Constraining mass, radius and tidal deformability of compact stars with axial wI modes: new universal relations including slow stable hybrid stars

We revisit asteroseismology with quadrupolar wI modes and present universal relationships for its fundamental and first overtone. In contrast to relationships proposed in the literature, our universal relationships are capable of including slow stable hybrid stars that appear when considering slow sharp hadron-quark phase transitions. We show that, if the frequency and damping time of the fundamental mode of a given pulsating object are measured, its mass, radius, and dimensionless tidal deformability can be inferred. Moreover, we show that the errors of such estimates are smaller than a few percent for the mass and radius. For the dimensionless tidal deformability, the errors are -- for compact objects with $M\gtrsim 1.4\,M_\odot$ -- in general smaller than ~100%. Comparison with previous universal relationships shows that the ones proposed in this work produce better estimates of the mass and radius of totally stable compact objects.