Theory and evidence of global Rossby waves in upper main-sequence stars: r-mode oscillations in many Kepler stars

Asteroseismic inference from pressure modes (p modes) and buoyancy, or gravity, modes (g modes) is ubiquitous for stars across the Hertzsprung-Russell diagram. Until now, however, discussion of r modes (global Rossby waves) has been rare. Here we derive the expected frequency ranges of r modes in the observational frame by considering the visibility of these modes. We find that the frequencies of r modes of azimuthal order m appear as groups at slightly lower frequency than m times the rotation frequency. Comparing the visibility curves for r modes with Fourier amplitude spectra of Kepler light curves of upper main-sequence B, A, and F stars, we find that r modes are present in many γ Dor stars (as first discovered by Van Reeth et al.), spotted stars, and so-called heartbeat stars, which are highly eccentric binary stars. We also find a signature of r modes in a frequently bursting Be star observed by Kepler. In the amplitude spectra of moderately to rapidly rotating γ Dor stars, r-mode frequency groups appear at lower frequency than prograde g-mode frequency groups, while in the amplitude spectra of spotted early A to B stars, groups of symmetric (with respect to the equator) r-mode frequencies appear just below the frequency of a structured peak that we suggest represents an approximate stellar rotation rate. In many heartbeat stars, a group of frequencies can be fitted with symmetric m = 1 r modes, which can be used to obtain rotation frequencies of these stars.