We calculate the dynamical tides raised by a close planetary companion on nonrotating stars of 1 M and 1.4 M . Using the Henyey method, we solve the fully nonadiabatic equations throughout the star. 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. Although this approximation generally applies in the low frequency limit, it also fails in the parts of the convection zone where the forcing frequency is small but larger than the Brunt-Väisälä frequency. 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. The relative surface flux perturbation is also significant, on the order of 0.1% for a system modelled on 51 Pegasi b. Observations affected by the horizontal displacement may therefore be more achievable than previously thought, and brightness perturbations may be the result of flux perturbations rather than due to the radial displacement. We discuss the implication of this on the possibility of detecting such tidally excited oscillations, including the prospect of utilising the large horizontal motion for observations of systems such as 51 Pegasi.
We calculate the conversion from non–adiabatic, non–radial oscillations tidally induced by a hot Jupiter on a star to observable spectroscopic and photometric signals. Models with both frozen convection and an approximation for a perturbation to the convective flux are discussed. 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 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.