳定机制是一种纯粹的引力效应，不依赖于伴星的物质类型。