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Space missions like CoRoT and Kepler have provided numerous new observationsof stellar oscillations in a multitude of stars by high precision photometry.This work compares the observed rich oscillation spectrum of the rapidlyrotating B3 IV star HD 43317 with the first results obtained by a new method tocalculate unstable oscillation modes in rapidly rotating stars in order to seewhether some of the observed modes can be identified. The new numerical methodconsists of two parts. We first search for modes resonant with a prescribedforcing symmetry by moving through relevant regions of complex frequency spaceand monitoring any increase of the stellar response to the applied forcing andzooming in onto the resonance. These resonant non-adiabatic 2D-solutions arethen fed into a 2D relaxation code with the same equations but without forcingterms. The complex oscillation frequency used in the forcing is now no longerprescribed, but added as an extra unknown. The corresponding free oscillationmode is usually obtained after a few ($<10$) iterations with only minoradjustment of the complex oscillation frequency. To compare with the observedlight variations we calculate the `visibility' of the found unstableoscillation modes, taking into account the cancellation of the various parts ofthe radiating oscillating stellar surface as seen by the observer. Thefrequencies of unstable axisymmetric g-modes, which have the highestvisibility, appear to nearly coincide with the observed largest amplitudephotometric variations of HD 43317, making an identification of the latteroscillations as $m$=0 modes plausible. The identification of $m$=1 g-modes isless straightforward, while many of the unstable even $m$=2 g-modes maycorrespond to observed weaker photometric variations.

Visibility of unstable oscillation modes in a rapidly rotating B star