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The major-axis density profiles of bars are known to be either exponential or 'flat'. We develop an automated non-parametric algorithm to detect flat profiles and apply it to a suite of simulations (with and without gas). We demonstrate that flat profiles are a manifestation of a bar's secular growth, producing a 'shoulder' region (an overdensity above an exponential) in its outskirts. Shoulders are not present when bars form, but develop as the bar grows. If the bar does not grow, shoulders do not form. Shoulders are often accompanied by box/peanut bulges, but develop separately from them and are independent tracers of a bar's growth. They can be observed at a wide range of viewing orientations with only their slope varying significantly with inclination. We present evidence that shoulders are produced by looped x1 orbits. Since the growth rate of the bar moderately correlates with the growth rate of the shoulder strength, these orbits are probably recently trapped. Shoulders therefore are evidence of bar growth. The properties of the shoulders do not, however, establish the age of a bar, because secondary buckling or strong spirals may destroy shoulders, and also because shoulders do not form if the bar does not grow much. In particular, our results show that an exponential profile is not necessarily an indication of a young bar. [ABSTRACT FROM AUTHOR]

Since thin disc stars are younger than thick disc stars on average, the thin disc is predicted by some models to start forming after the thick disc had formed, around 10 Gyr ago. Accordingly, no significant old thin disc population should exist. Using 6D coordinates from Gaia -DR2 and age estimates from Sanders & Das, we select ∼24 000 old stars (⁠|${\tau \gt 10\mbox{$\, \mathrm{Gyr}$}}$|⁠ , with uncertainties |$\lesssim 15{{\ \rm per\ cent}}$|⁠) within |$2\mbox{$\, \mathrm{kpc}$}$| from the Sun (full sample). A cross-match with APOGEE-DR16 (∼1000 stars) reveals comparable fractions of old chemically defined thin/thick disc stars. We show that the full sample pericentre radius (r per) distribution has three peaks, one associated with the stellar halo and the other two having contributions from the thin/thick discs. Using a high-resolution N -body + SPH simulation, we demonstrate that one peak, at |$\mbox{$r_\mathrm{per}$}\approx 7.1\mbox{$\, \mathrm{kpc}$}$|⁠ , is produced by stars from both discs that were born in the inner Galaxy and migrated to the Solar Neighbourhood. In the Solar Neighbourhood, ∼1/2 (∼1/3) of the old thin (thick) disc stars are classified as migrators. Our results suggest that thin/thick discs are affected differently by radial migration inasmuch as they have different eccentricity distributions, regardless of vertical scale heights. We interpret the existence of a significant old thin disc population as evidence for an early co-formation of thin/thick discs, arguing that clump instabilities in the early disc offer a compelling explanation for the observed trends. [ABSTRACT FROM AUTHOR]

The velocity distribution function (VDF) of dark matter (DM) haloes in A cold dark matter (ACDM) dissipationless cosmological simulations, which must be non-separable in its radial and tangential components, is still poorly known. We present the first single-parameter, non-separable, anisotropic model for the VDF in ACDM haloes, built from an isotropic q-Gaussian (Tsallis) VDF of the isotropic set of dimensionless spherical velocity components (after subtraction of streaming motions), normalized by the respective velocity dispersions. We test our VDF on 90 cluster-mass haloes of a dissipationless cosmological simulation. Beyond the virial radius, rvir, our model VDF adequately reproduces that measured in the simulated haloes, but no q-Gaussian model can adequately represent the VDF within rvir, as the speed distribution function is then flatter-topped than any q-Gaussian can allow. Nevertheless, our VDF fits significantly better the simulations than the commonly used Maxwellian (Gaussian) distribution, at virtually all radii within 5 rvir. Within 0.4 (1) rvir, the non-Gaussianity index q is (roughly) linearly related to the slope of the density profile and also to the velocity anisotropy profile. We provide a parametrization of the modulation of q with radius for both the median fits and the fit of the stacked halo. At radii of a few per cent of rvir, corresponding to the solar position in the Milky Way, our best-fitting VDF, although fitting better the simulations than the Gaussian one, overproduces significantly the fraction of high-velocity objects, indicating that one should not blindly use these q-Gaussian fits to make predictions on the direct detection rate of DM particles. [ABSTRACT FROM AUTHOR]