A "FIREWORK" OF H₂ KNOTS IN THE PLANETARY NEBULA NGC 7293 (THE HELIX NEBULA)^*

Figure 2 shows the MOIRCS image of NGC 7293 in the v→1–0 S(1) H₂ line, while Figure 3 shows a grid reference indicating the R.A. and decl. (J2000) overlaid on the image, together with a numbered grid to guide the reader to which region we are discussing. Clumps of H₂ gas are found throughout the entire image (except the area close to the CS), supporting Meixner et al. (2005) and Hora et al. (2006). The knots are isolated at the inner edge (distance from the CS r < 35) and these knots are accompanied by tails pointing directly away from the CS. The areas enlarged in Figure 4 are indicated in Figure 3. Individual knots and their tails remain resolved throughout the inner ring (35 < r < 45). While the H₂ emission is clumpy in the outer ring (45 < r < 64), the structures are different; individual knots are not as easy to distinguish, and tails do not appear to be collimated into the radial direction (Figure 4). The outer ring is brighter than the inner ring in H₂, as found by Speck et al. (2002). Our MOIRCS image clearly shows that the morphology of the knots changes from the inner edge to the outer ring. In general, the well resolved knots in the inner edge and inner ring show a "cometary" shape, i.e., an elliptical head including a bright crescent-shaped tip and a tail. In the inner region, the crescents always face the CS, and the tails stretch in the opposite direction. Examples of morphologies are found in Figures 4 and 5. Such knots are found up to r ∼ 45 (approximately the lower half of Figure 2) from the CS, i.e., the inner ring. From previous observations, the cometary morphology has only been recognized at the inner edge (Huggins et al. 2002; Hora et al. 2006; Matsuura et al. 2007). Our MOIRCS image shows that these morphologies are found throughout the inner ring.

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Beyond r ∼ 45 (the outer ring), tails are not always obvious; some knots appear to have crescents only (Figure 4), as described by Meixner et al. (2005) and O'Dell et al. (2007).

The shapes of the tails are best studied in H₂ due to its brightness. Matsuura et al. (2007) studied a knot at the inner edge of the H₂ emitting region and showed that the optical [N ii] +Hα intensity falls to less than 10% at 1'' away from the brightest tip, while the H₂ intensity decreases more gradually to 10% at 5''.

Figure 5 displays a variety in tail shapes. The knots in this figure are mostly located in the inner edge (Figure 3) and they are well isolated. The most common shape is a narrowing tail, which was also found for an individual knot at the highest angular resolution (005 per pixel; Matsuura et al. 2007, 2008). However, some tails first narrow then widen with distance from the bright tip, such as knot (h) in Figure 5. Similarly, some tails show a brightness gap at the midpoint along the tail (d) and (e). Such tail shapes have not been reported previously. There is one case of a continuously widening tail straight from the crescent (g). Knots occasionally show complex structures, with a secondary peak or sometimes multiple intensity peaks in the tail, often accompanied by a meandering tail (a), (c), and (f). The orientation of the tail often changes at the secondary peak (a) and (f). As the secondary peak is aligned with the tail, and no crescent is found nearby, the secondary peak is physically associated with the primary peak. The wide variety of tails may be linked with the formation mechanisms of knots and tails, or they trace an interaction with the local environment. This will be discussed in Section 4.3.

We counted the number density of knots and compared with the H₂ surface brightness. Figure 6 shows the number of knots counted in 1 × 1 arcmin² regions, as a function of average surface brightness within these regions calculated from Speck et al. (2002). In the inner ring, the surface brightness of H₂ correlates well with the number density of H₂ knots, rather than with the brightness of individual knots, or the distance from the CS.

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For a similar number density of knots, the outer ring has twice as high surface brightness as does the inner ring. This is due to a contribution from blended H₂ tails, which occupy a larger area than the knot heads in the outer ring, as found in Figures 2 and 4. On average, the H₂ surface brightness from the outer ring is higher than that from the inner ring.

In order to estimate the total number of knots in this nebula, we divide the nebula into three zones, the innermost edge (r = 22–35), the inner ring (r = 35–45), and the outer ring (r = 45–64). From the MOIRCS image, we estimate the knot number densities of these regions to be 20, 500, and 400 arcmin⁻², respectively. We assume that knots are uniformly distributed in these circular rings. The total number of knots is estimated to be 4 × 10⁴ in the entire nebula. This is a factor of 1.7 larger than the estimate by Meixner et al. (2005). The difference is caused by the assumed knot number densities in the inner ring; Meixner et al. (2005) used a lower number density (148 arcmin⁻²) throughout the entire nebula based on observations of the outer ring. We counted knot number densities in relatively less crowded regions within our image so as to minimize confusion problems. Despite that, these regions are bright in the Spitzer 3.6 μm image, where the 3.6 μm band also represents H₂ emission (Figure 1; Hora et al. 2006). Meixner et al. (2005) counted much fainter regions, where the density is lower. The total number of knots provides an estimate of the total molecular and neutral hydrogen gas mass. Adopting a knot mass of 1.5 × 10⁻⁵ M_☉ (O'Dell & Handron 1996), the total molecular mass is 0.6 M_☉ in this nebula. This estimate is a factor of 6 larger than the molecular mass estimated from CO observations (Young et al. 1999). The difference could be due to the large fluctuations of knot mass. Since the ionized gas mass is estimated as 0.3 M_☉ in this nebula (Henry et al. 1999), a substantial amount of molecular gas remains. Most of the H₂ gas is found in the outer ring, thus the distance from the CS, i.e., UV radiation strength is a key. Only knots with large optical depth could survive in the inner ring.

NGC 7293 has been targeted by various optical observations. Figures 7–9 show a comparison of the MOIRCS H₂ image with HST images in the F658N and F656N filters (O'Dell et al. 2005; O'Dell & Handron 1996, respectively). The F656N data at 656 nm are dominated by Hα with some contamination from [N ii], whereas the F658N data at 658 nm are dominated by [N ii], with negligible contamination from Hα. The F656N image has been taken only for smaller parts of the Helix Nebula.

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Figure 7 shows the overall images of H₂ and F658N. The brightest places in H₂ and [N ii] are found in different locations within the nebula. The inner ring is brighter than the outer ring in [N ii] whereas the outer ring is brighter in H₂. All knots in the optical image have counterparts in H₂ emission. Some knots cause extinction in the optical (and appear dark in the image), as found near the bottom of the [N ii] image (Figure 7). These knots are located in the foreground of diffuse ionized emission, and all of these absorption knots in [N ii] have emission counterparts in the H₂ image (compare with the case of NGC 6720; Speck et al. 2003). In contrast, not all H₂ knots have corresponding knots in the [N ii] image, particularly in the inner ring where [N ii], emission from the interknot region overwhelms the emission from knots, if any. Meixner et al. (2005) and O'Dell et al. (2007) suggested that H₂ knots always have some counterparts in [N ii] but this is only the case in the outer ring and at the inner edge. In the outer ring, diffuse [N ii] components are relatively weak, and in the inner edge, all of the knots are isolated. This contrast can be explained if NGC 7293 takes the morphology of a pole-on bipolar nebula projected onto two rings (O'Dell et al. 2004; Meaburn et al. 2005). Moreover, these rings are quite thick and contain layers of knots and diffuse components within.

Figure 8 shows a close-up comparison of the H₂, [N ii], and Hα images in the inner ring, labeled as regions 5 and 6 in Figure 3. The F656N image is available only for region 6 within the MOIRCS 13 regions defined in Figure 3. Knots are clearly found in the H₂ images for both regions 5 and 6, whereas less than one-third of those crescents/heads are recognized in [N ii] image. In the [N ii] images, there is little to no structure defining the knots, with the ionized emission being more diffuse. In region 6, the H₂ crescents have counterparts in Hα, except where indicated by arrows in Figure 8.

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H₂ is associated only with high-density knots, whereas the ionized gas is located both at the surface of the knots and in the interknot space. The high density of the knots leads to high brightness in the knot locations for H₂ and to a lesser extent, Hα. The Hα contrast is reduced by the interknot component.

We further compare H₂, [N ii], and Hα images of well isolated knots in the inner edge of the nebula (Figure 9). These images are aligned such that the tips of the knots are coincident at these three wavelengths. O'Dell et al. (2005) reported a displacement of the [N ii] tips with respect to those in NICMOS Hα and H₂ by ∼01: this displacement is minor compared to our 04 resolution. All knots except (b) were detected in [N ii], but only three were found in Hα. All crescents are found in all three wavelengths. The secondary peaks in knots (a), (c), and (f) are also found in all wavelength images: fainter local peaks in the H₂ image of knot (f) can be seen in the Hα image, but not in the [N ii] image. In the [N ii] and Hα images, high emission from the interknot region is found. Due to this high interknot emission and faintness of tail emission, the narrowing of the tails is not always clearly seen in the [N ii] image.

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Our observations show that at the inner edge and the adjacent regions of the nebula, the H₂ is found only in knots. In the outer ring, there is a faint dispersed H₂ component which can be interpreted as overlapping blended tails. Therefore, we conclude that the H₂ is associated solely with the knots, following Speck et al. (2002) and Meixner et al. (2005). There are two plausible explanations for such an association: (1) the large optical depth of the knots protects previously formed H₂ from the harsh UV radiation, or (2) the H₂ formed in situ in the knots, where high densities and low temperatures allow for molecule formation.

The choice between these two explanations is linked to the origin of the knots: did these form at late times, after ionization of the PNe began (e.g., Garcia-Segura et al. 2006), or did they originate in a molecular wind (e.g., Redman et al. 2003)? In the first case, H₂ must have formed in situ, while in the second case the molecular content may have survived from the asymptotic giant branch (AGB) wind.

In order to test whether H₂ formed during the AGB phase could have survived into the PN phase, we have investigated the lifetime of molecular hydrogen. Using the dissociation rate of H₂, including self-shielding (Draine & Bertoldi 1996) and G₀ = 8 and $n_{\rm H_2} = 8\times 10^4$ cm⁻³ (Matsuura et al. 2007), the timescale to dissociate H₂ is estimated to be 8 × 10⁷ yr. Thus, preexisting H₂ can survive in dense regions within the current conditions. Similar result is obtained using UCL-PDR (Bell et al. 2005). However, the UV radiation field will have been much stronger in the past. The star is currently on the cooling track, and is much less luminous than during its earlier post-AGB evolution. If G₀ = 10³, the dissociation timescale is 8 × 10⁴ yr. The high-luminosity regime phase for relatively massive stars lasts for less than 10,000 yr (Zijlstra et al. 2008). Hence, the H₂ associated with knots may have survived such an intense UV radiation field for this early post-AGB period.

In order to investigate whether H₂ can be formed in situ in PNe, Aleman & Gruenwald (2004) calculated H₂ formation in (partly) ionized gas. The reactions involved include H⁻ + H and H⁺₂ + H. The H₂ formation rate in the ionized gas is estimated to be 10^−10.5 cm⁻³ s⁻¹ in total, which is slightly larger than the H₂ destruction rate. However, the fraction of H₂ with respect to H is extremely small (10⁻⁵). Aleman & Gruenwald (2004) concluded that some H₂ could survive the ionized state, but it is not yet clear if H₂ can be formed from the ionized gas during the PN phase.

The densities within the knots are estimated to be 10⁶ cm⁻³ (Meaburn et al. 1998) to 3 × 10⁵ cm⁻³ (Huggins et al. 2002). At 10⁶ cm⁻³, H₂ formation on dust grains becomes significant; the timescale is of the order of 10³ yr. Thus, in the densest knots the formation can proceed faster than the age of the nebula. However, if the densities are lower, the required lifetime of the knots becomes similar to the age of the nebula. In such a case, the knots pre-date the ionization, removing the need to (re-)form the H₂ later.

In summary, the timescale suggest that part of the H₂ is primordial, i.e., formed during the AGB phase, and survived the ionization of the nebula. In dense knots, (re-)formation of H₂ is possible.

There have been various suggested mechanisms for knot formation. The two main scenarios are (1) the knots are primordial density enhancements, i.e., they started their formation during the AGB phase (e.g., Zanstra 1955; Dyson et al. 1989; Soker 1998);⁸ (2) the knots form in situ, as a result of the onset of the PN phase (e.g., Garcia-Segura et al. 2006; Capriotti 1971).

The in situ formation mechanisms can be further divided into subcategories: (i) turbulent (Rayleigh–Taylor; RT) instabilities as a result of interaction between the slow and fast winds (e.g., Mathews 1969; Vishniac 1994; Dwarkadas & Balick 1998; Garcia-Segura et al. 2006), (ii) turbulent (RT) instabilities at the ionization front (e.g., Capriotti 1971), (iii) shadowing effects (e.g., Van Blerkom & Arny 1972; Soker 1998), and (iv) radiative shocks (e.g., Walder & Folini 1998). Capriotti (1973) used his model to predict the mass (10⁻⁶ M_☉) and number of knots (∼10⁵) in a nebula, consistent with current observations.

A preionization origin of the knots appears to be plausible. The system of knots has an expansion velocity which is typical for AGB winds but is less than that of the ionized gas (Meaburn et al. 1998). The last point suggests that the knots formed after the AGB wind reached its terminal velocity (at ∼10 AU from the star), but before the overpressure from the onset of ionization caused further acceleration (e.g., Ueta et al. 2006). The fact that a very high fraction of the total mass is found in the knots, also is more easily reconciled with an early origin.

To form knots in an expanding wind requires compression of the gas, within an overpressured (heated) surrounding region. This may happen at the ionization front, as discussed above. Because the ionization front moves outward, the inner sets of knots would be older than the outer knots, in this model. The shock front between the fast and slow wind is another option but this front co-moves with the expanding nebula, so that one might expect the knots to be found only near the inner edge of the dense nebula. This interface is located within the ionized region, so that one may expect the knots to share the velocity with the ionized gas. This model cannot be entirely excluded but may be less in agreement with the observations. In this case, the H₂ would have to form from ionized gas. In either of these cases, the knots would be a very common phenomenon in PNe.

To form the knots much earlier, in the AGB wind, would require a denser region than normally expected in AGB winds. However, if the AGB star has a close binary companion, a spiral shock will form in the AGB wind behind the companion (Edgar et al. 2008). This shock causes a heated, compressed region, which a large fraction of the AGB ejecta pass through. This could provide a possible location for the origin of the knots. In the absence of detailed hydrodynamical models, this must remain speculative. In this model, the outer knots are older than the inner knots.

The problem of distinguishing between formation mechanisms becomes even more difficult once we consider the shaping of the knot heads and tails. Most recent studies of knot shapes assume a pre-existing density enhancement and do not consider whether it is primordial or formed during the PN phase. Consequently, observations of knot (head and tail) shapes, may be able to distinguish between shaping models, but are unlikely to reveal the origin of the original density enhancement.

The shaping mechanisms can be also classified into three basic categories, with some cross-fertilization: (1) hydrodynamic interaction between winds and density enhancements (e.g., Zanstra 1955; Vishniac 1994; Pittard et al. 2005; Dyson et al. 2006; Pittard et al. 2009), (2) interaction (including photoevaporation) of material with ionizing (UV) radiation (e.g., Mellema et al. 1998; Williams 2003; Garcia-Segura et al. 2006; López-Martín et al. 2001), (3) the effect of shadowing by density enhancements (e.g., Soker 1998; Cantó et al. 1998). These mechanisms may act together, and disentangling which mechanisms are mutually consistent and which are mutually inconsistent is a challenge.

In the following, we will first discuss streaming models, followed by photoevaporation and shadowing models. A combination is proposed based on the observational constraints.

In all cases discuss below, we use the term "core" to describe the density enhancement which is acted upon by the various mechanisms to create cometary knot shapes (heads and tails).

The first proposed mechanism was the interaction of a core with a wind (which may emanate from the CS or be caused by expansion of the interknot gas; Zanstra 1955). This basic concept was also the inspiration for Dwarkadas & Balick (1998), who showed that by including an evolution in the fast wind, small clumpy structures could be formed, but the resulting shapes are not described. A more recent attempt to modify this concept includes both an ambient wind, which can be sub- or supersonic, and a flow from the core itself, where flow is assumed to have a constant ablation. We call this a "stream" model. The wind is due to the differential velocity between the diffuse gas and the knots: there is no evidence for a hot wind from the CS.

The interaction between the core and the wind can create both the heads and the tails (Pittard et al. 2005; Dyson et al. 2006). In this model, the crescent tip is a bow shock (ignoring photoionization) and ram pressure creates a narrowing tail for subsonic ambient winds (Pittard et al. 2005) and a widening tail for supersonic ambient winds.

The second option, i.e., interaction of material with ionizing (UV) radiation, considers photoionization and photoevaporation models, ignoring streaming motions (e.g., Mellema et al. 1998; Garcia-Segura et al. 2006; López-Martín et al. 2001). In this case, the surface of a core facing the CS is illuminated by UV radiation, which causes heating and photoevaporation from the core, and creates the crescent tip. At this moment, there is no detailed hydrodynamical model present to reproduce narrowing, widening, and meandering tails, using photoevaporation. Williams (2003) calculated ionization front instabilities, and obtained a jet shape. No clear resemblance is found yet between the modeled shape and the knots observed in the Helix Nebula, however, the explored parameter space was limited.

The final possibility is the shadowing by density enhancement (Cantó et al. 1998), leading to nonionized regions in the shadow. Here, the knots can trace a large core, consisting of neutral gas and dust, with a bright sunny side and a dark shadow giving rise to the tail. UV photons from the CS do not reach the shadowed side directly, but diffuse UV radiation diffusion illuminates the tail. To explain narrowing tail (Cantó et al. 1998) and widening tail (O'Dell et al. 2005), varying angles of illumination are used.

The tails can be explained either with streaming motion, by interaction at the ionization front or by shadowing. Here, the streaming models or ionization models appear better able to fit the available data. The bright (and well isolated) inner knot located in our field shows clear acceleration in [N ii] along the tail (Meaburn et al. 1998), by about 10 km s⁻¹. The meandering tails are consistent with instabilities expected for streaming motions (e.g., Wareing et al. 2007) or interaction at ionization front (Williams 2003), whilst solely shadowing by density enhancement requires straight tails by necessity. (In some case ionization edges are visible within the tails.) Finally, the absence of clear tails in the outer regions is less easily explained with shadowing. The issue is controversial, and further velocity information would be required to resolve it.

As mentioned before, the knots change appreciably in appearance between the inner and outer nebulae. In the inner nebula, tails are always seen. In the outer nebula, the knots appear more diffuse and tails are absent. This implies a change in shaping mechanism. Whereas streaming motions appear important in the inner region, the structures in the outer nebula suggest that it does not play a role there. Within the streaming model, the implication is that the knots have a differential velocity with respect to the ambient medium in the inner nebula, but not or less so in the outer nebula. A plausible model is that the inner knots system is being overrun by faster expanding, lower density gas, but that this has not yet reached the outer knot system.

Meaburn et al. (1998) find a difference in expansion velocity between the system of knots and the ionized gas, of 17 km s⁻¹, with the knots moving slower. The wind speed in the nebula shows significant variations, with velocities up to 50 km s⁻¹ with respect to the nebula mean velocity (Walsh & Meaburn 1987). The sound speed in the ionized nebula is of the order of 10 km s⁻¹. This is similar to the velocity differential: we may expect both subsonic and supersonic winds, depending on the local conditions and on the flow velocity within the tail.

If the gas flow models are correct, it points to the prevalent wind interaction being subsonic, because of the common presence of narrowing tails. However, there are also cases of widening tails (knot (f)), which requires supersonic winds. It would be of interest to measure detailed velocity fields for the tails and the surrounding gas. The tail velocities may possibly be measured from the H₂ lines.

Some of the more complicated tail structures may be due to feedback, where an ambient wind is disturbed by another knot. The multiple brightness peaks and meandering tail in a knot (Figure 5) may be explained through the complex interaction between nearby cores (Pittard et al. 2005).

Figure 5 shows that some knots have a dip in brightness in the middle of the tail which remains unexplained. If this is due to the pressure balance, the temperature would be lowest at this point and increase again further out (related to the shadowing by the knot). It could also be due to a change to a supersonic flow at this point (Pittard et al. 2009). Detailed studies of temperature and velocity distribution along these tails may help distinguish the various models, in so far impossible.

It does not appear possible to view the three models in isolation. In reality, a combination of effects is likely required. Streaming motions can help explain the shapes, but the observed structures implies that streaming motions only occur in the inner nebula, not the outer. The crescent shapes trace photoionization, and photoevaporation. Shadowing will occur, but its importance to the shaping remains to be proven. Integrated models taken all effects into account would be desirable.