Low-frequency Variability in Massive Stars: Core Generation or Surface Phenomenon?

Bowman et al. reported low-frequency photometric variability in 164 O- and B-type stars observed with K2 and TESS. They interpret these motions as internal gravity waves, which could be excited stochastically by convection in the cores of these stars. The detection of internal gravity waves in massive stars would help distinguish between massive stars with convective or radiative cores, determine core size, and would provide important constraints on massive star structure and evolution. In this work, we study the observational signature of internal gravity waves generated by core convection. We calculate the wave transfer function, which links the internal gravity wave amplitude at the base of the radiative zone to the surface luminosity variation. This transfer function varies by many orders of magnitude for frequencies ≲1 days^-1, and has regularly spaced peaks near 1 days^-1 due to standing modes. This is inconsistent with the observed spectra that have smooth "red noise" profiles, without the predicted regularly spaced peaks. The wave transfer function is only meaningful if the waves stay predominately linear. We next show that this is the case: low-frequency traveling waves do not break unless their luminosity exceeds the radiative luminosity of the star; the observed luminosity fluctuations at high frequencies are so small that standing modes would be stable to nonlinear instability. These simple calculations suggest that the observed low-frequency photometric variability in massive stars is not due to internal gravity waves generated in the core of these stars. We finish with a discussion of (sub)surface convection that produces low-frequency variability in low-mass stars; this is very similar to that observed in Bowman et al. in higher-mass stars.