Mode visibilities in rapidly rotating stars⋆
Institut d’Astrophysique et Géophysique de l’Université de
Allée du 6 Août 17,
2 LESIA, Observatoire de Paris, CNRS, UPMC Univ. Paris 06, Univ. Paris-Diderot, 5 place Jules Janssen, 92195 Meudon, France
3 Kavli Institute for Theoretical Physics, Kohn Hall, University of California, Santa Barbara, CA 93106, USA
4 Universté de Toulouse, UPS-OMP, IRAP, 31400 Toulouse, France
5 CNRS, IRAP, 14 avenue Édouard Belin, 31400 Toulouse, France
6 GEPI, Observatoire de Paris-Meudon, CNRS, Université Paris Diderot, 92125 Meudon Cedex, France
7 High Altitude Observatory, National Center for Atmospheric Research, Boulder, CO 80307, USA
Accepted: 5 December 2012
Context. Mode identification is a crucial step to comparing observed frequencies with theoretical ones. However, it has proven to be particularly difficult in rapidly rotating stars. An important reason for this is the lack of simple frequency patterns such as those present in solar-type pulsators. This problem is further aggravated in δ Scuti stars by their particularly rich frequency spectra.
Aims. As a first step to obtaining further observational constraints towards mode identification in rapid rotators, we aim to accurately calculate mode visibilities and amplitude ratios while fully taking into account the effects of rotation.
Methods. We derive the relevant equations for calculating mode visibilities in different photometric bands while fully taking into account the geometric distortion from both the centrifugal deformation and the pulsation modes, the variations in effective gravity, and an approximate treatment of the temperature variations, given the adiabatic nature of the pulsation modes. These equations are then applied to 2D oscillation modes, calculated using the TOP code (Two-dimension Oscillation Program), in fully distorted 2D models based on the self-consistent field (SCF) method. The specific intensities come from a grid of Kurucz atmospheres, thereby taking into account limb and gravity darkening.
Results. We obtain mode visibilities and amplitude ratios for 2 M⊙ models with rotation rates ranging from 0 to 80% of the critical rotation rate. Based on these calculations, we confirm a number of results from earlier studies, such as the increased visibility of numerous chaotic modes at sufficient rotation rates, the simpler frequency spectra with dominant island modes for pole-on configurations, or the dependence of amplitude ratios on inclination and azimuthal order in rotating stars. In addition, we explain how the geometric shape of the star leads to a smaller contrast between pole-on and equator-on visibilities of equatorially-focused island modes. We also show that modes with similar (ℓ, |m|) values frequently have similar amplitude ratios, even in the most rapidly rotating models.
Key words: stars: oscillations / stars: rotation / stars: interiors / stars: variables:δScuti
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© ESO, 2013