From spectroscopic abundances to evolutionary [$α$/Fe] in stellar models
Large-scale, high-resolution spectroscopic surveys map detailed chemical abundance patterns for millions of stars. However, libraries of stellar evolution models and isochrones still rely on a simplified description of chemical abundances, generally assuming either solar-scaled compositions or a constant enrichment for all $α$-elements. Moreover, the definition of $α$-enrichment is survey-dependent and is not necessarily the most relevant quantity for stellar structure and evolution. In the era of precision stellar astrophysics, stellar models need to better account for the wealth of chemical information provided by spectroscopic surveys. We develop a perturbative method to compute stellar evolution tracks for stars with arbitrary patterns of $α$-elements. We quantify the response of stellar evolutionary tracks to variations of individual $α$-elements through polynomial expansions, which can be linearly combined to produce synthetic tracks for a given abundance pattern. We also introduce the evolutionary $α$-enhancement, [$α$/Fe]$_{\rm ev}$, a constant enhancement for all $α$-elements that reproduces the impact of an observed abundance pattern on stellar models. We validate both methods using stars with detailed APOGEE abundances and quantify the differences between spectroscopic [$α$/Fe] and [$α$/Fe]$_{\rm ev}$ for different surveys. We identify a minimal set of chemical elements required for accurate stellar models and present ALCHEMY, a simple and fast tool to compute [$α$/Fe]$_{\rm ev}$ for general $α$-element abundance patterns.