Mode visibilities in rapidly rotating stars

TL;DR

This paper develops a comprehensive method to calculate mode visibilities in rapidly rotating stars, accounting for geometric distortion and atmospheric effects, to improve mode identification accuracy.

Contribution

It introduces equations for mode visibility calculations in distorted stars, incorporating effects like gravity darkening and limb darkening, applied to 2D oscillation models.

Findings

Mode visibilities increase for chaotic modes.

Pole-on stars exhibit simpler frequency spectra.

Amplitude ratios depend on inclination and azimuthal order.

Abstract

Context: Mode identification is a crucial step to comparing observed frequencies with theoretical ones, but has proven to be difficult in rapidly rotating stars. Aims: To further constrain mode identification, we aim to accurately calculate mode visibilities and amplitude ratios in rapid rotators. 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. These equations are then applied to 2D oscillation modes, calculated using the TOP code, in fully distorted 2D models based on the 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_{\odot} models rotating at 0 to 80 % of the critical rotation rate. These calculations confirm previous results, such as the increased visibility of chaotic modes, the simpler frequency spectra of pole-on stars, or the dependence of amplitude ratios on inclination and azimuthal order. In addition, the geometric shape of the star reduces the contrast between pole-on and equator-on visibilities of island modes. We also show that modes with similar (ell, |m|) values frequently have similar amplitude ratios, even in the most rapidly rotating models.