Identification of pulsational modes in rotating slowly pulsating B-type stars

Knowledge of the geometry of pulsational modes is a prerequisite for seismic modelling of stars. In the case of slowly pulsating B-type (SPB) pulsators, the simple zero-rotation approach so far used for mode identification is usually not valid because pulsational frequencies are often of the order of the rotational frequency. Moreover, this approach allows us to determine only the spherical harmonic degree, $\ell$, while the azimuthal order, $m$, is beyond its reach. On the other hand, because of the density of oscillation spectra of SPB stars, knowledge of $m$ is indispensable if one wants to assign the radial order, $n$, to the observed frequency peaks. Including the effects of rotation via the traditional approximation, we perform identification of the mode angular numbers ($\ell,~m$) for 31 SPB stars with available multicolour time series photometry. Simultaneously, constraints on the rotational velocity, $V_{\rm rot}$, and the inclination angle, $i$, are determined assuming uniform rotation and a constant value of $V_{\rm rot}\sin i$. Dependence of the results on the adopted model is tested using HD\,21071 as an example. Despite some model uncertainties and limitations of the method, our studies show the correct approach to identifying the low-frequency oscillation modes.