6 Discussion and conclusions

We have presented the stellar kinematics of 4 galaxies hosting an active nucleus, namely NGC 1097, NGC 1365, NGC 1808 and NGC 5728, derived from ISAAC/VLT spectroscopy at 2.3 $\mu$m.

The essential results regarding the stellar kinematics of the nuclear bars are the confirmation of the decoupling of the nuclear component (with respect to the primary disc and bar), and the discovery of a central velocity dispersion drop in at least 3 targets out of 4 (being unable to derive the central kinematics for NGC 1365 due to the contribution of its Seyfert 1 nucleus). The observed central dispersion dips are not significantly affected when optimal templates are used to derive the kinematics (Paper II): it is therefore a robust result. We also observed a strong asymmetry in the stellar velocity profiles of NGC 1808, following the asymmetry in the photometry, and suggesting the existence of an m=1 mode in the central region of this galaxy. The detailed discussion of the double-bar dynamics is postponed to forthcoming papers, where it will be interpreted in terms of numerical simulations (through hydrodynamical N-body simulations and through determination of the orbital families with the Schwarzschild's method). In the following, we will discuss possible interpretations for the observed velocity dispersion drops.

The observation of a velocity dispersion drop at the centre of spiral galaxies is rare. Such a drop has been observed in NGC 6503 by Bottema (1989), where the dispersion decreases within the central 12 $^{\prime\prime}$. The phenomenon could be more widespread at smaller radii, as it would be difficult to recognize it with limited spatial resolution. In NGC 1097, the dip extends only 4 $^{\prime\prime}$ in radius, about $1\hbox{$.\!\!^{\prime\prime}$ }5$ in NGC 1808, and $1\hbox{$^{\prime\prime}$ }$ in the case of NGC 5728. The physical extent of the dispersion drop in NGC 1097 (radius of $\sim$ $4\hbox{$^{\prime\prime}$ }\equiv 325$ pc at 16.8 Mpc) is comparable to the one of NGC 6503 ($\sim$ $12\hbox{$^{\prime\prime}$ }\equiv 350$ pc at 6 Mpc), but significantly larger than the ones in NGC 5728 ($\sim$ $1\hbox{$^{\prime\prime}$ }\equiv 180$ pc at 37 Mpc) and in NGC 1808 ($\sim$ $1\hbox{$.\!\!^{\prime\prime}$ }5 \equiv 80$ pc at 10.9 Mpc).

Bottema (1993) made a compilation of the velocity dispersion profiles of a dozen spiral galaxies, and only NGC 6503 exhibits this drop. In general, the dispersion profile is well fitted by an exponential law, decreasing with a characteristic scale of twice the photometric scale-length for the disc. When the bulge is significant, the fit is compatible with a constant dispersion for the bulge. This exponential law for the disc is naturally explained for face-on galaxies, i.e. for the vertical velocity dispersion profiles. Indeed, it has been shown by van der Kruit & Searle (1981, 1982) that the galactic discs have a constant scale-height with radius. Since the surface density in the plane has an exponential distribution (Freeman 1970), the vertical equilibrium of a self-gravitating disc implies that the dispersion varies as the square root of the surface density, therefore in ${\rm e}^{{-r}\over{2h}}$, where h is the disc radial scalelength. If the ratio between the radial and vertical dispersions is maintained constant with radius, this will also imply the same exponential behaviour for the in-plane dispersion. Observations of the velocity profiles in inclined galaxies seem to support this hypothesis of a constant ratio (Bottema 1993).

Also an interpretation in terms of disc stability and self-regulation with the Toomre Q parameter has been advanced (Bottema 1993). Stars are heated by gravitational instabilities like spirals and bars. When the Q parameter is too small, instabilities set in, until the velocity dispersion has increased up to the threshold Q. The gaseous component allows a much richer feedback regulation, since it can cool down through dissipation and provoke recurrent instabilities. Young stars are formed out of the gas with relatively low velocity dispersion. It is easy to see how gravitational instabilities could lead to a constant Q value all over the stellar discs.

Bottema & Gerritsen (1997) have re-examined the problem of the dispersion drop in the centre of NGC 6503, and find no intrinsic explanation. An hypothesis is to assume a very thin and cold disc in the centre, but it is difficult to avoid heating of this disc through gravitational instabilities. They have undertaken N-body simulations to check the stability of such a disc, and found only negative results: no dispersion drop was ever observed in the simulations, whatever the initial conditions. They conclude that the only solution is to assume the existence of an independent system in the nucleus, a different population, that could have been recently accreted from outside. The accretion must be quite recent. Another explanation is the existence of two counter-rotating bars, as suggested by Friedli (1996). This hypothesis is not supported by the observed kinematics in any of the three cases studied in the present paper.

It could also be considered that fresh gas is radially falling inwards, because of gravitational torques from a bar for instance, and that this gas is piling up in a thin disc in the centre, then forming new stars with a low velocity dispersion. There should have been then a recent starburst in the centre of the galaxy. This scenario is likely for NGC 1808, as we indeed detect a young stellar component in its centre (Paper II). The case of NGC 1097 may be more difficult to assess. Kotilainen et al. (2000) did find some recent (6-7 Myr ago) star formation in the central region of NGC 1097, but well distributed along its well-known (ILR) ring-like structure. There is no evidence so far for a recent starburst inside the ring, although we can not discard this hypothesis. New self-consistent N-body simulations including star formation however support this scenario as an explanation for the observed central dispersion drop (Wozniak et al. 2001, in preparation). We still need to understand how common this phenomenon is, among galaxies with and without bars (single or double), and how it is linked to the nuclear activity.