The GALAH+ survey: Third data release

The recent exponential increase in spectroscopic, astrometric & photometric data has highlighted the scientific opportunities afforded by obtaining an ensemble of chemical element abundances for stars with precision distance & orbit measurements. With this third data release of the Galactic Archaeology with HERMES (GALAH) survey, we publish 678 423 spectra for 588 571 mostly nearby stars (81.2% of stars lie within 2 kpc), observed with the HERMES spectrograph at the Anglo-Australian Telescope. This release (referred to as GALAH+ DR3) includes all observations from GALAH Phase 1 (bright, main, & faint survey, 70%), the K2-HERMES (17%) & TESS-HERMES (5%) surveys, as well as additional GALAH-related projects (8%) including the bulge & observations of more than 75 stellar clusters. We derive stellar parameters $T_\text{eff}$, $\log g$, [Fe/H], $v_\text{mic}$, $v_\text{broad}$ & $v_\text{rad}$ using Spectroscopy Made Easy (SME) & 1D MARCS model atmospheres. We also derive abundance ratios [X/Fe] for 30 elements (11 of which based on non-LTE computations), that cover 5 nucleosynthetic pathways: Li, C, O, Na, Mg, Al, Si, K, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Zn, Rb, Sr, Y, Zr, Mo, Ru, Ba, La, Ce, Nd, Sm, Eu. We describe our validations for accuracy & precision, flagging of peculiar stars or measurements & stress that all users should take these flags into account. Our catalogue comprises 65% dwarfs, 34% giants & 1% other/unclassified stars. Based on unflagged abundances & age, we find 62.5% young low-alpha stars, 8.8% young high-alpha stars, 26.9% old stars & 1.8% stars with [Fe/H] < -1. Based on kinematics, we find 4% halo stars. Value-Added-Catalogs for stellar ages, dynamics, $v_\text{rad}$ & binary systems accompany this data release. Together they provide a high-dimensional data set to study the chemodynamic evolution of the local Milky Way, as we showcase with a few chemodynamic analyses.