11 Discussion and concluding remarks

In the previous sections of this paper dedicated to the Little Gem we have (partially) extracted and interpreted the huge amount of physical information contained in the ESO NTT+EMMI echellograms by means of the 3-D procedure developed in Papers I to IV for all types of extended, expanding nebulae.

NGC 6818 results to be a young (3500 yr), optically thin (quasi-thin in some directions) double-shell at a distance of 1.7 kpc, projected almost equatorial-on: a tenuous, patchy spheroid ( $r\simeq 0.090$ pc) encircles an inner, dense, inhomogeneous ellipsoid ( $a/2\simeq 0.077$ pc, $a/b\simeq 1.25$, $b/c \simeq 1.15$) empty along the major axis and optically thick in a pair of equatorial moustaches.

We recall that outer attached shells have been found in both the 1D and 2D hydrodynamical models (see e.g. Mellema 1995; Corradi et al. 2000; Villaver et al. 2002), due to a D-type ionization front in the early evolution of the PN. However, all these models fail to reproduce the smooth, innermost radial density profile observed in NGC 6818 (Fig. 7); they predict an empty region (the hot bubble) and a quick density rise (the gas compression is provided by the thermal energy of the hot bubble formed by the adiabatic shock at the interaction region between the high velocity stellar wind and the material ejected during the superwind phase).

The central star of NGC 6818 is a visual binary: a faint, red companion appears at 0.09 arcsec in PA $=190\hbox{$^\circ$ }$, corresponding to a separation $\ge$150 AU. For an orbit of low eccentricity the Kepler's third law provides a period $\ge$1500 yr. Note that (by chance?) the two stellar components appear aligned with the major axis of the nebula.

Figure 12: The structure of NGC 6818 for a rotation around the East-West axis centered on the exciting star. Opaque reconstruction at $\lambda$4686 Å of He II, seen from 13 directions separated by 15 $\hbox {$^\circ $ }$. The line of view is given by ( $\theta ,\psi$), where $\theta$ is the zenith angle and $\psi$ the azimuthal angle. Each horizontal couple represents a "direct'' stereoscopic pair, and the whole figure provides 12 3-D views of the nebula in as many directions, covering a straight angle. Following Paper III: to obtain the three-dimensional vision, look at a distant object and slowly insert the figure in the field of view, always maintaining your eyes parallel. Alternatively, you can use the two small dots in the upper part of the figure as follows: approach the page till the two dots merge (they appear out of focus); then recede very slowly, always maintaining the two dots superimposed, till the image appears in focus. The upper-right image is the rebuilt-nebula seen from the Earth (West is up and North to the left, to allow the reader the stereo-view).

Figure 13: Same as Fig. 12, but for [O III] at the flux cut log E($\lambda$5007 Å) = -17.32 erg s-1 cm-3 ( $N{\rm e}\simeq 1500$ cm-3 for $T{\rm e}=12~000$ K and $\epsilon _{\rm l}=1$).

Figure 14: Same as Fig. 13, but for the [O III] flux cut log $E(\lambda 5007~{\rm \AA})=-17.75$ erg s-1 cm-3 ( $N{\rm e} \simeq 900$ cm-3 for $T{\rm e}=12~000$ K and $\epsilon _{\rm l}=1$).

Figure 15: Same as Figs. 12 to 14, but for [N II] at the flux cut log $E(\lambda 6584~{\rm \AA})=-18.20$ erg s-1 cm-3 (bright low ionization layers).

Figure 16: Same as Fig. 15, but for the [N II] flux cut $\log E(\lambda 6584~{\rm \AA})=-18.80$ erg s-1 cm-3 (faint low ionization layers).

Figure 17: Multicolor appearance of NGC 6818 ( $\rm blue=He~II$, green = [O III], red = [N II]) for a rotation around the N-S axis centered on the exciting star. The right panel, (0,0), corresponds to the re-built nebula seen from the Earth (North is up and East to the left). Same scale as Figs. 12 to 16. Recall that projection( $\theta ,\psi$) = projection ( $\theta \pm 180\hbox {$^\circ $ },\psi \pm 180\hbox {$^\circ $ }$).

Figure 18: Same as Fig. 17, but for a rotation around the E -W axis.

Despite some pioneering studies, the physical effects produced by a wide binary system on the PN ejection and shaping are still poorly known. Following Soker (1994), an orbital period comparable or longer than the mass-loss episode generating the nebula causes a density enhancement in the equatorial plane and/or spiral structures. Soker (2001) suggests that in wide binary systems (final orbital periods in the range 40 to 10⁴ yr) an outer, spherical structure is formed by the early AGB wind. Toward the end of the AGB phase, the increased mass-loss rate creates an accretion disk around the companion. If this blows jets or a collimated fast wind, two lobes appear in the inner nebula (a multi-lobed structure in the case of a precessing accretion disk). Always according to Soker (2001), a fraction of 5$\%$to 20$\%$ of all PNe originate in such wide binary systems. Curiously, the same author (Soker 1997) includes (with a high degree of confidence) NGC 6818 among the PNe resulting from the common envelope evolution with a sub-stellar companion (planet(s) and/or a brown dwarf). It is evident that the argument deserves further attention.

The Little Gem is in a peculiar evolutionary phase, i.e. at the very beginning of the recombination process. This is caused by the luminosity decline of the 0.625 $M_\odot$ central star ( $\log T_*\simeq 5.22$ K; $\log L_*/L_\odot\simeq 3.1$), which has recently exhausted the nuclear shell burning and is rapidly moving towards the white dwarf region. The stellar drop being fated to continue, NGC 6818 will become thicker and thicker, and the amount of neutral, dusty gas in the outermost layers will increase with time. The ionization front will re-grow only in some hundreds years, when the gas dilution due to the expansion will overcome the slower and slower luminosity decline.

Concerning the observational analogies between NGC 6818 (this paper) and NGC 6565 (Paper IV), in Sect. 8 we have pointed out the probable evolutive contiguity of the two nebulae. We stress here a more facet of the affair, e.g. the importance of the temporal factor: thanks to the excellent spatial and spectral resolutions achieved by the 3-D analysis applied to high quality spectra, we can no longer regard a PN as a static, uniform and un-changeable object; it is a dynamical, inhomogeneous and evolving plasma.

Ironically, this quite reverses the gap between theory and practice outlined in the Introduction: now the existing "steady'' photo-ionization models appear inadequate to interprete the observational data. A 3-D "evolving'' code is highly desired, providing for the gas reactions to the changing UV flux of the central star.

In summary: we have inferred a self-consistent picture of the Little Gem by means of ESO NTT+EMMI echellograms. Deeper observations at even higher spatial and spectral resolutions will disentangle the still unresolved problems, like the accurate $T{\rm e}$[N II] and $N{\rm e}$[S II] radial profiles (Sect. 5), the intriguing ionization structure of the cometary knot in PA $=150\hbox{$^\circ$ }$ (Sect. 4) and the possible blowing of the gas in the Northern and Southern holes (Sect. 4). Moreover, a gradual change of the [N II]/[O III] morphology is expected in the future HST imagery, due to the peculiar evolutionary phase of the nebula. Concerning the exciting star, a painstaking search in the world-wide archives (both spectroscopic and photometric), and new, deep, UV to IR spectra of the stellar system (hot central star + cold companion) are needed.

At last, the "vexata quaestio'': which are the mechanisms and the physical processes ejecting and shaping a PN like NGC 6818? In our opinion the question appears premature, and the answer is beyond the aims of the paper, given the "forest'' of proposed models (see Icke et al. 1992; Mellema 1997; Dwarkadas & Balick 1998; Garcia-Segura et al. 1999; Frank 1999; Blackman et al. 2001; Soker & Rappaport 2001; Balick & Frank 2002), and the "desert'' of carefully studied true nebulae. We are confident that new, reliable and deep insights on each object and on the whole class will come out of the comparative analysis of a representative sample of PNe and proto-PNe.

This is the final goal of our survey carried out with ESO NTT+EMMI and TNG+SARG. Indeed, the superb quality of these echellograms constitutes a powerful tool for unveiling the evolutional secrets of the PNe (as well for masking the cultural gaps of the authors).

Acknowledgements

It is a pleasure to thank Gary Ferland, Arsen Hajian, Garrelt Mellema (the referee), Detlef Schönberner and Noam Soker for their suggestions, comments, encouragements and criticisms.

This paper has been financied by the grant Cofin MM02905817 of the Italian Ministry of Education (MIUR) and partially supported by the grant ASI (Agenzia Spaziale Italiana) I/R/70/00.