7 The nebular distance, mass and age

The only individual distance reported in the literature (based on rough parameters for the star and the nebula) goes back to Gurzadyan (1970), who derived an indicative value of 2.2 kpc from the observed to expected size of the He⁺⁺ zone.

 

Table 4: Statistical distances of NGC 6818.

Author	Distance (kpc)	Method
O'Dell (1962)	1.7	Shklovsky (1956), i.e. ionized mass = const.
Cahn & Kaler (1971)	1.82-2.38	Shklovsky
Cudworth (1974)	1.95	proper motions
Milne & Aller (1975)	2.07	Shklovsky (radio)
Cahn (1976)	2.2	Shklovsky
Acker (1978)	1.6	published statistical distance scales re-calibrated with individual distances
Maciel & Pottasch (1980)	1.46	ionized mass-radius relation
Daub (1982)	1.29	ionized mass-radio surface brightness relation
Phillips & Pottasch (1984)	4.45	observed vs. predicted radio fluxes
Maciel (1984)	1.5	ionized mass-radius relation
Amnuel et al. (1984)	0.95	radio surface brightness-radius relation
Kingsburgh et al. (1992)	2.46	Shklovsky
Cahn et al. (1992)	1.87	ionized mass-surface brightness relation
van de Steene & Zijlstra (1995)	1.58	radio continuum surface brightness temperature-radius relation
Zhang (1995)	1.68	ionized mass-radius and radio cont. surface bright. temp.-radius relations
Gorny et al. (1997)	2.1	theoretical evolutionary tracks vs. observed nebular and stellar parameters
Mal'kov (1997)	2.5	theoretical evolutionary age vs. observed dynamical age
Cazetta & Maciel (2000)	>2.9	Peimbert & Torres-Peimbert (1983) $\rm class\getsto stellar$ $\rm mass\getsto stellar$ gravity and
		temperature$\getsto$stellar luminosity
Bensby & Lundström (2001)	2.23	ionized mass-radius relation
Phillips (2002)	0.63	radio surface brightness-radius relation

As compensation the nebula is present in a good 20 catalogues of statistical distances (listed in Table 4). They provide the following mean values:

<D>(Shklovsky)$\simeq$2.0($\pm$0.4) kpc;

<D>(ionized mass-radius relation)$\simeq$1.7($\pm$0.4) kpc;

<D>(surface brightness-radius relation)$\simeq$1.3($\pm$0.4) kpc;

<D>(other methods)$\simeq$2.8($\pm$1.0) kpc.

To be noticed that the overall properties inferred in the previous sections (in synthesis: NGC 6818 is an optically thin, almost thin in some directions, quite "normal'' PN) suggest that <D>(Shklovsky), <D>(ionized mass-radius relation) and <D>(surface brightness-radius relation) are, at least grossly, reliable.

In order to derive the dynamical parallax we have analysed the first and second epoch (1998.30 and 2000.45, respectively) HST images of NGC 6818, searching for the angular expansion of the ionized gas; when combined with Eq. (1), it provides a reliable nebular distance (Reed et al. 1999; Palen et al. 2002). Since the target is at the centre of the planetary camera (PC) chip in the 2000.45 images, whereas it is quite off-axis in the 1998.30 ones, the correction for optical camera distortions was performed with the IRAF/STSDAS task "drizzle'' (see Fruchter & Hook 2002) using the Trauger coefficients.

No apparent shift is obtained from the couples of [O III] and [N II] frames.

According to Reed et al. (1999), we infer that the angular expansion of the gas is <1.2$\times$10^-2 arcsec, that is $\frac{{\rm d}\theta}{{\rm d}t} <5.5\times 10^{-3}$ arcsec yr^-1. Since $D({\rm pc})=0.211[V{\rm exp}$ (km s^-1)/ $\frac{{\rm d}\theta}{{\rm d}t}$ (arcsec yr^-1)], we derive $D\rm (NGC~6818)> 1300$ pc.

We have attempted a better quantification of D(NGC 6818) through the interstellar absorption-distance relation (Lutz 1973; Gathier et al. 1986; Saurer 1995) given by the field stars with accurate m_V, m_B, spectral type and luminosity class. They were selected using the SIMBAD facilities of the CDS, Strasbourg Astronomical Observatory. The resulting $A_{\rm V}$-distance law is presented in Fig. 8, where the small cluster of data at the right edge refers to the super-giant stars of NGC 6822 (Barnard's galaxy), a nearby Ir galaxy projected at about 40 arcmin S-SE of our nebula.

Figure 8 indicates that:
- the galactic absorption rapidly changes in direction (note the spread of the low-weight points). This is confirmed by the inspection of both the ESO/SERC and the Palomar Schmidt surveys, showing a variable background crossed by a series of extended, broad and faint emitting filaments;
- close to the nebula direction (high-weight data), $A_{\rm V}$ quickly increases up to $D\simeq 1.0$-1.5 kpc, and later is constant (as expected of the large galactic latitude of the field, $\vert b II\vert\simeq 18\hbox{$^\circ$ }$). Note that for the super-giant stars of the nearby galaxy NGC 6822 we have $A_{\rm V}{\rm (tot)}=A_{\rm V}$(galactic) $+ A_{\rm V}$(NGC 6822), where $A_{\rm V}$(NGC 6822) changes from star to star, and $A_{\rm V}$(galactic) = const. For $A_{\rm V}$(NGC 6822) = 0 we infer $A_{\rm V}{\rm (galactic)}\simeq 0.80(\pm 0.1$), in excellent agreement with the literature reports (see Gallart et al. 1996; Bianchi et al. 2001);

- from $A_{\rm V}=2.18\times c({\rm H}\beta$) (Acker 1978) we have $A_{\rm V}$ $({\rm NGC}~6818)=0.81(\pm 0.06$) and D(NGC 6818) $\ge$1.5 kpc.
Although in Fig. 8 all the solutions for $D{\rm (NGC~6818)}\ge 1.5$ kpc appear legitimate, both the large galactic latitude of the nebula ( $\vert b II\vert\simeq 18\hbox{$^\circ$ }$) and the low radial velocity relative to the Local Standard of Rest, $V_{\rm LSR}=-1.7$ km s^-1 (Sect. 4), decidedly favour the lowest values, i.e. $1.5~{\rm kpc} \le D({\rm NGC}~6818)\le 2.0$ kpc (in agreement with the information previously obtained from the statistical distance scales).

In the following we will adopt $D({\rm NGC}~6818)= 1.7(^{+0.3}_{-0.2}$) kpc, corresponding to a distance from the galactic plane $\vert z\vert\simeq$ 0.5 kpc.

The local filling factor in the nebula is $\epsilon_{\rm l}\simeq 0.5$. The ionized mass (obtained in different ways: from the H$\beta$ flux, the radio flux and the observed $N{\rm e}$ distribution; Aller 1984; Pottasch 1984; Osterbrock 1989 and Paper IV) results to be  $M_{\rm ion}\simeq 0.13(\pm 0.03)~M_\odot$, and the kinematical age $t_{\rm kin}\propto r/V{\rm exp} \simeq 2300(\pm 300$) yr.

$M_{\rm ion}$ is close to the total nebular mass, NGC 6818 being an optically thin (almost thin in some directions) PN, whereas  $t_{\rm kin}$ represents a lower limit to the actual age, $t_{\rm NGC~6818}$, since the dynamical history of the gas is unknown. We can obtain a reliable estimate of $t_{\rm NGC~6818}$ by assuming a nebular ejection at $V{\rm exp}$ $_{\rm superwind}$ $<V{\rm exp}$ $_{\rm NGC~6818}$, followed by a constant acceleration up to $V{\rm exp}$ $_{\rm NGC~6818}$. $V{\rm exp}$ $_{\rm superwind}$ comes from the OH/IR sources, commonly regarded as the PNe precursors (Habing 1996). For $V{\rm exp}$ $_{\rm superwind} =15(\pm 5)$ km s^-1 (Chengalur et al. 1993; David et al. 1993; Sjouwerman et al. 1998) we derive $t_{\rm NGC~6818} = 3500(\pm 400$) yr, i.e. our nebula is rather young.