4 The gas kinematics

According to Papers I to IV, the expansion velocity ( $V{\rm exp}$) of the ionized gas can be derived from the analysis of the "central star pixel line'' (cspl) in the different ions. The cspl is parallel to the dispersion, selects the nebular material projected at the apparent position of the star (whose motion is purely radial) and is the same in all the frames, the slit being radially arranged. Thus, in order to improve the S/N of the faintest emissions, the nine echellograms have been combined.

The results are contained in the last column of Table 1, where the ions are put in order of increasing ionization potential (IP). Typical errors are 1.5 km s^-1 for the strongest forbidden emissions (like $\lambda$6584 Å of [N II] and $\lambda$5007 Å of [O III]) to 3.0 km s^-1 for the faintest ones (in particular: $\lambda$6300 Å of [O I], because of the knotty structure, and $\lambda$7319.87 Å of [O II], which is partially blended with $\lambda$7318.79 Å  also belonging to the O⁺ red quartet). The corresponding uncertainties for the recombination lines are: 2.5 km s^-1 for $\lambda$6563 Å (H I), and 2.0 km s^-1 for $\lambda$5876 Å (He I) and $\lambda$4686 Å (He II).

Columns 3 to 6 of Table 1 report the kinematical results from the literature. In detail:
- Wilson (1950) obtained a single Coudè spectrum of NGC 6818 (without de-rotator) at spectral resolution $R\simeq 30~000$;
- Sabbadin (1984) observed the nebula at four PA (long-slit echellograms at $R\simeq 15~000$);
- Meatheringham et al. (1988, long-slit echellograms at unspecified position, $R\simeq 26~000$) also measured the width at 10$\%$ maximum intensity of $\lambda$5007 Å  obtaining $2V{\rm exp}\rm [O~III]= 87.6$ km s^-1 (following Dopita et al. 1985, this corresponds to the largest expansion velocity of the gas);
- Hyung et al. (1999, $R\simeq 33~000$) studied four bright regions located along the apparent minor and major axes (4-5 arcsec East and West, and 9-10 arcsec North and South of the central star); their values represent lower limits to $V{\rm exp}$(various ions), due to projection effects.

In Table 1 the kinematical variety reported by the different authors is symptomatic of the difficulties connected to the analysis of the high dispersion spectra, and, according to Hyung et al. (1999), stresses the fact that only the detailed coverage at adequate spatial and spectral resolutions can provide a reliable information on the structure of a chaotic object like NGC 6818.

As cspl refers to the kinematical properties of the matter projected at the apparent position of the star, so the "zero velocity pixel column'' (zvpc), corresponding to the recession velocity of the whole nebula, gives the radial distribution of the ionized gas which is expanding perpendicularly to the line of sight (Paper IV and references therein).

The intensity peak separations, 2 $r_{\rm zvpc}$, in the different emissions at the nine PA of NGC 6818 are presented in Table 2. Both Fig. 2 and Table 2 indicate complex zvpc profiles, often multi-peaked (inner and outer shell), fast changing in direction, and variable (at a given PA) from ion to ion. The observed line structure depends on the radial matter distribution, the ionization and the intensity of the emission (the same occurs for the cspl assuming $V{\rm exp} \propto r$, as normally observed in PNe).

To be noticed: the "relative'' spectral and spatial resolutions of our echellograms, as introduced in Paper III, differ by a factor of two. The former is given by $RR=V{\rm exp}/\Delta V \simeq 6$, $\Delta V$ being the spectral resolution, and the latter by $SS=r/\Delta r \simeq 12\ (r=\rm apparent$ radius, $\Delta r=\rm seeing$). In practice this means that the spatial information of NGC 6818 is twice as detailed as the kinematical one.

In order to assemble the kinematical and the spatial results (corresponding to a single radial direction and to nine tangential directions, respectively) we must identify the PA at which $r_{\rm zvpc}\simeq r_{\rm cspl}$. The solution comes from the qualitative picture resulting from both the imaging (Sect. 2) and the spectra (Sects. 3 and 4). Let's consider for the main component of NGC 6818 the most general spatial structure, i.e. a tri-axial ellipsoid. The major axis, projected in PA $\simeq 10\hbox{$^\circ$ }$, is almost perpendicular to the line of sight, since the emissions, although inhomogeneous and distorted by irregular motions, appear un-tilted. The intermediate and the minor axes lie in PA $\simeq 100\hbox{$^\circ$ }$, and the line-tilt observed at PA $=90\hbox {$^\circ $ }$ and 110 $\hbox {$^\circ $ }$ indicates that we are misaligned with both these axes. Thus, $r_{\rm zvpc}\simeq r_{\rm cspl}$ along the apparent minor axis of the nebula, that is between PA $=90\hbox {$^\circ $ }$ and 110 $\hbox {$^\circ $ }$.

The cspl-zvpc connection for the inner and the outer shells is illustrated in Fig. 3, showing both $r_{\rm zvpc}$ (at PA $=90\hbox {$^\circ $ }$ and 110 $\hbox {$^\circ $ }$) and $V{\rm exp}$ vs. IP. For reasons of homogeneity each zvpc peak separation is normalized to the corresponding [O III] value.

 

Table 2: Peak separation in the zvpc at the nine observed PA of NGC 6818.

Ion					2 $r_{\rm zvpc}$	(arcsec)
	${\rm PA}=10\hbox{$^\circ$ }$	${\rm PA}=30\hbox{$^\circ$ }$	${\rm PA}=50\hbox{$^\circ$ }$	${\rm PA}=70\hbox{$^\circ$ }$	${\rm PA}=90\hbox{$^\circ$ }$	${\rm PA}=110\hbox{$^\circ$ }$	${\rm PA}=130\hbox{$^\circ$ }$	${\rm PA}=150\hbox{$^\circ$ }$	${\rm PA}=170\hbox{$^\circ$ }$
[O I]	23.5:	23.0:	22.0:	--; 22.5:	--; 22.5:	--; 22.5:	--; 22.0:	--; 22.5:	22.3:
[S II]	23.5	22.4	22.0	15.6; 22.4	--; 22.3:	15.8; 22.5	14.0; 22.0	--; 22.4	22.6
[O II]	23.1:	22.8:	21.7:	--; 22.2:	--; 21.7:	--; 22.5:	--; 22.0:	--; 22.0:	21.8:
HI	19.2:	16.7:	16.4:	14.0:; 21.0:	12.8:; 19.5:	13.0:; 21.0:	13.1:; 20.5:	14.7:; 21.0:	20.2:
[N II]	23.5	22.4	22.0	15.8; 22.4	--; 22.2	15.6; 22.4	14.5; 22.4	16.0; 22.4	21.8
[S III]	21.3	20.5	18.4:	15.3; --	15.5:; --	14.5:; --	13.4; 21.3:	15.0; 20.5:	19.9:
He I	22.2	20.5	18.1	15.7; 22.2	14.5; 20.6	14.5:; 21.0	13.2:; 21.3	--; 19.2:	20.8
[Ar III]	22.5	19.8	17.6	15.4; 22.2	14.6; 20.5	14.7; 21.0	13.7; 21.4	15.4; 21.9	21.1
[O III]	20.7	20.0	18.5	15.3; 21.2	15.0; 20.2	15.0; 21.0	13.8; 20.0	15.9; 21.0	20.4
[Ar IV]	17.9:	15.3	13.1:	12.3; --	11.0; --	11.1; --	12.0; --	12.7; --	16.4
[Ne III]	21.7:	20.9:	20.0:	15.3:; --	15.2:; 21.0:	14.5; 21.0	14.3; 20.4	--; 21.3:	21.6
He II	19.0	15.2	12.3	11.8; --	11.0; --	11.0; --	12.1; --	12.6; --	16.6
[Ar V]	17.7:	13.3:	10.6:	9.8; --	8.0:; --	8.5; --	9.9; --	10.9; --	13.7

Figure 3: Expansion velocity in the cspl (left) and peak separation in the zvpc for the inner and the outer shells of NGC 6818 at PA $=90\hbox {$^\circ $ }$ and 110 $\hbox {$^\circ $ }$ (right) vs. IP. Each zvpc peak separation is normalized to the corresponding [O III] value. The ions in peculiar positions are marked.

NGC 6818 is characterized by a large stratification of the radiation and of the kinematics, in agreement with the Wilson's (1950) law. However, $V{\rm exp}$ and $r_{\rm zvpc}$ of [Ar IV] and [Ne III] considerably deviate from the sequence defined by the other ionic species. This behavior, also noticed in NGC 6565 (Paper IV), is typical of a PN powered by a high temperature central star (for details, see the above-mentioned reference and Sect. 9). Instead, the anomalous position of H I in Fig. 3 is the obvious consequence of the mono-electron atomic structure of hydrogen.

The $r_{\rm zvpc}$ vs. IP relation being the same at all the observed PA (from Table 2), we can assess that in NGC 6818 the expansion velocity is proportional to the distance from the central star through the relation:

$$V{\rm exp}~({\rm km~s}^{-1}) = 3.5 (\pm0.3)\times r'' .$$ (1)

Weedman (1968) has derived $V{\rm exp}({\rm km~s}^{-1}) =5.9\times(r''-0.8)$, which is almost twice as steep as Eq. (1). The Weedman's expansion law appears questionable, since it is based on the [O III] profile in a single, quite under-exposed Coudè spectrum ( $R\simeq 60~000$) taken along the apparent major axis (PA $\simeq 10\hbox{$^\circ$ }$). Weedman noticed that $\lambda$5007 Å, although distorted by irregular motions, is un-tilted, and assumed "a priori'' the following model: a prolate spheroid with a=17.3 arcsec and a/b=1.5, seen perpendicular to the major axis.

Therefore in the following we will consider Eq. (1) as representative of the whole nebular kinematics.

All this is synthesized in Fig. 4, showing the position-velocity (P-V) maps, i.e. the complete radial velocity field at the nine observed PA. They are relative to the systemic heliocentric velocity of the nebula, $Vr_{\odot}=-14.5(\pm 1.0$) km s^-1, corresponding to $V_{\rm LSR}=-1.7(\pm 1.0$) km s^-1, and are scaled according to Eq. (1). In other words, they reproduce the tomographic maps in the nebular slices covered by the slit. We have selected He II, [O III] and [N II] as representative of the high, medium and low ionization regions, respectively.

These multicolor P-V maps highlight the large stratification of the radiation and the chaotic nebular structure. NGC 6818 is optically thin in most directions. The low excitation [N II] emission is associated to the presence of some inner and dense layer (see the moustaches, for example). The outermost, faint [N II] spikes detected in PA $=10\hbox {$^\circ $ }$, 90 $\hbox {$^\circ $ }$, 150 $\hbox {$^\circ $ }$ and 170 $\hbox {$^\circ $ }$ belong to the external shell.

The existence of a prominent hole to the North and of a smaller one to the South, as suggested by Rubin et al. (1998), is confirmed. The southern cavity is less evident in Fig. 4, being only grazed by our spectra at PA $=170\hbox{$^\circ$ }$ and 10 $\hbox {$^\circ $ }$. Further hollows are present (like at PA $=70\hbox{$^\circ$ }$ and 90 $\hbox {$^\circ $ }$, in the approaching gas at West of the central star position).

The radial ionization structure of the S-SE edge at PA $=150\hbox{$^\circ$ }$, corresponding to the region of the "cometary knot'' visible in Fig. 1, is puzzling: [O III] is lacking, whereas He II and [N II] are intense in the inner and the outer layers, respectively.

In summary: although some spectral features of the northern and southern holes can be tentatively interpreted in terms of ionized gas moderately accelerated by some blowing-up agent (as suggested by Rubin et al. 1998), the linear expansion law here adopted represents a valid approximation of the overall nebular kinematics.