... practice

Based on observations made with ESO Telescopes at the La Silla Observatories (program ID 65.I-0524), and TNG (Telescopio Nazionale Galileo) at La Palma, Canary Islands (program AOT10-10). We extensively apply the photo-ionization code CLOUDY, developed at the Institute of Astronomy of the Cambridge University (Ferland et al. 1998).

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...

Movies are available in electronic form at http://www.edpsciences.org

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... PNe

We overlook other possible excitation mechanisms, namely, (a) Bowen resonance fluorescence (a photon emitted by one ion is absorbed by another and degraded in a cascade of emission lines via intermediate levels); (b) starlight and/or nebular continuum fluorescence (a strong local UV radiation field pumps an ion into an excited state); (c) dielectronic recombinations (a core electron is excited by capture of a free electron); and (d) charge-exchange reactions (an electron is exchanged during the collision of a ion with H or He, the most abundant species). Their possible role in a specific application (i.e. abundance dichotomy from optical recombination and collisionally excited lines) will be introduced in Sect. 5.

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... 4.1)

The twelve spectral images in Fig. 1 refer to NGC 6741 at $\rm PA=15\hbox{$^\circ$ }$ (ESO NTT+EMMI).

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... form

In this and the following equations, the proportionality constant is [4$\pi$(206265)$^3\times$A(km s^-1 arcsec^-1)]/[ $1.15\times \delta$V(km s $^{-1})\times s$(arcsec$)\times w$(arcsec $) \times{\it D}$(cm)] for ${\it V}_{\rm exp}=A\times R''$ and[4$\pi$(206265) $^3\times{\it V}_{\rm exp}(\lambda)$(km s^-1]/[ $1.15\times \delta$V(km s $^{-1})\times R(\lambda$)(arcsec $)\times s($arcsec$)\times w$(arcsec $) \times{\it D}$(cm)] for ${\it V}_{\rm exp}\not= A \times R\hbox{$^{\prime\prime}$ }$.

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... eV)

Note, however, that ionic species higher than Ar⁴⁺ are expected in the innermost layers of a PN powered by a central star with $T_*\ge100~000$ K. In this case, $\lambda$7005 $\rm\AA\/$ and/or $\lambda$6435 $\rm\AA\/$ of Ar⁴⁺ become poor density diagnostics for the internal, highest-excitation regions ($\lambda$3425 $\rm\AA\/$ of [Ne V], IP range 97 to 126 eV, should be preferable).

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... zvpc

Moreover, (a) the combination of Eqs. (15) and (17) gives the radial ionization structure of each element (more details are in Sect. 4.1) and (b) the accurate He/O and Ar/O radial chemical profiles can be obtained by assembling Eqs. (18)-(20), (23) and (27); we will go more deeply into this topic in a future, dedicated paper.

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... 3

Although the adopted matter distribution of the model nebula is open to criticism (it is arbitrary, schematic, static, etc.), we underline that the choice of more sophisticated and/or time-dependent density profiles does not modify the general results illustrated here and in the following sub-sections.

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... flux

Only "relative'' fluxes are considered here, since the observations have been secured in non-photometric sky conditions. Note, however, that an absolute calibration can be obtained by means of the H$\beta$, H$\alpha$, and [O III] HST imagery of NGC 6572; in fact, the absolute flux within the $0.40\hbox{$^{\prime\prime}$ }\times26.7\hbox{$^{\prime\prime}$ }$ rectangle of HST image intercepted by the spectrograph slit matches the integrated flux of the corresponding spectral emission.

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... report

Weedman obtained ${\it V}_{\rm exp}$(km s $^{-1})=3.4\times R\hbox{$^{\prime\prime}$ }$ assuming $R_{\rm zvpc}$ (apparent major axis) $\simeq R_{\rm cspl}$.

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... nebula

According to Fig. 1, the zvpc of a true-PN crosses the entire object and provides two independent density profiles in opposite directions (in Fig. 3 the central star position is at r=0.0 arcsec and the slit orientation is indicated in the top panel). Of course, the two zvpc gas distributions should coincide for a spherically symmetric nebula (as in the case of the standard model-PN adopted in this paper; that is why Fig. 2 and the next figures concerning the model-PN show the radial density profile in a single direction).

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... I(O⁺⁺, 5007)>0

Please note that the radial ionization structure given by Eq. (32) is independent of the nebular spatio-kinematics (i.e. expansion velocity field and matter distribution), since both the numerator and denumerator refer to the same pixel of the zvpc.

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... further

Points (a) and (c) explain the central hollow normally observed in the H$\alpha$, [O III] and [N II] imagery of evolved PNe, like NGC 6720 (Ring Nebula) and NGC 7293 (Helix Nebula).

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... scenario

Note, however, that the collisional de-excitation of forbidden lines is important for a typical, very-high density ( ${\it N}_{\rm e}\ge 3\times10^4$ cm^-3) proto-PN. The collisional de-excitation rate is

$$q_{\rm de-ex}(\lambda)=8.63 \times 10^{-6}\left(\frac{\Omega}{\omega_1}\right) {\it T}_{\rm e}^{-0.5},$$ (33)

thus, in the high-density case, Eq. (6) becomes

$$q_{\rm eff}(\lambda)=8.63 \times 10^{-6}\left(\frac{\Omega}{\... ...^{-0.5} \times ({\rm e}^\frac{-\Delta E}{k{\it T}_{\rm e}}-1).$$ (34)

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... TNG+SARG

The spectra of BD+30 $\hbox {$^\circ $ }$3639 and NGC 6572 have been obtained in the same (non-photometric) night and with the same instrumental configuration. Thus, the observational information presented in Sect. 4.1 also apply to the echellograms of BD+30 $\hbox {$^\circ $ }$3639.

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... arcsec

In other words, BD+30 $\hbox {$^\circ $ }$3639 is a rare case of PN exhibiting the "U''-shaped expansion profile mentioned in Sect. 1.

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... fluxes

Please note the affinity between the zvpc given by high-resolution slit spectroscopy and the rest frame of imaging Fabry-Perotinterferometry.

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... star

For a deep analysis of the FLIERs, ansae and caps of NGC 7009, see Sabbadin et al. (2004).

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