An astrophysical interpretation of the remarkable g-mode frequency groups of the rapidly rotating $\gamma$ Dor star, KIC 5608334

Abstract

The Fourier spectrum of the $\gamma$-Dor variable KIC 5608334 shows remarkable frequency groups at $\sim$3, $\sim$6, $\sim$9, and 11--12\,d$^{-1}$. We explain the four frequency groups as prograde sectoral g modes in a rapidly rotating star. Frequencies of intermediate-to-high radial order prograde sectoral g modes in a rapidly rotating star are proportional to $|m|$ (i.e., $\nu \propto |m|$) in the co-rotating frame as well as in the inertial frame. This property is consistent with the frequency groups of KIC 5608334 as well as the period vs. period-spacing relation present within each frequency group, if we assume a rotation frequency of $2.2$\,d$^{-1}$, and that each frequency group consists of prograde sectoral g modes of $|m| = 1, 2, 3,$ and 4, respectively. In addition, these modes naturally satisfy near-resonance conditions $\nu_i\approx\nu_j+\nu_k$ with $m_i=m_j+m_k$. We even find exact resonance frequency conditions (within the precise measurement uncertainties) in many cases, which correspond to combination frequencies.