4 Shock excitation of the nebular spectra

Given recent evidence for high velocity winds in planetary nebulae (e.g. Cuesta et al. 1995), and for the formation of jets and highly collimated flows at various stages of PN evolution (cf. references cited in Sect. 1), it has become apparent that many planetary nebulae are likely to display a range of shock related activity. Thus, for instance, Bohigas (1994), Goodrich (1991), Trammell & Goodrich (1996) and Lopez et al. (1995) have noted spectral signatures consistent with shocks extending throughout large fractions of the nebular ionised regimes, whilst Cuesta et al. (1993, 1995) have found that the spatio- kinematic structures of certain sources are consistent with shock interaction between interior winds and external (superwind) envelopes. These latter models (see also Balick et al. 1987; Icke & Preston 1989; Icke et al. 1992) also bear a striking resemblance to the radiative modelling structures of Hyung et al. (1994, 1995) and Hyung & Aller (1996), and it is pertinent to ask whether such radiative analyses should not also make allowance for components of shock excitation.

Finally, recent high resolution imaging has revealed that the helical structure of NGC 6543 may arise through interaction between precessing jets and the primary shell (Harrington 1995); whilst high velocity condensations ("FLIERs") are also likely to be associated with strong shocks (although Balick et al. (1994) have voiced doubts concerning the viability of this mechanism; see later).

It is apparent, therefore, that shock excitation may dominate emission in certain post-main-sequence sources, and it is relevant to ask whether the present work offers any guide to identifying further such nebulae.

In fact, and apart from CRL 618, very few sources can be unambiguously identified as being shock-excited; the level of dilution by radiative components of emission appears in most cases to be appreciable. Thus, whilst [OI]/H$\beta$ line ratios are higher than would be anticipated from radiative modelling, and may be partially enhanced by shocks (see Sect. 3.1), they are distinctly smaller than would be expected through shock modelling (a disparity which reflects the predominance of radiatively excited H$\beta$ emission). Similarly, whilst [OIII] line strengths are larger than predicted through shocks, [NI] intensities appear to extend well into the shock regime of Fig. 1j; although as part of a trend between [OI] and [NI] which extends primarily outside of the shock zone.

Various nebulae may, nevertheless, represent strong candidates for possible shock excitation, including the ubiquitous CRL 618 and some 13 other sources (Table 2, where spectral identification regimes are also indicated; [SII]/([OI][OIII]) would imply detection in the [SII]-[OI] and [SII]-[OIII] shock regimes). Certain of these sources have previously been identified as likely shock candidates (viz. CRL 618 and M2-56; Goodrich 1991), and/or possess strong shock excited H₂ S(1) emission (e.g. NGC 6853, NGC 6720, NGC 2440, NGC 650, NGC 2899 and CRL 618 (e.g. Zuckerman & Gatley 1988; Kastner et al. 1994, 1996; Webster et al. 1988)). In addition, a large proportion also possess bipolar morphologies; and these (with their typically high velocities of outflow) constitute one of the most likely subcategories in which such emission might be observed. We have therefore indicated separately in the figures all of those nebulae for which the observed morphology is bilobal.

  

Table 2: Candidate shock excited nebulae

  

Figure 5: Histograms of observed expansion velocities in bipolar nebulae, where we have indicated both the primary shell velocities (Low), and the velocities associated with accelerated winds (High)

4.1 Bipolar sources

Apart from the sources cited individually in the previous section, it appears that the majority of BPN fall outside of the shock regimes in Fig. 1; although there are, nevertheless, various trends to suggest that shock excitation may be important for the group as a whole.

In the representation of [NI] against [OI] (Fig. 1j), for instance, it is apparent that 74% of BPN fall into the shock regime, whereas for the more general nebular sample the proportion is 28%. Although this may be partly explicable in terms of enhanced N abundances (viz. Peimbert & Torres-Peimbert 1983; Corradi & Schwartz 1995), such contributions are unlikely to account for all of the bias. Similar trends (although perhaps less distinctive) are to be found in plots of [OI] versus [OII] (Fig. 1d), [OI] versus HeI (Fig. 1f), and so on.

These disparities are also illustrated in a slightly differing way in Fig. 6, where following the prescription in Sect. 3.1. we have defined a function R(BPN) = $\langle \log (I_{\rm BPN})\rangle - \langle \log (I_{\rm G})\rangle$; where $\langle \log (I_{\rm BPN})\rangle$ is the logarithmic mean transition ratio for bipolar nebulae. Sample numbers are typically N= 500 for the primary nebular sample, and N= 40 for the BPN (where we have used the listing of Phillips (1997) for BPN identification).

  

Figure 6: Variation of observed values R(BPN) as a function of transition, wherein are also indicated the trends expected for a variety of shock models

As a result, it is apparent that emission in BPN departs considerably from that of other planetary nebulae, with values I([OII]) exceeding those of the general population by a factor $\sim 2.3$. Such excesses are not however uniform, and the enhancement in HeI ratios is considerably more modest (of order 7%).

The interpretation of such figures requires considerable caution since, as we have noted above, CNO processing of nebular material leads to anomalous abundances in type I/bipolar sources, whilst central star temperatures and shell masses are systematically higher than in the majority of PN. The procedure is also open to uncertainties regarding the mode of [OI] line formation, and possible variations in this mechanism between differing nebular sub-groups.

Where such excesses are interpreted primarily in terms of shocks, however, then it is possible to place relatively tight constraints upon shock parameters. In particular, a multi-dimensional least squares fit between the present results and the models of Hartigan et al. (1987) indicates that planar shocks with velocity $V\rm _s = 80\Rightarrow 100~km~s^{-1}$ (models I80, I100 and B100) come closest to representing observed excesses. These trends, also illustrated in Fig. 6, follow observed variations reasonably closely; the most serious casualty ([NI]) reflecting probable enhanced N abundances in the BPN. Given that model grids are rather coarse, and that a small change in $V\rm _s$ by 20 km s^-1 would cause order of magnitude variations in line ratios, it is unlikely that shock velocities will (in the mean) depart greatly from the values cited above.

How consistent is such a result with what is known of BPN shell kinematics? To assess this, we have illustrated a compilation of [OIII] and HI expansion velocities for the primary outflow shells (e.g. Kimeswenger 1997), together with maximum shell velocities from Corradi & Schwartz (1995) (Fig. 5); the latter corresponding to high velocity winds which may, in certain sources, be responsible for driving the lower velocity (higher mass) shells. It is clear, from this, that deduced shock velocities would be most consistent with higher shell outflow velocities $V\rm _h$ ($\langle V\rm _h\rangle = 161~km~s^{-1}$); primary shell velocities ($\rm \cong 18~km~s^{-1}$) are too low. It is therefore conceivable that much of the excess emission arises through interaction between the differing kinematic outflow components.

  

Table 3: Search for FLIERs in high-excitation nebulae

4.2 Shocks associated with FLIERs

Recent investigations by Balick et al. (1993, 1994) have emphasised the unusual spectral characteristics of high velocity compact regions within the primary shells of planetary nebulae; features which these authors have dubbed FLIERs. Although it would be anticipated that the spectra of these components are dominated by shock excitation, Balick et al. have suggested that the observed ionisation structures are inconsistent with such a hypothesis, with [OI] peaking at larger radial distances than is the case for higher excitation lines. This conclusion would, in turn, be somewhat perplexing, given that there is so much other evidence to favour shock excitation; not least, in the clear similarity of the spectra to those of HH sources, and the difficulty in explaining these trends through any other mechanism. We shall here briefly attempt to resolve this paradox, before proceeding to investigate the spectral characteristics of nebulae in which FLIERs are found.

A linchpin in the analysis of Balick et al. (1994) is the assumption that the compact zones represent projections of post-shock cooling regimes in the plane of the sky - that is, that the observed ionisation stratification arises through post-shock cooling and recombination. This, in fact, is unlikely to be the case. On the basis of planar shock modelling, for instance, Hartigan et al. (1987) have noted that cooling zones would have typical widths

$$\Delta s = 5.8\ 10^{-5} \left[\frac{V_{\rm s}}{10^2\ {\rm k... ....67} \left[\frac{10^2\ {\rm cm}^{-3}}{n_{\rm p}}\right] \rm pc$$

for shock velocities $V\rm _s \gt 60~km~s^{-1}$, where $n\rm _p$ is the pre-shock density of neutrals plus ions. Given $n\rm _p \sim 10^3~cm^{-3}$and $V\rm _s = 100~km~s^{-1}$ this would then imply $\Delta s \sim 5.8\ 10^{-6}$ pc, whilst bow shocks more consistent with typical FLIER velocities $\rm \sim 50~km~s^{-1}$ would yield even lower values for $\Delta s$. It would appear, in brief, that the post-shock recombination zone is likely to be all but unresolvable, and that the physical dimensions of the FLIERs ($\sim .01$ pc) correspond to the projected bow-shock structures themselves.

Viewed in this light, it can be seen that peak [OI] intensities would indeed be expected to occur where $V\rm _s$ is largest (e.g. Hartigan et al. 1987) - that is, at the location (the tip of the bow shock) where largest intensities appear actually to be observed.

A further query which concerns Balick et al. is the influence of ionisation by the central star radiation field; and it is certainly true that some post-shock ionisation of the cooling zone might be expected to lead to reduced low-excitation intensities. Here again, however, it is likely that the effect of this contribution can be greatly overstated. In particular, the flux of ionising photons at the location of most FLIERs is likely to be reduced through geometrical dilution, and the re-ionisation of neutral atomic species at lower radii. This, together with the appreciable post-shock densities expected for high M shocks, would presumably imply that radiative penetration of the post-shock cooling zone is likely to be very small indeed.

Taken as a whole, therefore, there seems little reason to doubt that the high velocity condensations of Balick et al. do indeed represent bow-shock features.

Given these circumstances, one may then reasonably ask whether such nebulae also possess excess lower excitation line strengths, as we have shown to be the case for BPN.

Such a trend, would, in fact be most unlikely, given that the shocked components appear to be highly compact, and contribute only a small proportion of the overall nebular spectrum; the primary nebular spectra are likely to be radiatively excited. Inspection of Figs. 1a largely confirms this expectation, revealing that most of the line intensities fall well outside of the shock regimes. Two further features are however well worth noting, and represent trends quite separate from the majority of sources.

It is apparent, in the first place, that relative line ratios are a highly variable function of position within the nebular shells - much more so than applies for most "normal" sources (viz. the connected line ratios for NGC 6543 and NGC 7009 in Figs. 1a). This, in turn, might be expected where observations are acquired at locations variously on and off the shock features.

A second characteristic of such sources is perhaps even more striking, and less open to anticipation.

Most of the line intensities for these sources, far from being located close to the shock regimes, appear to be in fact located at the opposite end of the excitation scale, and to contribute a very large fraction of the points at the lower limits of the [SII], [OI], [OII], [SIII] and [NI] line ratios (as well as clustering at the higher end of the HeII scale). Of the 25 nebulae having log([SII]) $\leq 0.4$ and log([OII]) $\leq 1.4$, for instance, fully 52% correspond to FLIER nebulae. The nebulae containing such high velocity features are clearly, in short, relatively high excitation sources, and it seems likely that the phenomenon of FLIERs must be in some way associated with this particular sub-category of nebula.

This, in turn, suggests that such spectral characteristics may represent a useful diagnostic tool in the search for further high velocity features.

The results of a provisional survey of this nature are summarised in Table 1, wherein we list all sources (excepting those of Balick et al. 1993, 1994) having log(10²[OII]/H$\beta$) $\leq 1.4$ and log(10²[SII]/H$\beta$) $\leq 0.4$. None of the nebulae possess widely disparate line ratios (as is the case with NGC 6543 and NGC 7009), although multiple spectra are available in only a few of the sources. Similarly, where nebular images are available in the catalogues of Schwartz et al. (1992; SCHW), Manchado et al. (1996; IAC), and Perek & Kohoutek (1967; P&K) only a minority are resolved.

Of the PN which have been adequately imaged, however, fully half show evidence for FLIER activity (J 320), shock structures (NGC 6537), or low excitation asymmetries and condensations which may be interpretable in terms of FLIERs (IC 351, NGC 6879). The other half possess broadly symmetric shells which may repay further investigation ; although it is apparent that all of these sources would benefit from a program of imaging at higher spatial resolutions, and in a broader range of transitions.