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 which emerges in models of axion-like 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 as 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 2-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 non-linear 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.