A new window to tidal asteroseismology: non-linearly excited stellar eigenmodes and the period spacing pattern in KOI-54

We revisit the Tidally Excited Oscillations (TEOs) in A-type, main-sequence, eccentric binary KOI-54, prototype of heartbeat stars. Although linear tidal response star is a series orbital-harmonic frequencies which are not stellar eigenfrequencies, we show that non-linearly excited non-orbital-harmonic TEOs eigenmodes. By carefully choosing modes satisfy mode-coupling selection rules, period spacing ($\Delta P$) pattern quadrupole gravity P \approx 2520-2535$ sec) can be discerned Fourier spectrum, with detection significance level $99.9\%$. The inferred value agrees remarkably well theoretical $l=2,m=0$ g from model measured mass, radius and effective temperature. also find two largest-amplitude at $N=90, 91$ harmonics very close to resonance eigenmodes, likely come different Previous works on oscillations primarily focus modeling TEO amplitudes phases, high sensitivity amplitude frequency detuning (tidal forcing minus closest eigenfrequency) requires extremely dense grids models prevents us constraining physical parameters easily. This work, however, opens window real asteroseismology by using eigenfrequencies non-linear possibly very-close-to-resonance TEOs. Our seismic these identified eigen g-modes shows best-matching have ($M 2.20, 2.35 M_{\odot}$) super-solar metallicity, good agreement previous measurements.