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We investigate the structure of our Galaxy’s young stellar disc by fitting the distribution functions (DFs) of a new family to 5D Gaia data for a sample of $47\, 000$ OB stars. Tests of the fitting procedure show that the young disc’s DF would be strongly constrained by Gaia data if the distribution of Galactic dust were accurately known. The DF that best fits the real data accurately predicts the kinematics of stars at their observed locations, but it predicts the spatial distribution of stars poorly, almost certainly on account of errors in the best-available dust map. We argue that dust models could be greatly improved by modifying the dust model until the spatial distribution of stars predicted by a DF agreed with the data. The surface density of OB stars is predicted to peak at $R\simeq 5.5\, \mathrm{kpc}$, slightly outside the reported peak in the surface density of molecular gas; we suggest that the latter radius may have been underestimated through the use of poor kinematic distances. The velocity distributions predicted by the best-fitting DF for stars with measured line-of-sight velocities v∥ reveal that the outer disc is disturbed at the level of $10\, \mathrm{km\, s}^{-1}$ in agreement with earlier studies, and that the measured values of v∥ have significant contributions from the orbital velocities of binaries. Hence the outer disc is colder than it is sometimes reported to be.

A seven-parameter distribution function (DF) is fitted to $20\, 000$ RR-Lyrae stars for which only astrometric data are available. The observational data are predicted by the DF in conjunction with the gravitational potential of a self-consistent model Galaxy defined by DFs for the dark halo, the bulge, and a four-component disc. Tests of the technique developed to deal with missing line-of-sight velocities show that adding such velocities tightens constraints on the DF only slightly. The recovered model of the RR-Lyrae population confirms that the population is flattened and has a strongly radially biased velocity distribution. At large radii, its density profile tends to ρ ∼ r−4.5 but no power law provides a good fit inside the solar sphere. The model is shown to provide an excellent fit to the data for stars brighter than r = 16.5 but at certain longitudes it predicts too few faint stars at Galactocentric radii $\sim 20\, \mathrm{kpc}$, possibly signalling that the halo is not axisymmetric. The DF is used to predict the velocity distribution of BHB stars for which space velocities are available. The z components are predicted successfully but too much anisotropy in the vRvϕ plane is expected.