Aims. We investigate the growth of bar instability in stellar disks embedded in a dark matter halo evolving in a fully consistent cosmological framework. Methods. We perform seven cosmological simulations to emphasise the role of both the disk-to-halo mass ratio and of the Toomre parameter, Q, on the evolution of the disk.We also compare our fully cosmological cases with corresponding isolated simulations where the same halo is extracted from the cosmological scenario and evolved in physical coordinates. Results. A long living bar, lasting about 10 Gyr, appears in all our simulations. In particular, disks expected to be stable according to classical criteria form weak bars. We argue that such a result is due to the dynamical properties of our cosmological halo which is far from stability and isotropy, typical of the classical halos used in the literature; it is dynamically active, has substructures and undergoes infall. Conclusions. At least for mild self-gravitating disks, the study of the bar instability using isolated isotropic halos in gravitational equilibrium can lead to misleading results. Furthermore, the cosmological framework is needed to quantitatively investigate such an instability.

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Context. The thick disk rotation-metallicity correlation, ∂V φ /∂[Fe/H] = 40 ÷ 50 km s −1 dex −1 represents an important signature of the formation processes of the galactic disk. Aims. We use nondissipative numerical simulations to follow the evolution of a Milky Way (MW)-like disk to verify if secular dynamical processes can account for this correlation in the old thick disk stellar population. Methods. We followed the evolution of an ancient disk population represented by 10 million particles whose chemical abundances were assigned by assuming a cosmologically plausible radial metallicity gradient with lower metallicity in the inner regions, as expected for the 10-Gyr-old MW. The two cases of a disk with and without a bar were simulated to compare the evolution of their kinematics and radial chemical properties.Results. Migration processes act in both cases and appear to be enhanced in the presence of a central bar. Essentially, inner disk stars move towards the outer regions and populate layers located at higher |z|. In the case of an evolved barred disk, a rotation-metallicity correlation appears, which well resembles the behaviour observed in our Galaxy at a galactocentric distance between 8 kpc and 10 kpc. In particular, we measure a correlation of ∂V φ /∂ [Fe/H] 60 km s −1 dex −1 for particles at 1.5 kpc < |z| < 2.0 kpc that persists up to 6 Gyr. Conclusions. Our pure N-body models can account for the V φ vs. [Fe/H] correlation observed in the thick disk of our Galaxy, suggesting that processes internal to the disk such as heating and radial migration play a role in the formation of this old stellar component. In this scenario, the positive rotation-metallicity correlation of the old thick disk population would represent the relic signature of an ancient inverse chemical (radial) gradient in the inner Galaxy, which resulted from accretion of primordial gas.

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