Meredith L. Rawls edited subsubsection_Identifying_the_oscillating_star__.tex  over 8 years ago

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\subsubsection{Identifying the oscillating star}\label{identifying}  The asteroseismic mass and \revise{radius are consistent with those from the ELC model for both stars. The surface gravity of Star 2 nearly agrees with the asteroseismic value, while the gravity of Star 1 does not.} Neither star's mean density agrees with the asteroseismic value, but Star 2 is closer than Star 1. \revise{Since the scaling equations can be combined to give a mean density that is independent of temperature and $\nu_{\rm max}$ (Equation \ref{density}), one might na{\"i}vely expect a better asteroseismic estimation of density compared to surface gravity. Overall, the evidence strongly suggests the source of the oscillations is Star 2.}  However, we cannot definitely conclude this without considering the temperature dependence of the scaling relations. From \citet{gau13}, \citet{gau14}, and the present work, asteroseismic masses and radii were reported to be $(1.7 \pm 0.3 \ M_\odot, 7.7 \pm 0.4 \ R_\odot)$, $(2.06 \pm 0.13 \ M_\odot, 8.10 \pm 0.18 \ R_\odot)$, and $(2.17 \pm 0.12 \ M_\odot, 8.26 \pm 0.16 \ R_\odot)$, respectively. Among these, $\nu_{\rm{max}}$ does not vary much ($102.2, 106.4, 106.4 \ \mu\rm{Hz}$), and $\Delta \nu$ varies even less ($8.3, 8.32, 8.31 \ \mu\rm{Hz}$), while the assumed temperatures were 4699 K (from the KIC), 4857 K (from \citealt{hub14.2}), and 5000 K (this work). Even if temperature is the least influential parameter on stellar masses and radii in the asteroseismic scalings, we are at a level of precision where errors on temperature dominate the global asteroseismic results. While a more in-depth ``peak-bagging'' analysis of individual oscillation modes is beyond the scope of this paper, we strongly suspect the main  oscillating star is Star 2. \subsubsection{Surface gravity disagreement}\label{gravity_compare}  The asteroseismic $\log g$ measurement nearly agrees with those from ELC, yet all three are some 0.3 dex lower than the spectroscopic $\log g$ values, as can be seen in Table \ref{table2}. This discrepancy is similar to the difference found for giant stars by \citet{hol15}. They investigate a large sample of stars from the ASPCAP (APOGEE Stellar Parameters and Chemical Abundances Pipeline) which have $\log g$ measured via spectroscopy and asteroseismology. They find that spectroscopic surface gravity measurements are roughly 0.2--0.3 dex too high for core-He-burning (red clump) stars and roughly 0.1--0.2 dex too high for shell-H-burning (red giant branch) stars. \citet{hol15} speculate the difference may be partially due to a lack of treatment of stellar rotation, and derive an empirical calibration relation for a ``correct'' $\log g$ for red giant branch stars only. However, the stars in KIC 9246715 do not rotate particularly fast ($v_{\rm{rot}} \sin i \lesssim 8 \ \rm{km \ s}^{-1}$, which includes a contribution from macroturbulence as discussed in Section \ref{parameters}), so we cannot dismiss this discrepancy so readily.