Identifying the oscillating star

\label{identifying}

The asteroseismic mass and radius are consistent with those from the ELC model for both stars. The surface gravity of the two stars from ELC are nearly identical, and both agree with the asteroseismic value. While neither star’s mean density agrees with the asteroseismic value, Star 2 is slightly closer than Star 1. Since one of the scaling equations gives mean density independent of temperature and \(\nu_{\rm max}\) (Equation \ref{density}), one might naïvely expect a better asteroseismic estimation of density compared to surface gravity. It is therefore important to consider the temperature dependence of Equation \ref{gravity}. 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 \((2.17\pm 0.14\ M_{\odot},8.26\pm 0.18\ R_{\odot})\), 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 in the asteroseismic scalings, we are at a level of precision where errors on temperature dominate the global asteroseismic results. In this case, while Star 2 appears to be a better candidate for the main oscillator at a glance, scaling relations alone cannot be used to prefer one star over the other. However, in Section \ref{actrot} we demonstrate that Star 2 is likely less active than Star 1. Based on this, we tentatively assign Star 2 as the main oscillator.

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.