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


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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., $ u 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 $ u_iapprox u_j+ u_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.

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