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

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8. Discussion

A general statement can be made about the evolution of bars. In general as a bar grows, its strength increases until a critical value is reached beyond which the Lagrangian points are all fully unstable in the galaxy plane. While the instability around [FORMULA] may concern a relatively modest fraction of the corotation circle, because the rest may be trapped by stable banana orbits circling around the stable [FORMULA], this possibility disappears completely when the points [FORMULA] become complex unstable. Phase space is then largely composed of unstable or chaotic orbits: a general orbital instability must be expected around the corotation circle, including the amplification of the oscillations transverse to the galactic plane.

When corotation is fully unstable, one expects a fast, mostly radial diffusion of its stars toward several times the corotation radius. But the z -amplitude increases almost linearly with R, up to several kpc at [FORMULA] from the centre. This is clearly a new channel for lifting matter out of the galactic plane beside the vertical Inner Lindblad resonances able to feed a bulge as described in P84, Combes et al. (1990) and Pfenniger & Friedli (1991). The average orbital density of diffusing chaotic orbits outside corotation is exponentially decreasing in R, as shown in P85b. This is interesting because a stellar bar is a well known mechanism to produce the double exponential distribution observed in typical stellar disks (Hohl 1971; PF91; Courteau et al. 1996), the transition from the inner steep exponential to the outer shallower one being just fixed by the corotation radius.

In P90 we had shown that self-consistent N -body bars tend to reach the marginal stability state around [FORMULA], as if the whole system self-regulates its degree of instability around corotation to a minimum. So the stability of the Lagrangian points seem to play a global role in barred galaxies.

Schematically, the evolution of barred galaxies can be described by the following stages. First, an axisymmetric disk becomes bar unstable for various reasons, such as a disk kinematical cooling by star formation (Carlberg & Sellwood 1984), or by a tidal interaction (Noguchi 1988, 1996). The bar growth becomes then rapidly non-linear and proceeds with a time-scale of order of the rotation period. When the bar becomes strong enough, the Lagrangian points [FORMULA] reach the threshold of complex instability (P90) and matter around them is evacuated away, diffusing by about [FORMULA] around the galactic plane and several [FORMULA] in the radial direction in a few rotational periods. This latter effect is suggested by observations: several barred galaxies do appear particularly dark in the region corresponding to the Lagrangian points [FORMULA]. Examples are NGC 3504, or NGC 4394 in the Hubble Atlas (Sandage 1961). These holes in the stellar distributions can only be repopulated by fast moving stars able to cross the corotation circle. Therefore the average stellar kinetic "temperature" must rise, moderating or even stopping the bar growth. Eventually a marginal stable state of the Lagrangian points [FORMULA] follows.

As discussed previously (e.g., Pfenniger & Norman 1990; Hasan, Pfenniger & Norman 1993), secularly gas or infalling satellite accumulating within the ILR are able to dissolve completely the bar, which is another process determining the subsequent evolution of barred galaxies.

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© European Southern Observatory (ESO) 1998

Online publication: June 2, 1998