The Effect of Different Methods for Accounting for $\alpha$-enhancement on the Asteroseismic Modeling of Metal-Poor Stars

TL;DR

This study compares different methods of accounting for $\

Contribution

It demonstrates that detailed $\

Findings

Stellar properties are consistent across $\

Uncertainties in stellar parameters are comparable between methods.

The $ u_{ ext{max}}$ scaling relation breaks down at low metallicities.

Abstract

Constraining stellar models using asteroseismic and spectroscopic observations is a powerful method for precisely determining the fundamental properties of stars in different kinematic components of our galaxy. We use spectroscopy and individual oscillation mode frequencies to perform a homogeneous modeling study of eight evolved metal-poor stars enhanced in $\alpha$-elements. We compare a full treatment of $\alpha$-enhancement against an ad hoc correction to the total metallicity and show that the stellar properties inferred from asteroseismic modeling using both sets of models agree with each other. Additionally, we find that the uncertainties on stellar parameters derived from the both $\alpha$-enhanced modeling methods are comparable. This is in qualitative disagreement with existing works showing red-giant ages constrained by only the global asteroseismic parameters to depend strongly on the opacities and abundances assumed in 1D modeling. We also show that the observed frequency of maximum oscillation power ($\nu_{\text{max}}$) is larger than the value predicted from applying the $\nu_{\text{max}}$ scaling relation to the masses, radii, and temperatures inferred from the detailed modeling. This discrepancy is pronounced at low metallicities, consistent with recent findings indicating a breakdown of the $\nu_{\text{max}}$ scaling relation for metal-poor stars. Understanding the extent to which the $\nu_{\text{max}}$ scaling relation fails for low-metallicity solar-like oscillators through detailed modeling will enable more accurate mass and age determinations for hundreds of giant stars in the Galactic Halo for which only global asteroseismic parameters are available.