The distribution of [α\alpha/Fe] in the Milky Way disc

Using a sample of red giant stars from the Apache Point Observatory Galactic Evolution Experiment (APOGEE) Data Release 16, we infer the conditional distribution $p([\alpha/\text{Fe}]\,|\,[\text{Fe/H}])$ in the Milky Way disk for the $\alpha$-elements Mg, O, Si, S, and Ca. In each bin of [Fe/H] and Galactocentric radius $R$, we model $p([\alpha/\text{Fe}])$ as a sum of two Gaussians, representing "low-$\alpha$" and "high-$\alpha$" populations with scale heights $z_1=0.45\,\text{kpc}$ and $z_2=0.95\,\text{kpc}$, respectively. By accounting for age-dependent and $z$-dependent selection effects in APOGEE, we infer the [$\alpha$/Fe] distributions that would be found for a fair sample of long-lived stars covering all $z$. Near the Solar circle, this distribution is bimodal at sub-solar [Fe/H], with the low-$\alpha$ and high-$\alpha$ peaks clearly separated by a minimum at intermediate [$\alpha$/Fe]. In agreement with previous results, we find that the high-$\alpha$ population is more prominent at smaller $R$, lower [Fe/H], and larger $|z|$, and that the sequence separation is smaller for Si and Ca than for Mg, O, and S. We find significant intrinsic scatter in [$\alpha$/Fe] at fixed [Fe/H] for both the low-$\alpha$ and high-$\alpha$ populations, typically $\sim 0.04$-dex. The means, dispersions, and relative amplitudes of this two-Gaussian description, and the dependence of these parameters on $R$, [Fe/H], and $\alpha$-element, provide a quantitative target for chemical evolution models and a test for hydrodynamic simulations of disk galaxy formation. We argue that explaining the observed bimodality will probably require one or more sharp transitions in the disk's gas accretion, star formation, or outflow history in addition to radial mixing of stellar populations.Comment: Accepted for publication in MNRA

StarHorse: A Bayesian tool for determining stellar masses, ages, distances, and extinctions for field stars

Understanding the formation and evolution of our Galaxy requires accurate distances, ages and chemistry for large populations of field stars. Here we present several updates to our spectro-photometric distance code, that can now also be used to estimate ages, masses, and extinctions for individual stars. Given a set of measured spectro-photometric parameters, we calculate the posterior probability distribution over a given grid of stellar evolutionary models, using flexible Galactic stellar-population priors. The code (called {\tt StarHorse}) can acommodate different observational datasets, prior options, partially missing data, and the inclusion of parallax information into the estimated probabilities. We validate the code using a variety of simulated stars as well as real stars with parameters determined from asteroseismology, eclipsing binaries, and isochrone fits to star clusters. Our main goal in this validation process is to test the applicability of the code to field stars with known {\it Gaia}-like parallaxes. The typical internal precision (obtained from realistic simulations of an APOGEE+Gaia-like sample) are $\simeq 8\%$ in distance, $\simeq 20\%$ in age,$\simeq 6\$ in mass, and $\simeq 0.04$ mag in $A_V$. The median external precision (derived from comparisons with earlier work for real stars) varies with the sample used, but lies in the range of $\simeq [0,2]\%$ for distances, $\simeq [12,31]\%$ for ages, $\simeq [4,12]\%$ for masses, and $\simeq 0.07$ mag for $A_V$. We provide StarHorse distances and extinctions for the APOGEE DR14, RAVE DR5, GES DR3 and GALAH DR1 catalogues.Comment: 21 pages, 12 figures, accepte