On the possibility of a tidally excited low - frequency g + - mode in 51 Peg

The possibility of a resonant excitation of a free oscillation mode with an observed period of 4.2311 d in the star 51 Pegasi by the tidal action of a low-mass companion is investigated. A free oscillation mode with the observed period is shown to correspond to a g+-mode of a high radial order. For the determination of the tidal displacement in a component of a close binary system of stars near resonance between a dynamic tide and a free oscillation mode of the star, expressions established by Smeyers et al. (in preparation) are used. For the numerical calculations, a standard solar model is used. It results that, in a favourable case, the relative difference between the frequency of the tidally excited oscillation mode and the frequency of the resonant dynamic tide must be smaller than 10−8 for the radial velocity variations to be of the order of 10m s−1. The probability for such a close resonance is less than 10−5. Since 51 Peg is not the only member of its class, it then seems unlikely that forced oscillations caused by a low-mass companion are responsible for the radial velocity variations that were reported for 51 Peg.