Revisiting the Red-giant Branch Hosts KOI-3886 and $\iota$ Draconis. Detailed Asteroseismic Modeling and Consolidated Stellar Parameters

Asteroseismology is playing an increasingly important role in the characterization of red-giant host stars and their planetary systems. Here, we conduct detailed asteroseismic modeling of the evolved red-giant branch (RGB) hosts KOI-3886 and $\iota$ Draconis, making use of end-of-mission Kepler (KOI-3886) and multi-sector TESS ($\iota$ Draconis) time-series photometry. We also model the benchmark star KIC 8410637, a member of an eclipsing binary, thus providing a direct test to the seismic determination. We test the impact of adopting different sets of observed modes as seismic constraints. Inclusion of $\ell=1$ and 2 modes improves the precision on the stellar parameters, albeit marginally, compared to adopting radial modes alone, with $1.9$-$3.0\%$ (radius), $5$-$9\%$ (mass), and $19$-$25\%$ (age) reached when using all p-dominated modes as constraints. Given the very small spacing of adjacent dipole mixed modes in evolved RGB stars, the sparse set of observed g-dominated modes is not able to provide extra constraints, further leading to highly multimodal posteriors. Access to multi-year time-series photometry does not improve matters, with detailed modeling of evolved RGB stars based on (lower-resolution) TESS data sets attaining a precision commensurate with that based on end-of-mission Kepler data. Furthermore, we test the impact of varying the atmospheric boundary condition in our stellar models. We find mass and radius estimates to be insensitive to the description of the near-surface layers, at the expense of substantially changing both the near-surface structure of the best-fitting models and the values of associated parameters like the initial helium abundance, $Y_{\rm i}$. Attempts to measure $Y_{\rm i}$ from seismic modeling of red giants may thus be systematically dependent on the choice of atmospheric physics.