Investigating the Metallicity-Mixing Length Relation

Abstract

Stellar models typically use the mixing length approximation as a way to implement convection in a simplified manner. While conventionally the value of the mixing length parameter, $\alpha$, used is the solar calibrated value, many studies have shown that other values of $\alpha$ are needed to properly model stars. This uncertainty in the value of the mixing length parameter is a major source of error in stellar models and isochrones. Using asteroseismic data, we determine the value of the mixing length parameter required to properly model a set of about 450 stars ranging in $\log g$, $T_{\mathrm{eff}}$, and $[Fe/H]$. The relationship between the value of $\alpha$ required and the properties of the star is then investigated. For Eddington atmosphere, non-diffusion models, we find that the value of $\alpha$ can be approximated by a linear model, in the form of $\alpha /{\alpha }_{\odot }=5.426-0.101\log (g)-1.071\log (T_{\mathrm{eff}})+0.437([Fe/H])$. This process is repeated using a variety of model physics as well as compared to previous studies and results from 3D convective simulations.

arXiv comment20 pages, 17 figures, accepted for publication in ApJ

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