Universal relations between the quasinormal modes of neutron stars and magnetic tidal deformability

Tidal deformabilities are one of the observable quantities characterizing neutron stars, which are strongly associated with the stellar compactness, the ratio of the stellar mass to the radius. In addition to the tidal deformability, the quasinormal modes excited in a neutron star are also an important property for extracting information about the neutron star interior, adopting gravitational wave asteroseismology. In this study, we especially focus on the magnetic tidal deformability, which acts on the gravitational waveform from a neutron star binary merger as a higher-order effect than the electric tidal deformability, and derive the universal relations expressing the quasinormal modes, such as the fundamental ($f$-), 1st pressure ($p_1$-), and 1st spacetime ($w_1$-) modes, as a function of the magnetic tidal deformability. The universal relations derived in this study exhibit accuracy more or less comparable to those of the electric tidal deformability.