Tidally induced non-adiabatic stellar oscillations: how planets make stars wobble

We calculate the dynamical tides raised by a close planetary companion on non-rotating stars of 1 M⊙ and 1:4 M⊙. Using the Henyey method, we solve the fully non-adiabatic equations throughout the star, both for the case of frozen convection and for the case where an approximation for the perturbation to the convective flux is used. The horizontal Lagrangian displacement is found to be 10 to 100 times larger than the equilibrium tide value in a thin region near the surface of the star. This is because non-adiabatic effects dominate in a region that extends from below the outer edge of the convection zone up to the stellar surface, and the equilibrium tide approximation is inconsistent with non-adiabaticity. We derive analytical estimates which give a good approximation to the numerical values of the magnitude of the ratio of the horizontal and radial displacements at the surface. We calculate the conversion of these oscillations into observable spectroscopic and photometric signals. Observables are calculated for some real planetary systems to give specific predictions. Time-dependent line broadening and the radial velocity signal during transit are both investigated as methods to provide further insight into the nature of the stellar oscillations. The photometric signal is predicted to be roughly proportional to the inverse square of the orbital period, P-2, as in the equilibrium tide approximation. However, the radial velocity signal is predicted to be proportional to P-1, and is therefore much larger at long orbital periods than the signal corresponding to the equilibrium tide approximation, which is proportional to P-3. The prospects for detecting these oscillations and the implications for the detection and characterisation of planets are discussed.