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We study the axial quasi-normal modes of neutron stars in scalar-tensortheories with massive scalar field including a self-interacting term in thepotential. Various realistic equations of state including nuclear, hyperonicand hybrid matter are employed. Although the effect of spontaneousscalarization of neutron stars can be very large, binary pulsar observationsand gravitational wave detections significantly constrain the masslessscalar-tensor theories. If we consider a properly chosen nonzero mass for thescalar field, though, the scalar-tensor parameters cannot be restricted by theobservations, resulting in large deviation from pure general relativity. Withthis motivation in mind, we extend the universal relations for axialquasi-normal modes known in general relativity to neutron stars in massivescalar-tensor theories with self-interaction using a wide range of realisticEOS. We confirm the universality of the scaled frequency and damping time interms of the compactness and scaled moment of inertia for neutron stars withand without massive scalarization.

Axial quasi-normal modes of scalarized neutron stars with massive self-interacting scalar field