More concerning the anelastic and subseismic approximations for low-frequency modes in stars

Two approximations, namely the subseismic approximation and the anelastic approximation, are presently used to filter out the acoustic modes when computing low frequency modes of a star (gravity modes or inertial modes). In a precedent paper (Dintrans & Rieutord 2001), we observed that the anelastic approximation gave eigenfrequencies much closer to the exact ones than the subseismic approximation. Here, we try to clarify this behaviour and show that it is due to the different physical approach taken by each approximation: On the one hand, the subseismic approximation considers the low frequency part of the spectrum of (say) gravity modes and turns out to be valid only in the central region of a star; on the other hand, the anelastic approximation considers the Brunt-Vaisala frequency as asymptotically small and makes no assumption on the order of the modes. Both approximations fail to describe the modes in the surface layers but eigenmodes issued from the anelastic approximation are closer to those including acoustic effects than their subseismic equivalent. We conclude that, as far as stellar eigenvalue problems are concerned, the anelastic approximation is better suited for simplifying the eigenvalue problem when low-frequency modes of a star are considered, while the subseismic approximation is a useful concept when analytic solutions of high order low-frequency modes are needed in the central region of a star.Comment: 5 pages 3 fig, to appear in MNRA

Identification of gravity waves in hydrodynamical simulations

The excitation of internal gravity waves by an entropy bubble oscillating in an isothermal atmosphere is investigated using direct two-dimensional numerical simulations. The oscillation field is measured by a projection of the simulated velocity field onto the anelastic solutions of the linear eigenvalue problem for the perturbations. This facilitates a quantitative study of both the spectrum and the amplitudes of excited g-modes.Comment: 12 pages, 11 figures, Appendices only available onlin

A test of time-dependent theories of stellar convection

Context: In Cepheids close to the red edge of the classical instability strip, a coupling occurs between the acoustic oscillations and the convective motions close to the surface.The best topical models that account for this coupling rely on 1-D time-dependent convection (TDC) formulations. However, their intrinsic weakness comes from the large number of unconstrained free parameters entering in the description of turbulent convection. Aims: We compare two widely used TDC models with the first two-dimensional nonlinear direct numerical simulations (DNS) of the convection-pulsation coupling in which the acoustic oscillations are self-sustained by the kappa-mechanism. Methods: The free parameters appearing in the Stellingwerf and Kuhfuss TDC recipes are constrained using a chi2-test with the time-dependent convective flux that evolves in nonlinear simulations of highly-compressible convection with kappa-mechanism. Results: This work emphasises some inherent limits of TDC models, that is, the temporal variability and non-universality of their free parameters. More importantly, within these limits, Stellingwerf's formalism is found to give better spatial and temporal agreements with the nonlinear simulation than Kuhfuss's one. It may therefore be preferred in 1-D TDC hydrocodes or stellar evolution codes.Comment: 7 pages, 5 figures, 2 tables, accepted for publication in A&

Convective quenching of stellar pulsations

Context: we study the convection-pulsation coupling that occurs in cold Cepheids close to the red edge of the classical instability strip. In these stars, the surface convective zone is supposed to stabilise the radial oscillations excited by the kappa-mechanism. Aims: we study the influence of the convective motions onto the amplitude and the nonlinear saturation of acoustic modes excited by kappa-mechanism. We are interested in determining the physical conditions needed to lead to a quenching of oscillations by convection. Methods: we compute two-dimensional nonlinear simulations (DNS) of the convection-pulsation coupling, in which the oscillations are sustained by a continuous physical process: the kappa-mechanism. Thanks to both a frequential analysis and a projection of the physical fields onto an acoustic subspace, we study how the convective motions affect the unstable radial oscillations. Results: depending on the initial physical conditions, two main behaviours are obtained: (i) either the unstable fundamental acoustic mode has a large amplitude, carries the bulk of the kinetic energy and shows a nonlinear saturation similar to the purely radiative case; (ii) or the convective motions affect significantly the mode amplitude that remains very weak. In this second case, convection is quenching the acoustic oscillations. We interpret these discrepancies in terms of the difference in density contrast: larger stratification leads to smaller convective plumes that do not affect much the purely radial modes, while large-scale vortices may quench the oscillations.Comment: 15 pages, 17 figures, 3 tables, accepted for publication in A&