Fermion-axion stars: Static solutions and dynamical stability

We construct spherically symmetric static solutions of the Einstein-Klein-Gordon-Euler system involving a complex scalar field governed by a periodic potential that emerges in models of axionlike particles and fermionic matter modeled by a perfect fluid with a polytropic equation of state. Such solutions describe gravitationally bound composites of fermions and axions, which we dub fermion-axion stars. Sequences of pure axion stars in the existence domain may show the presence of multiple stable branches depending on the value of the decay constant parameter in the potential; this reflects in the appearance of multiple islands of stability in the two-dimensional parameter space of fermion-axion configurations. We investigate the domain of existence for three different values of the decay constant, identifying one or more regions of linear stability, making use of a method we already employed in previous works. We confirm the results from the linear analysis performing fully nonlinear numerical relativity evolutions. In this context, we perform several numerical simulations to identify regions in the parameter space where unstable models face different fates: the collapse to a Schwarzschild black hole, the migration to a stable model, and finally the dispersion of the scalar field together with the dilution of the fermionic matter, which approaches a static fermion star model with very low mass. This latter scenario was never observed in previous models without the periodic potential.