The standard model for AFGL2688 does not explain the offset between the N and S reflection lobes, the kinematics of the H2 emission, the ansae seen in H2 or the morphology of the H2 emission. Our alternative model is designed to explain all these results. Nor can the standard model account for the rectangular appearance of the nebula at low surface brightness levels in the near-IR and mid-IR. Such a morphology also arises quite naturally in our model.
The model presented here for AFGL2688 is certainly very different from the `standard model', and initially some aspects, for example the inhomogeneity of the nebula and its asymmetry, may seem unattractive. Such clumpiness as we postulate here has in fact already been inferred from observations of AFGL2688 and its cousin AFGL618. Schmidt & Cohen (1981) discussed spectropolarimetry of the lobes of the bipolar nebula AFGL618. They observed both ionized and neutral species in the lobes, and concluded that the lobes must bear a fast, hot wind responsible for the ionic lines, but there must be embedded in it denser condensations inside which and in whose shadows various neutral and molecular species could exist. Cernicharo et al. (1989) observed a rich variety of molecules in the outflow of AFGL618, many of which were seen at very high velocity, suggesting that they were in the fast wind. The relatively hard radiation field from the central star of AFGL618 in the lobes should photodissociate molecules in the fast wind, and their reformation ought to be suppressed by the low density at points where the temperature in the wind could be low enough for molecule formation. The existence of dense clumps in the wind could allow the formation of molecules. Likewise, in the bipolar lobes of AFGL2688, spectropolarimetry by Cohen & Kuhi (1977) indicated the existence of C2 in two different density regimes, once again indicating that there are probably dense clumps in the lobes. They speculated that the clumps may even allow the condensation of C-rich grains inside the bipolar lobes. The structure of the inner `blob' of H2 to the east of AFGL2688 strongly suggests a filament consisting of a series of large clumps. The mid-IR images of the young PN IRAS21282+5050 presented by Meixner et al. (1993), and the mm-wave interferometer images of the same source (Shibata et al., 1989) indicate that its envelope is extremely clumpy, and the inhomogeneity exists on rather large scales. Finally, the same conclusion is reached from the variety of images presented by Graham et al. (1993) of the prototypical young PN NGC7027. Thus a large degree of inhomogeneity is seen in a variety of well resolved post-AGB nebulae and young PN.
The asymmetry of the nebula, in particular the appearance of the optical lobes over towards one edge of each cone in the bipolar outflow, may seem worrisome. In fact, once again the young PN NGC7027, and the extensive observations of it by Graham et al. (1993), should be examined. Both the inner and outer loops of H2 in NGC7027 are asymmetric. The inner loop is almost a complete ring. The outer loop exhibits a similar asymmetry to that seen in AFGL2688 - specifically, the H2 appears concentrated in two opposing corners of a box structure, and offset from the apparent axis of a bipolar outflow. If we were to evolve this PN backwards in time as far as the point when it had just recently left the AGB, we could well see a structure very much like that which we see in AFGL2688. In fact, if we examine any of the near-IR images of NGC7027 presented by Graham et al. (1993), we see a remarkable similarity in shape to the box-like nebula we see around AFGL2688 in the mid-IR, or at low flux levels even in the near-IR in the L and K bands.
Remarkably, shortly before completing the manuscript of this paper, we received a preprint discussing new 13 CO images of AFGL2688 (Yamamura et al. 1995), which provides strong support for our model. Yamamura et al. find that the 13 CO emission, which is optically thin, consists of three components - a bright, circular core, a fainter more extended halo, and higher velocity components. The core is unresolved and so the toroidal structure which we expect to be present must be smaller than about 4" in size, which is consistent with our dust model. The higher velocity components (corresponding to the `medium velocity wind' discussed by Young et al. 1992) consist of two red- and blue-shifted lobes separated by about 3" on an axis at PA 60 - exactly the PA we claim for the bipolar flow. The shapes and sizes of the 13 CO high velocity lobes are such that they fit nicely inside the biconical structures which we have proposed are delineated by the H2 emission, beautifully confirming the presence of gas streaming at high velocity in the large bipolar flows as we predict. The 13 CO emission is shown overlaid on our H2 image in Fig. 15. The high velocity lobes appear to be resolved, and so seem to confirm our suggestion that the opening angle of the bipolar flow is very large. The considerable overlap of the two lobes also implies a significant angle between the axis of the flow and the plane of the sky, as we have suggested.
6.2. CO emission
The observations by Yamamura et al. (1995) described above strongly suggest that the interpretation of CO line profiles of the type displayed by AFGL2688 should be thought about very carefully. First of all, we note in passing that the bipolar flow speed appears to have previously been calculated incorrectly for AFGL2688 (Young et al. 1992) and for AFGL618 (Cernicharo et al. 1989). These authors have assumed that the maximum velocity observed in faint wings in the CO line profiles of these objects represents the projected bipolar flow speed. They have then divided the maximum observed velocity by the sine of the angle of inclination of the bipolar flow axis to the plane of the sky. However, the geometric term which should have been employed is not just the angle of inclination of the bipolar axis to the plane of the sky, but this angle summed with the half angle of the bicone, in order to allow for the projection effects of the finite opening angle of the bicones. (See Fig. 16 for an explanation.) Using this procedure, the inclination angle of the bipolar axis in our model (25 ) should be added to the large cone opening half-angle ( 50 ) in order to determine the maximum velocity which will be seen in the bipolar flow region, which is then . Given the maximum velocity of 100km/sec determined by Young et al. (1992), the bipolar flow speed is then 100km/sec. This is not much different from the bipolar flow speed seen in the binary system OH231.8+4.2 (Morris et al. 1987), depending on the uncertain inclination angle in that system, and is an altogether much more reasonable result than those quoted earlier for AFGL2688. In AFGL618, if we adopt the half angle of 10 determined by Latter et al. (1992), the overall angle is then 55 rather than 45 , reducing the bipolar flow speed from 270km/sec to 190km/sec. However, the single scattering models used by Latter et al. (1993) appear to underestimate the inclination and opening angles compared to the multiple scattering models of Yusef-Zadeh, Morris & White (1984) and, thus, the bipolar flow speed in AFGL618 could be lower yet than 190km/sec.
More importantly though, we wish to point out that the rather faint and very broad wings seen in the CO lines of a number of post-AGB stars do not in any case appear consistent with an interpretation in terms of bipolar flows (even if the velocity calculations are done correctly). We illustrate the problem in Fig. 17. A uniformly expanding, optically thick, spherical outflow, with velocity V , as pertains to the typical AGB star, generates a roughly parabolic CO line with full width at zero intensity of 2v (Fig. 17a). In a simple kinematic model comprising such a slow, isotropic outflow, plus a well collimated, fast, bipolar flow, with tiny opening angle and flow speed v, on an axis inclined at angle to the line of sight, we see once again the standard parabolic profile, plus two narrow components at velocities of vcos (Fig. 17b; we assume the central star to have zero velocity in the local standard of rest). Finally, if we now allow the bipolar outflow to be biconical with reasonable cone opening angles, the two narrow features are broadened by projection, so that the composite line profile for such an object is as depicted in Fig. 17c, comprising three distinct features. In practise, no such line profile has been observed in any of the post-AGB sources. Instead, what are observed are standard AGB type line profiles plus very broad wings which appear to be more or less Gaussian, peaking close to the systemic velocity. It is easy to see in Fig. 17 that if the angle approaches 90 , so that the bipolar axis lies roughly in the plane of the sky, then the two peaks generated by the bipolar flow in the CO line profiles will lie on top of one another, and the result will indeed be simply broad wings either side of the AGB wind profile, as observed in the case of AFGL2688. As mentioned earlier, the near-IR images do not appear consistent with an axially symmetric structure with an axis in the plane of the sky, but instead imply an inclination angle of more like 25 . At such an inclination angle, and with a bipolar flow speed of 100km/sec, the two bipolar flow spectral features would peak around 45km/sec to each side of the center of the AGB wind profile. This is not entirely ruled out by the observations, but does appear unlikely. However, in the case of AFGL618 the much larger inclination angle (45 ) and bipolar flow speed (190km/sec) mean that the two bipolar flow peaks should be clearly seen in CO line profiles, and so in this case the spectra are quite inconsistent with a bipolar flow model. The same applies to OH231.8+4.2. The fact that no such features are seen in any of these sources would imply that the bipolar flow axis lies very close to the plane of the sky in every case, which statistically is of course highly unlikely. In the observations of Yamamura et al. (1995) we clearly see the bipolar flow from AFGL2688 (Fig. 15). The bipolar flow is seen at velocities consistent with the `medium velocity wind' component described by Young et al. (1992). Given that this `medium volcity' component is actually the bipolar flow, and given our inclination and opening angles, the two bipolar flow peaks in the CO line profiles should be so close together that they will lie on the AGB wind part of the profile, and thus be very difficult to identify. Neri et al. (1993) suggested that the very broad wings in the molecular line profiles of AFGL618 were basically generated thermally by hot, post-shock gas, rather than kinematically in a wind, and we suggest that this proposal by Neri et al. very nicely explains the CO line profiles in AFGL2688 also. Thus in our model the `low velocity wind' of Young et al. (1992) corresponds to the spherical AGB wind, the `medium velocity wind' to the bipolar flow observed by Yamamura et al., and the `high velocity wind' to hot, possibly post-shock gas. The latter component may be identified with the region of shocked molecular hydrogen emission (Fig. 5, 15), but there are other possibilities just as outlined by Neri et al. for the case of AFGL618. The fact that the `high velocity' component appears to become steadily stronger, relative to the `low velocity' component, with increasing rotational transition in the CO observations of AFGL2688 by Young et al. (1992), is consistent with our suggestion that the `high velocity' component arises in hot gas. Furthermore, the high rotational lines observed in AFGL2688 by Justtanont et al. (1997) demand very warm and dense gas which can realistically only be provided by a Photo-Dissociation Region or a shock. Thus all the available CO data appear to be consistent with this model.
CO maps (Truong-Bach et al. 1990; Yamamura et al. 1995) of AFGL2688 show that the overall density distribution of the outer AGB wind is spherically symmetric, with which our model is entirely consistent. The scattering models of Yusef-Zadeh, Morris & White (1984) and Latter et al. (1993), on the contrary, take the density distribution of the entire envelope to be equatorially peaked, with evacuated biconical cavities extending throughout the envelope. This appears unrealistic since, as mentioned before, the available evidence suggests that AGB winds are more or less spherically symmetric, and that in this source the biconical flow regions only extend a small distance through the envelope. For realism these scattering models should take low density cones carved through a spherically symmetric envelope with the usual law of density. Bieging & Rieu (1988) claimed the existence of a rotating toroid from their HCN interferometer data. Their maps did not clearly resolve a toroid, indicating that it can only be at most a few arc seconds in diameter. An unambiguous determination of the geometry of the AFGL2688 nebula will have to await interferometers with high enough spatial resolution to fully resolve the central torus (whose presence is always assumed), for instance in HCN (a tracer of warm, high density gas), and/or through the use of high enough sensitivity to map the high velocity flow, which is very faint, in CO.
The spherically symmetric CO maps mentioned above are important. The low excitation CO rotational lines (e.g. J=1-0) imply a mass-loss rate of order 10-4 M /yr (Morris 1980; Knapp et al. 1982; Knapp & Morris 1985). This is in reasonable agreement with the value for the AGB wind which we have used in our radiative transfer model. For mass-loss rates in this range, the excitation of CO is entirely collisional (Justtanont, Skinner & Tielens 1994), and so the CO maps reflect the density structure of the AGB wind. Thus these maps strongly suggest that AFGL2688's envelope is mostly quite spherical, except for the superwind at its core. The dust on the other hand is entirely radiatively excited, and so the combination of dust and gas maps allows us to resolve the effects of temperature and density on the appearance of the nebula.
6.3. Thermal pulsing during the AGB phase
The possible connections between helium shell flashes (thermal pulses) in AGB stars and the ejection of planetary nebulae have been reviewed by Wood & Vassiliadis (1993). The duration of the energy generation peak that is associated with the helium shell flash is of the order of 100-200 years (see e.g. Fig. 5 of Iben 1983), while diffusion through the star can spread the associated surface luminosity spike out over a timescale of 500 years (Wood & Vassiliadis 1993). Wood & Faulkner (1986) noted that for sufficiently massive AGB stars the luminosity at a helium shell flash could exceed the Eddington luminosity L at the edge of the core, such that no hydrostatic solution for the envelope could exist, with the likely result of complete envelope ejection. They showed that L L could occur at the peak of the luminosity spike in AGB stars having a degenerate core mass 0.9 M , provided the envelope mass was 1.5 M . Thus Wood & Vassiliadis (1993) noted that degenerate core masses 0.9 M are only likely to develop in AGB stars with a total mass 5 M (so that the initial envelope mass would have been 4 M ), but that the radiation pressure mechanism could only act to remove 1.5M of envelope material.
The above requirements are in excellent agreement with the masses and timescales that we have derived for AFGL2688. The current luminosity of 2.7 L estimated for AFGL2688 (Table 2) implies a relatively high core mass for the central object - if it is currently hydrogen-shell burning, the core mass versus luminosity relation of Vassiliadis & Wood (1994) implies a core mass of 0.98 M , while the helium-shell burning tracks of Wood & Faulkner (1986) yield a similar mass. The derived supershell mass of 0.76 M (Table 2) and its ejection timescale of 200 years are consistent with ejection by a super-Eddington luminosity spike following a helium shell-flash. Our estimate of 2.2 M for the total mass ejected by the preceding AGB wind (Table 2), together with the supershell mass of 0.72 M and the current degenerate core mass of 1 M imply an initial AGB mass of 4 M for the precursor (our model only includes mass lost from the star within the last 2 104 yrs, and its AGB lifetime is likely to have been many times longer than this), consistent with the requirement above that the initial AGB mass should have exceeded 5 M .
Despite the good agreement between our derived mass-loss parameters for AFGL2688 and thermal pulse theory as outlined above, the theory currently cannot explain the toroidal geometry found in the supershells of AFGL2688 and other post-AGB objects.
6.4. Magnetic fields
One of the mechanisms which might possibly be invoked to explain the toroidal morphologies of post-AGB star supershells is focussing of an outflow by a magnetic field. Hu et al. (1993) have commented on the possible effects of magnetic fields on the evolution of post-AGB nebulae. They suggest that closed magnetic field lines around the stellar equatorial region could restrict the outflow of material in the equatorial region, leading to a build-up of dense material in the equatorial plane, which indeed is what is observed in many post-AGB nebulae. Nothing is known about the dynamo which generates stellar magnetic fields, so that any discussion of the likely behaviour of, and effects of, magnetic fields during AGB and post-AGB evolution can only be treated as speculation at present. The simple calculations of kinetic and magnetic energy flux densities in the case of the PPN IRAS17150-3224 by Hu et al. (1993) may be extended to the case of AFGL2688 very straightforwardly. Bieging & Rieu (1988) suggest a magnetic field strength at the surface of the AFGL2688 central star of 3kG. If we assume that the magnetic dipole has remained functioning in the same manner and with the same efficiency throughout late AGB and post-AGB evolution of this star, assume that the magnetic field through the stellar envelope acts like a dipole, extrapolate back in time to the AGB, and assume a standard AGB luminosity of 6000L , the magnetic field strength at the surface of the AGB star would have been 100G, entirely consistent with magnetic field strengths measured in the winds of OH/IR stars by circular polarisation of OH and SiO maser lines (e.g. Cohen 1989; Barvainis, McIntosh & Predmore 1987). In the superwind phase, the stellar wind would have been so dense that the gas kinetic energy density was probably very much greater than the magnetic energy density, so that the magnetic field can have had little influence on the outflow. In the post-AGB phase, however, things may well have become very different. For the magnetic field to dominate the gas flow characteristics, it is a necessary condition that for a system like AFGL2688 where the outflow is presumably mostly neutral. At the stellar surface, if we take B =3kG, =40km/sec (similar to the medium velocity outflow component of Young et al. 1992) and 10-6 M /yr, this condition is certainly satisfied. In the equatorial region, continued outflow from the warm central star can then be impeded, whilst in the polar direction the magnetic field lines are more or less open and allow gas to flow away rapidly in a bipolar fashion. If the magnetic polar axis were offset from the star's rotational axis, then the axes along which ejected material preferentially flows would precess about the rotational axis. Clumps of dust forming in the bipolar flow would then arise preferentially in a direction offset from the rotational axis, and lead to opposing sides of the bipolar nebula being shadowed. Such a scenario would account for the geometry of the AFGL2688 nebula (see Fig. 18), but we stress that while there is observational justification for much of this idea, it must currently remain as conjecture. The spatial resolution of the Keck Telescope at 20 m may be sufficient to investigate this hypothesis observationally (a wavelength as long as 20 m is needed because at shorter wavelengths the nebula is optically thick). Intuitively an offset between the rotational and magnetic polar axes sounds unlikely. However, we repeat that the stellar magnetic dynamo is not understood yet, and there is some evidence in a number of pre-main sequence stars for precessing, magnetically confined, bipolar jets (e.g. Lightfoot & Glencross, 1986). In such systems the `jet' follows a helical path away from the star because of the precession of the magnetic polar axis. However, very tight collimation is required to obtain a helical jet such as that in HH7-11 (Lightfoot & Glencross, 1986).
6.5. Relationship to other bipolar nebulae
AFGL2688 is not the first post-AGB nebula to show asymmetric structure. The young PN M1-16 has a strongly bipolar outflow, but the axis of the outflow as seen in H2 is at a substantial angle to that suggested by optical images (Aspin et al 1993). This suggests that asymmetric outflows such as that in AFGL2688 might not be unusual. Moreover helical outflows in post-AGB stars may not be rare either: we point out that many of the bipolar PN studied by Corradi & Schwarz (1993) have position-velocity diagrams with sinusoidal patterns along the long slit of their spectrometer. The simplest explanation for such sinusoidal patterns is that the outflow structures are helical. Of course this would not necessarily imply that material flows along a helical path. If the outflow were to some extent magnetically confined close to the star, we need not expect it to remain such as it reaches larger distances from the star. The helical pattern then simply represents a record of the direction of the magnetic polar axis at the time the material was ejected from the star.
Spectacular bipolar post-AGB nebulae such as AFGL2688 are rare. There are four well known examples - AFGL2688, AFGL618, AFGL915 (the Red Rectangle) and Roberts 22. Another fainter member of this class, IRAS17150-3224, has only recently been discovered (Hu et al., 1993). There are many more post-AGB stars which optically appear point-like, although they may have extended thermally emitting nebulosity in the IR. One might suppose that the bipolar nebula is a phase which many stars pass through but only briefly. However, AFGL618 has evolved almost to the status of a young PN, and yet still retains its optical bipolar nebula. Next there is the possibility that the point-like and bipolar post-AGB nebulae are the same class of objects viewed from different angles. The relative numbers of objects then dictate that most post-AGB stars must have geometrically very thin, but dense, disks, so that the bipolar nebulae could only be tipped very slightly away from edge-on. The large inclination angle suggested for OH231.8+4.2 (47 ), AFGL618 (45 ) and AFGL2688 (25 ) rule out this possibility. Finally, we are left with the possibility that only a very few post-AGB stars generate spectacular bipolar nebulae. AFGL2688 and AFGL618 are both extraordinarily heavily obscured for such evolved stars, and whilst most post-AGB stars have observable CO lines in their mm-wave and sub-mm spectra, these two have remarkably strong lines, implying that they had very large AGB mass loss rates. All these facts point towards the bipolar post-AGB nebulae being descendants of the most massive AGB stars, as are the Type I PN (Peimbert 1978). NGC7027, whose similarities to AFGL2688 have been commented on earlier, has one of the hottest PN central stars and a very high excitation and very massive nebula. It is presumably likewise descended from a relatively massive AGB star, and we speculate that AFGL2688 and GL618 will both evolve into PN similar to NGC7027.
6.6. The case of the missing UIR bands
Among the currently known C-rich post-AGB stars, AFGL2688 is unusual in being almost the only one with very weak UIR band emission. The Red Rectangle, for example, has strong UIR band emission throughout its IR spectrum. The 21 m sources are a growing group of post-AGB stars discovered on the basis of their unusual mid-IR spectra (Kwok, Volk & Hrivnak 1989; Justtanont et al. 1996), which are dominated by very broad emission features attributed to hydrocarbon molecular groups. AFGL2688, in contrast, has an almost featureless mid-IR spectrum apart from a possible weak emission feature around 8 m (Fig. 14). Why should AFGL2688 be so different to its C-rich cousins in this respect?
Most of the sources so far shown to exhibit the UIR bands have warm or hot exciting stars. These sources include post-AGB stars, PN, HII regions and reflection nebulae associated with young stars. In almost all of these objects, the radiation field includes a substantial flux of UV photons. The UIR bands are usually attributed to hydrocarbon containing materials, either PAHs (Polycyclic Aromatic Hydrocarbons) or HAC (Hydrogenated Amorphous Carbon). In either case, the generation of UIR bands requires photons with UV (or short optical) wavelengths. The most prominent known exceptions to this general rule are the 21 m sources (Kwok et al. 1989; Justtanont et al. 1996), which are all G or F stars with relatively soft radiation fields. In these objects the emission is dominated by very broad plateau features, instead of the narrow features seen in PN, so that the difference in the nature of the radiation field has a major effect on the characteristics of the IR spectra. In the case of AFGL2688, we might expect further differences, because the radiation is effectively even softer. Although the central star appears to have a spectral type of F, the dust shell is remarkably optically thick. We adopted in Sect. 5 an optical depth at 10 m of order 2.0 in our line of sight. This yields an optical depth at 0.4 m (a wavelength short enough to excite UIR bands) of 50, so that photons with wavelengths short enough to excite the UIR bands can penetrate only a very tiny distance into the supershell before being absorbed. Under these circumstances, we cannot expect to see strong UIR band emission whether the carriers are present or not.
In practise, however, the 3.3 m UIR band has been observed in the spectrum of AFGL2688 (Geballe et al. 1992). The flux at the peak of the band is roughly comparable to that of the underlying continuum. The continuum at 11.3 m is about a thousand times brighter than that at 3.3 m (Fig. 14). For a wide range of sources, Jourdain de Muizon, d'Hendecourt & Geballe (1990) found that the ratio of the intensities of the 11.3 and 3.3 m UIR bands was of order ten. Adopting this value, we would expect any 11.3 m UIR band in the AFGL2688 spectrum to have a flux of only about 1% of the underlying continuum - in other words, we would probably not detect it even if it is present.
However, it is worth considering further the nature of the 3.3 m emission. The optical depth at 3.3 m is, on the basis of our radiative transfer model, about 6. This means that we should only be able to see 3.3 m emission from material close to the outer edge of the supershell. However, as pointed out above, the optical depth at the wavelength of the exciting photons is of order 50, so that material close enough to the surface of the supershell to be visible to us cannot then be excited by radiation from the central star. It would seem that the only ways we can observe 3.3 m emission from AFGL2688 are if the emitting material is close to the inner edge of the supershell, and the radiation is scattered towards us out of the reflection lobes, or if the emitting material is itself inside the lobes. In the former case we would predict that the 3.3 m feature in AFGL2688 should be strongly polarised. There appear to be roughly comparable fluxes of thermally emitted and scattered radiation at 3.3 m. If the 3.3 m feature is primarily scattered, then because the scattering cross-section drops rapidly with increasing wavelength the 11.3 m feature should be very much weaker than the 3.3 m feature. Temperature maps made with the various combinations of the 8.8, 10.0 and 11.5 m images do not differ significantly from one another, confirming that even in the outer parts of the mid-IR images, where direct emission from the UIR band carriers might be important, the UIR bands (which should contribute to the 8.8 and 11.5 m images, but not to the 10.0 m image) are very weak. This tends to favour the suggestion that the 3.3 m UIR band is principally emission from the inner edge of the torus scattered out of the reflection lobes, but the evidence is far from conclusive. Polarization images in the 3.3 m UIR band and in the nearby continuum will be enormously valuable in constraining the structure of this nebula and the nature and distribution of solid state material in it.
© European Southern Observatory (ESO) 1997
Online publication: March 24, 1998