Torsional oscillations of neutron stars in scalar-tensor theory of gravity

We study torsional oscillations of neutron stars in the scalar-tensor theory of gravity using the relativistic Cowling approximation. We compute unperturbed neutron star models adopting realistic equations of state for the neutron star's core and crust. For scalar-tensor theories that allow for spontaneous scalarization, the crust thickness can be significantly smaller than in general relativity. We derive the perturbation equation describing torsional oscillations in scalar-tensor theory, and we solve the corresponding eigenvalue problem to find the oscillation frequencies. The fundamental mode (overtone) frequencies become smaller (larger) than in general relativity for scalarized stellar models. Torsional oscillation frequencies may yield information on the crust microphysics if microphysics effects are not degenerate with strong-gravity effects, such as those due to scalarization. To address this issue, we consider two different models for the equation of state of the crust and we look at the effects of electron screening. The effect of scalarization on torsional oscillation frequencies turns out to be smaller than uncertainties in the microphysics for all spontaneous scalarization models allowed by binary pulsar observations. Our study shows that the observation of quasi-periodic oscillations (QPOs) following giant flares can be used to constrain the microphysics of neutron star crusts, whether spontaneous scalarization occurs or not.