Probing Red Giant Interiors with g-Dominated Mixed Modes II: The Cases of KIC 6117517, KIC 9475697, KIC 10123207 and KIC 10200377

Abstract

Building on Paper~I, which constrained core overshooting to $f_{\rm ov} < 0.01$ for $M < 1.4\,M_{\odot}$ and found $α_{\rm MLT} \simeq 2.0$ for metal-rich red giants, we extend this analysis to four lower-mass \textit{Kepler} red giants spanning a broad metallicity range: KIC~6117517, KIC~9475697, KIC~10123207, and KIC~10200377. Two complementary model grids are constructed: Grid~A fixes $α_{\rm MLT} = 2.0$ while varying metallicity; Grid~B adopts spectroscopic metallicities with $α_{\rm MLT}$ as a free parameter. Grid~A successfully reproduces both asteroseismic and spectroscopic constraints for the metal-rich targets (KIC~6117517 and KIC~9475697), confirming $α_{\rm MLT} = 2.0$ for metal-rich red giants. For the metal-poor targets (KIC~10123207 and KIC~10200377), Grid~B yields larger mixing-length parameters of $α_{\rm MLT} \approx 2.16$--$2.18$. Although only four stars are analyzed with unequal sensitivity to $α_{\rm MLT}$, these results suggest a tentative increase in convective efficiency toward lower metallicity, consistent with 3D hydrodynamical simulations but opposite to some 1D empirical calibrations. The best-fitting overshooting parameters ($f_{\rm ov} = 0.006$--$0.007$) independently support the Paper~I constraint and are consistent with a mass-dependent overshooting relation. The parameter uncertainties reach $0.6$--$2.5\%$ in mass, $0.2$--$0.9\%$ in radius, $2$--$13\%$ in age, and below $0.6\%$ in helium-core mass and below $0.2\%$ in helium-core radius. Surface-effect corrections are negligible for g-dominated mixed modes, validating $χ^2_{l=1g}$ as a robust fitting metric. For KIC~9475697, the core rotation rate is determined to be $Ω_{\rm core} = 0.6945 \pm 0.0190\,μ$Hz from model-based trapping parameters.