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Oscillation modes in the rapidly rotating Slowly Pulsating B-type star $\bmu$ Eridani

We present results of a search for identification of modes responsible for the six most significant frequency peaks detected in the rapidly rotating SPB star $μ$ Eridani. All published and some unpublished photometric data are used in our new analysis. The mode identification is carried out with the method developed by Daszyńska-Daszkiewicz et al. employing the phases and amplitudes from multi-band photometric data and relying on the traditional approximation for the treatment of oscillations in rotating stars. Models consistent with the observed mean parameters are considered. For the five frequency peaks, the candidates for the identifications are searched amongst unstable modes. In the case of the third frequency, which is an exact multiple of the orbital frequency, this condition is relaxed. The systematic search is continued up to a harmonic degree $\ell =6$. Determination of the angular numbers, $(\ell,m)$, is done simultaneously with the rotation rate, $V_{\rm rot}$, and the inclination angle, $i$, constrained by the spectroscopic data on the projected rotational velocity, $V_{\rm rot}\sin i$, which is assumed constant. All the peaks may be accounted for with g-modes of high radial orders and the degrees $\ell\le 6$. There are differences in some identifications between the models. For the two lowest--amplitude peaks the identifications are not unique. Nonetheless, the equatorial velocity is constrained to a narrow range of (135, 140) km/s. Our work presents the first application of the photometric method of mode identification in the framework of the traditional approximation and we believe that it opens a new promising direction in studies of SPB stars.