The fundamental oscillation mode of boson stars and universal relations*

Boson stars are exotic compact objects characterized by a self-gravitating complex scalar field. For a given mass and self-interaction coupling constant of the scalar field, boson stars can act as neutron star mimickers and are possible candidates for gravitational-wave sources. We investigate the possibility of distinguishing neutron stars and boson stars through universal relations between the fundamental quadrupolar oscillation mode (f-mode) and the compactness (C), as well as the tidal deformability (Love number) of these objects. We consider the quartic potential for the scalar field and work in the strong coupling limit. We obtain that, depending on the normalization choice for the complex frequency, neutron stars and boson stars are distinguishable in terms of the f-C and f-Love relations. For instance, we discuss how these relations could be used to place bounds on the central pressure of neutron stars and boson stars.