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 neighbourhoo d. A detailed orbital analysis within an analytical 2D rotating barred pote ntial reveals that this splitting is mainly dictated by the value of the Ha miltonian 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 wi th H. For reasonable bar strengths, the contour H = H-12 corresponding to t he effective potential at the Lagrangian points L-1/2 marks the average tra nsition from regular to chaotic motion, with the majority of orbits being c haotic 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 ba r. Test particle simulations of exponential discs in the same potential and a more realistic high-resolution 3D N-body simulation reveal how the decou pled evolution of the distribution function in the two kind of regions and the process of chaotic mixing lead to overdensities in the H greater than o r similar to H-12 chaotic part of the disc velocity distributions outside c orotation. In particular, for realistic space positions of the Sun near or slightly beyond the outer Lindblad resonance and if u is defined positive t owards the anti-centre, the eccentric quasi-periodic orbits trapped around the stable x(1)(1) orbits - i.e. the bar-aligned closed orbits which asympt otically become circular at larger distances - produce a broad u less than or similar to 0 regular arc in velocity space extending within the H > H-12 zone, whereas the corresponding u greater than or similar to 0 region appe ars as an overdensity of chaotic orbits forced to avoid that arc. This chao tic overdensity provides an original interpretation, distinct from the anti -bar elongated quasi-periodic orbit interpretation proposed by Dehnen (2000 ), for the prominent stream of high asymmetric drift and predominantly outw ard moving stars clearly emerging from the Hipparcos data. However, the mos t appropriate interpretation for this stream remains uncertain. The effects of spiral arms and of molecular clouds are also briefly discussed within t his context.