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We explore the fundamental relations governing the radial and vertical velocity dispersions of stars in the Milky Way, from combined studies of complementary surveys including GALAH, LAMOST, APOGEE, the NASA Kepler and K2 missions, and Gaia DR2. We find that different stellar samples, even though they target different tracer populations and employ a variety of age estimation techniques, follow the same set of fundamental relations. We provide the clearest evidence to date that, in addition to the well-known dependence on stellar age, the velocity dispersions of stars depend on orbital angular momentum Lz, metallicity, and height above the plane |z|, and are well described by a multiplicatively separable functional form. The dispersions have a power-law dependence on age with exponents of 0.441 ± 0.007 and 0.251 ± 0.006 for σz and σR, respectively, and the power law is valid even for the oldest stars. For the solar neighbourhood stars, the apparent break in the power law for older stars, as seen in previous studies, is due to the anticorrelation of Lz with age. The dispersions decrease with increasing Lz until we reach the Sun's orbital angular momentum, after which σz increases (implying flaring in the outer disc) while σR flattens. For a given age, the dispersions increase with decreasing metallicity, suggesting that the dispersions increase with birth radius. The dispersions also increase linearly with |z|. The same set of relations that work in the solar neighbourhood also work for stars between 3 < R/kpc < 20. Finally, the high-[α/Fe] stars follow the same relations as the low-[α/Fe] stars.

Asteroseismology is a promising tool to study Galactic structure and evolution because it can probe the ages of stars. Earlier attempts comparing seismic data from the Kepler satellite with predictions from Galaxy models found that the models predicted more low-mass stars compared to the observed distribution of masses. It was unclear if the mismatch was due to inaccuracies in the Galactic models, or the unknown aspects of the selection function of the stars. Using new data from the K2 mission, which has a well-defined selection function, we find that an old metal-poor thick disc, as used in previous Galactic models, is incompatible with the asteroseismic information. We use an importance-sampling framework, which takes the selection function into account, to fit for the metallicities of a population synthesis model using spectroscopic data. We show that spectroscopic measurements of [Fe/H] and [α/Fe] elemental abundances from the GALAH survey indicate a mean metallicity of log (Z/Z☉) = −0.16 for the thick disc. Here Z is the effective solar-scaled metallicity, which is a function of [Fe/H] and [α/Fe]. With the revised disc metallicities, for the first time, the theoretically predicted distribution of seismic masses show excellent agreement with the observed distribution of masses. This indirectly verifies that the asteroseismic mass scaling relation is good to within five per cent. Assuming the asteroseismic scaling relations are correct, we estimate the mean age of the thick disc to be about 10 Gyr, in agreement with the traditional idea of an old α-enhanced thick disc.

The Galactic Archaeology with HERMES (GALAH) survey is a large-scale stellar spectroscopic survey of theMilkyWay, designed to deliver complementary chemical information to a large number of stars covered by the Gaia mission. We present the GALAH second public data release (GALAH DR2) containing 342 682 stars. For these stars, the GALAH collaboration provides stellar parameters and abundances for up to 23 elements to the community. Here we present the target selection, observation, data reduction, and detailed explanation of how the spectra were analysed to estimate stellar parameters and element abundances. For the stellar analysis, we have used a multistep approach. We use the physics-driven spectrum synthesis of Spectroscopy Made Easy (SME) to derive stellar labels (Teff, logg, [Fe/H], [X/Fe], vmic, vsin i, AKS) for a representative training set of stars. This information is then propagated to the whole sample with the data-driven method of The Cannon. Special care has been exercised in the spectral synthesis to only consider spectral lines that have reliable atomic input data and are little affected by blending lines. Departures from local thermodynamic equilibrium (LTE) are considered for several key elements, including Li, O, Na, Mg, Al, Si, and Fe, using 1D MARCS stellar atmosphere models. Validation tests including repeat observations, Gaia benchmark stars, open and globular clusters, and K2 asteroseismic targets lend confidence to our methods and results. Combining the GALAH DR2 catalogue with the kinematic information from Gaia will enable a wide range of Galactic Archaeology studies, with unprecedented detail, dimensionality, and scope.