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The $β$ Cep/SPB star 12 Lacertae: extended mode identification and complex seismic modelling

Results of mode identification and seismic modelling of the $β$ Cep/SBP star 12 Lacertae are presented. Using data on the multi-colour photometry and radial velocity variations, we determine or constrain the mode degree, $\ell$, for all pulsational frequencies. Including the effects of rotation, we show that the dominant frequency, $ν_1$, is most likely a pure $\ell=1$ mode and the low frequency, $ν_A$, is a dipole retrograde mode. We construct a set of seismic models which fit two pulsational frequencies corresponding to the modes $\ell= 0,$ p$_1$ and $\ell= 1,$ g$_1$ and reproduce also the complex amplitude of the bolometric flux variations, $f$, for both frequencies simultaneously. Some of these seismic models reproduce also the frequency $ν_A$, as a mode $\ell= 1,$ g$_{13}$ or g$_{14}$, and its empirical values of $f$. Moreover, it was possible to find a model fitting the six 12 Lac frequencies (the first five and $ν_A$), only if the rotational splitting was calculated for a velocity of $V_{\rm rot}\approx 75$ km/s. In the next step, we check the effects of model atmospheres, opacity data, chemical mixture and opacity enhancement. Our results show that the OP tables are preferred and an increase of opacities in the $Z-$bump spoils the concordance of the empirical and theoretical values of $f$.