Polar Quasinormal Modes of Neutron Stars in Massive Scalar-Tensor Theories

We study polar quasinormal modes of relativistic stars in scalar-tensor theories, where we include a massive gravitational scalar field and employ the standard Brans-Dicke coupling function. For the potential of the scalar field we consider a simple mass term as well as a potential associated with $R^2$ gravity. The presence of the scalar field makes the spectrum of quasinormal modes much richer than the spectrum in General Relativity. We here investigate radial modes ($l=0$) and quadrupole modes ($l=2$). The general relativistic $l=0$ normal modes turn into quasinormal modes in scalar-tensor theories, that are able to propagate outside of the stars. In addition to the pressure-led modes new scalar-led $\varphi$-modes arise. We analyze the dependence of the quasinormal mode frequencies and decay times on the scalar field mass.