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Mode Identification of the Slowly Pulsating F0V Star V398 Aurigae (9 Aur)

We have investigated the F0V star V398\,Aurigae (= 9 Aur) under the assumption that it is undergoing non-radial gravity mode oscillations and that the two principal periods given by Krisciunas et al. (1995) are correct. We find that the two periods are manifestations of an $\ell=3, |m|=1$ spheroidal mode and its toroidal corrections due to the rotation of the star. As far as we know, this is the first detection of toroidal correction terms in a real star. The two modes probably are the result of rotational splitting. Our analysis provides for the first time a physical explanation of certain characteristics of the observed behavior of the star. The amplitude of the radial part of the pulsation for $f_1 = 0.795$\,d$^{-1}$ is a factor of 4 larger than the one for $f_2 = 0.346$\,d$^{-1}$. Since the photometric variability is determined mostly by temperature variations, which in turn are determined by the radial part of the pulsation, the photometric variability is dominated by the mode with frequency $f_1$. On the other hand, $f_2$ is the more pronounced one in all three spectroscopic moment variations (including the radial velocity), reflecting that the transverse displacement of $f_2$, and not the one of $f_1$, dominates the velocity behavior.