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Astron. Astrophys. 334, 829-839 (1998)

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9. Conclusions

The 3D dynamical structure of phase space in barred galaxies around the Lagrangian points has been investigated. For parameters close to the ones suited to realistic barred galaxies the Lagrangian points [FORMULA] and [FORMULA] are not far from a marginal stability state. Beyond a critical bar strength these points become complex unstable, which means that the whole corotation circle become unstable and instability is not restricted to a particular plane but is three-dimensional, though the approximate third-integral still constrains diffusion in z outside the corotation circle. Thus, stellar diffusion, and even for practical purpose escape, are particularly important in the radial direction.

Therefore stars in the corotation region can not only make wide excursions within the plane, but also substantial ones out of the plane. This important conclusion can be reached after the orbit analysis around [FORMULA] because the associated Hopf-like bifurcation is of inverse type. Besides the already well-discussed vertical instabilities existing in bars, particularly the 2/1 vertical Inner Lindblad Resonance able to induce the formation of peanut-shaped bulges (e.g., Combes et al. 1990), this full instability provides an interesting channel for lifting matter into an extended thick disk made of stars born in the few inner kpc of a galaxy. Because this instability occurs at corotation, the diffusion of stars further out is much easier than in the case of the Inner Lindblad Resonance, because chaotic motion is no longer bounded by the zero-velocity surface linked to the Jacobi integral.

Several barred galaxies do appear to be particularly dark in the region corresponding to the Lagrangian points [FORMULA]. Besides the convenience to mark the location of corotation, these mass deficit regions suggest a secular evolution of these galaxies during which the strength of the bar increases up to the point that the Lagrangian point [FORMULA] become complex-unstable, clearing for a while the region around them. Unless fully destabilized the system should react collectively by slowing down and even stopping the growth of the bar. In N -body experiments without dissipation (P90) it has been indeed found that the asymptotic state of pure stellar bars is to tend to keep the [FORMULA] points marginally stable.

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998