deletions | additions       diff --git a/subsection_A_hint_of_a__.tex b/subsection_A_hint_of_a__.tex  index 3717686..ac5f93b 100644  --- a/subsection_A_hint_of_a__.tex  +++ b/subsection_A_hint_of_a__.tex 
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Given that the giants in KIC 9246715 are nearly twins, with $L_1/L_2 = 0.94$, $R_1/R_2 = 0.95$, $M_1/M_2 = 1.01$, and $T_1/T_2 = 1.01$, we test whether it is possible that we see only one set of oscillation modes because both stars are oscillating with virtually identical frequencies. It is unlikely that two sets of solar-like oscillations lie on top of one another, because the predicted $\nu_{\rm{max}}$ for these not-quite-identical stars are $115.47 \pm 4.46$ and $102.9 \pm 3.46\ \mu$Hz for Star 1 and Star 2 respectively (from an inversion of Equations \ref{density} and \ref{gravity}), and the predicted $\Delta\nu_{\rm{obs}}$ are $8.85 \pm 0.15$ and $8.14 \pm 0.12 \ \mu$Hz for Star 1 and Star 2 respectively. The effective frequency resolution of the power spectrum for four years of \emph{Kepler} data is about $0.008 \ \mu \rm{Hz}$, and, more importantly, the intrinsic observed mode line widths is about $0.5 \ \mu \rm{Hz}$. Given this, the oscillation pattern from a second star (if present) should \emph{not} appear to lie exactly on top of the oscillation pattern we do see.  A However, a  careful observation of the \'echelle diagram (Fig. \ref{fig:echelle}) shows tilted alignments of low-amplitude peaks on the upper left side of the $l=1$ ridge. The same is less clear on the $l=0,2$ side. Even though oscillation modes cannot perfectly overlap, as explained above, modes of degrees $0,1$ of one star can almost overlap modes of degrees $1,0$ of the other. Thus, we searched what large frequency spacing could can  reproduce such  alignments tilted in that way. of peaks.  For this, we used the universal pattern of red-giant oscillations, which is extensively described in \citet{mos11}, to identify that a $\Delta\nu = 8.60\ \mu$Hz is able to both fit the trend that we see and globally overlap the modes of the main oscillator.  To search for the signature of a second set of oscillations, we consider variants of Figure \ref{fig:echelle} with slightly larger $\Delta \nu$ values. This is motivated by the broad, mixed-mode-like appearance of the $l=0$ modes in Figure \ref{fig:echelle}, where mixed modes are not physically possible, and by the faint diagonal structure in both the $l=1$ and $l=0,2$ mode regime. We find that $\Delta \nu \simeq 8.60 \ \mu \rm{Hz}$ reveals a hint of a second set of oscillation modes. Even if these are real and attributable to Star 1, the signal is extremely low-amplitude and cannot be measured robustly. 
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