Our star does oscillate and we have studied its oscillations in great depth within asteroseismology (specifically helioseismology). But I'm overall doubtful of

Our star does oscillate and we have studied its oscillations in great depth within asteroseismology (specifically helioseismology). But I'm overall doubtful of the conclusions of this paper, specifically the Fourier transforms they show don't appear special to me -- it looks like granulation background you get in effectively every star (though they do say they subtracted a "smoothed spectrum").