Order and chaos in the local disc stellar kinematics induced by the Galactic bar

The Galactic bar causes a characteristic splitting of the disc phase space into regular and chaotic orbit regions which is shown to play an important role in shaping the stellar velocity distribution in the Solar neighbourhood. A detailed orbital analysis within an analytical 2D rotating barred potential reveals that this splitting is mainly dictated by the value of the Hamiltonian H and the bar induced resonances. In the $u-v$ velocity plane at fixed space position, the contours of constant H are circles centred on the local solid rotation velocity of the bar frame and of radius increasing with H. For reasonable bar strengths, the contour $H=H_{12}$ corresponding to the effective potential at the Lagrangian points $L_{1/2}$ marks the average transition from regular to chaotic motion, with the majority of orbits being chaotic at $H> H_{12}$. On top of this, the resonances generate an alternation of regular and chaotic orbit arcs opened towards lower angular momentum and asymmetric in u for space positions away from the principal axes of the bar. Test particle simulations of exponential discs in the same potential and a more realistic high-resolution 3D N-body simulation reveal how the decoupled evolution of the distribution function in the two kind of regions and the process of chaotic mixing lead to overdensities in the $H\ga H_{12}$ chaotic part of the disc velocity distributions outside corotation. In particular, for realistic space positions of the Sun near or slightly beyond the outer Lindblad resonance and if u is defined positive towards the anti-centre, the eccentric quasi-periodic orbits trapped around the stable $x_1(1)$ orbits -i.e. the bar-aligned closed orbits which asymptotically become circular at larger distances -produce a broad $u\la 0$ regular arc in velocity space extending within the $H> H_{12}$ zone, whereas the corresponding $u\ga 0$ region appears as an overdensity of chaotic orbits forced to avoid that arc. This chaotic overdensity provides an original interpretation, distinct from the anti-bar elongated quasi-periodic orbit interpretation proposed by Dehnen ([CITE]), for the prominent stream of high asymmetric drift and predominantly outward moving stars clearly emerging from the Hipparcos data. However, the most appropriate interpretation for this stream remains uncertain. The effects of spiral arms and of molecular clouds are also briefly discussed within this context