Excitation of oscillation modes by tides in close binaries: constraints on stellar and orbital parameters

The parameter space favourable for the resonant excitation of free oscillation modes by dynamic tides in close binary components is explored using qualitative considerations to estimate the order of magnitude of the tidal force and the frequency range covered by the tidally induced oscillations. The investigation is valid for slowly rotating stars with masses in the interval between 2 and  20 M_⊙  , and an evolutionary stage ranging from the beginning to the end of the main sequence. Oscillation modes with eigenfrequencies of the order of five times the inverse of the dynamical time-scale  τ_dyn  of the star, i.e. the lowest-order p -modes, the f -mode and the lowest-order g ⁺-modes, are found to be outside the favourable parameter space since their resonant excitation requires orbital eccentricities that are too high for the binary to stay detached when the components pass through the periastron of their relative orbit. Resonances between dynamic tides and g ⁺-modes with frequencies of the order of half of the inverse of the dynamical time-scale of the star on the other hand are found to be favourable for orbital periods up to  ～200τ_dyn  , provided that the binary mass ratio q is larger than 1/3, and the orbital eccentricity e is larger than ～0.25. This favourable range comes down to orbital periods of up to 5–12 d in the case of  2–20 M_⊙  zero-age main-sequence binary components, and orbital periods of up to 21–70 d in the case of terminal main-sequence binary components.