$\phi$-modes of neutron stars in a massless scalar-tensor theory

Scalar-tensor theories allow for a rich spectrum of quasinormal modes of neutron stars. The presence of the scalar field allows for polar monopole and dipole radiation, as well as for additional higher multipole modes led by the scalar field. Here we present these scalar-led $\phi$-modes for the lowest multipoles, $l=0$, 1 and 2 for a massless scalar-tensor theory of the Brans-Dicke type, motivated by $R^2$ theory, and compare with those of a minimally coupled scalar field in general relativity. We consider a set of six realistic equations of state and extract universal relations for the modes.