Neutron stars offer unique natural laboratories for probing the interaction between dark matter and baryonic matter — a central open question in modern astrophysics and high-energy physics. In this talk, I will present our recent work modeling dark matter as an ultralight bosonic field that accretes onto neutron stars, forming composite objects — fermion-boson stars — bound through gravity.
I will discuss our long-term numerical relativity simulations in spherical symmetry, through which we extract and analyze the radial oscillation mode spectra of these systems. A key result I will highlight is the gravitational synchronization between the fermionic and bosonic components: regardless of the equation of state, both components lock in phase, enriching the oscillation spectrum and giving rise to new multi-state scalar configurations that reshape the hierarchy of neutron-star radial modes. I will also present a practical procedure we developed to compute the dominant oscillation mode frequencies as a function of the bosonic mass, and I will close by discussing the broader implications of these findings for neutron-star physics and the prospects for gravitational-wave detection.