Mario Livio
Space Telescope Science Institute,
3700 San Martin Drive, Baltimore, MD 21218,
e-mail: mlivio@stsci.edu
The first point that has to be made is that axisymmetric nebulae
resulting from stellar outflows and explosions are
very common. They are found not only in planetary nebulae (PNe),
but also in a variety of other astrophysical objects ranging
from Luminous Blue Variables (e.g., 
Car and R 127; Nota
et al. 1995, see Fig. 1), to novae (e.g., DQ Her; Barden & Wade 1988, and V1974 Cyg;
Paresce et al. 1995, see Fig. 2) and supernovae (e.g., SN 1987A; Burrows et al.
1995, see Fig. 3). Thus, Occam's Razor would require the identification of a
shaping mechanism that can operate in all of these classes of
objects.
Figure: a. HST/WFPC2 image of 
Car. (Coutesy of D. Ebbets
and R. White).
Figure: b. An image of R127, obtained with the Johns Hopkins
Adaptive Optics Coronagraph. (From Nota et al. 1995)
Figure: A sequence of HST images showing the temporal
development of the nebula around Nova Cyg 1992 (V 1974 Cyg).
Figure: HST/WFPC2 image of SN 1987A. (Courtesy of C. Burrows).
Secondly, it is important to note that PNe, in particular, exist in a variety of axisymmetric morphologies. These include rings (e.g., Sc We 2; Schwarz, Corradi & Melnick 1992), bipolar bubbles (e.g., NGC 2346; Bond & Livio 1990) and highly collimated jets (e.g., NGC 7009; Schwarz et al. 1992). In addition, there exist PNe which are point-symmetric (e.g., IC 4634; Schwarz et al. 1992, see Fig. 4). In some cases, many of these features appear together (e.g., NGC 6543; Harrington & Borkowski 1995, see Fig. 5).
Figure: HST/WFPC2 image of SN 1987A. (Courtesy of C. Burrows).
Figure: HST/WFPC2 image of PN NGC 6543. (Courtesy of
J. P. Harrington and K. J. Borkowski).
One important clue towards the understanding of the mechanism(s) that is (are) responsible for the formation of the axisymmetric PNe lies in the fact that many late asymptotic giant branch (AGB) stars, post AGB stars and proto PNe show already a bipolar structure (e.g., Meixner 1993, Kwok 1993, Trammell, Dinerstein & Goodrich 1994). Examples are: OH 0739-14, HD 44179, IRAS 21282+5050, 17150--3224, and 17441--2411.
In the following three sections, I shall review possible mechanisms for the formation of axisymmetric and point-symmetric morphologies and conclusions will follow.
There exist only two models that have demonstrated convincingly that they are able (in principle at least) to produce a variety of axisymmetric morphologies. These are: (i) the interacting winds model in the presence of an equatorial to polar density contrast, and (ii) a model involving the magnetic tension of a toroidal field.
I shall first review briefly the main physical ingredients of the second model.
The most important property on which this model relies, is the fact that the toroidal component of the magnetic field in the wind from a rotating star becomes increasingly more important with the distance from the star (Chevalier & Luo 1994, Pascoli 1987, Pascoli, Leclercq, & Poulain 1992). At a large distance from the star the ratio of the toroidal to radial component is given by
where 
is the equatorial rotational velocity, 
is the terminal
wind velocity and 
is the stellar radius.
Thus, provided that the rotational velocity is not too low, one might expect a situation in which in the shocked wind region, the toroidal field can dominate over the thermal pressure. This can lead to an axisymmetric configuration by the fact that the magnetic tension can slow down the flow in the equatorial direction, while not interfering with the flow in the polar direction. The minimum field required to produce this magnetic shaping was found to be of order (Chevalier & Luo 1994)
Here, 
is the ratio of the magnetic energy density to the
kinetic energy density in the wind and 
is the velocity of
the fast wind.
The main questions that arise in relation to this mechanism are: (1)
Are the fields inside AGB stars sufficiently large to produce the
effect? and (2) Is the toroidal field configuration stable?
Concerning the first question, it is important to note that if the star rotates very slowly, the minimum required field may be unattainable (see Eqn. (2)), and since single AGB stars forming PNe are expected to be very slow rotators this may be a problem for this model. However, if the AGB star has even a low-mass companion, substantial spin-up of the envelope can be obtained (see .3 below), thus reducing the required field. The question of stability will have to be examined further.
Following the original suggestion by Balick (1987), numerical
simulations have demonstrated that when the ``interacting winds''
model (Kwok 1982, Kahn 1982) is allowed to operate in the presence
of a ``density contrast'' in the slow stellar wind, a bipolar
morphology is indeed obtained (Soker & Livio
1989, Icke, Balick & Frank 1992, Frank et al. 1993, Mellema
1993). This model works as follows: it is
assumed that the slow wind ejected
by the star (e.g., the 
km s
wind of an AGB star) contains a non-spherical
density distribution, with
the material being denser in the equator than in the polar
direction. The fast, spherically
symmetric wind that is emitted later, by either the exposed nucleus
in the case of PNe, or a blue supergiant (e.g., in the case of
SN 1987A), catches up with the slowly moving material and shocks it. Because
of the density contrast between the equatorial and polar directions,
the fast wind can penetrate more easily at the poles, thus forming
an axisymmetric nebula. The works of Frank et al. (1993) and Mellema
(1993) have demonstrated then when the nebular
inclination angle is taken into consideration, most of the
observed morphologies can be reproduced (point-symmetric nebulae
and the highly collimated jets observed in some nebulae probably require
additional ingredients, see § 4). The main question that, therefore,
arises in the context of this model is: what is the mechanism that
is responsible for the formation of a density contrast (in the slow
wind) between the equatorial and polar directions?
I will briefly review a few mechanisms which can potentially produce the desired density contrast.
In several objects which exhibit a bipolar morphology, it has been
suggested that the wind interacted with the inner rim of the
protostellar disk. Specifically, this model has been proposed for
some PNe (Balick & Preston 1988), for the ``Egg Nebula,'' CRL 2688
(Pringle 1989) and for SN1987A (McCray & Lin 1994).
There is no doubt that such protostellar disks indeed form
during the process of star formation. One of the main reasons that
led McCray & Lin (1994) to suggest the protostellar disk as a model
for SN1987A was the fact that the observed main ring (e.g., Panagia
et al. 1991) is very thin (thickness to radius 
), which
requires a very high density contrast. A similar reasoning could be
applied to the 
Car case, where a simulation that attempted to
reproduce the observed morphology showed that an equator/pole
density ratio of about 100 was required (Frank, Balick, & Davidson 1995). However, the
HST image of 
Car shows what appears to be fragments of
material ejected radially at high velocities
(
km s
) at the narrow ``waist'' region
(Nota et al. 1995), with
no clear evidence for the existence of an entire disk surrounding
that region. Furthermore, while both SN1987A and 
Car are
massive and, therefore, young objects, PNe represent late stages in
the evolution of intermediate to low mass stars. The main question
is, therefore (regarding the protostellar disk scenario), do these
disks indeed survive until the PN stage? Observationally, the
presence or absence of such a disk in SN1987A can be tested
directly, when the disk (if it is present) will be illuminated,
shortly after the
supernova ejecta strikes the ring (in AD1999
3).
The winds from rapidly rotating stars can be strongly focused
towards the equatorial plane (due to conservation of angular
momentum). The wind can be shocked there, to form an equatorially
compressed outflow (Bjorkman & Cassinelli 1993, Owocki, Cranmer, &
Blondin 1994). This has been suggested as a mechanism that in
early-type stars leads to the formation of the ``disks'' observed in
Be stars. Livio (1994) suggested that under certain circumstances,
such an equatorially compressed outflow can also form in AGB stars,
thus generating the necessary density contrast. The main properties
of this flow that are important for our present purposes are
(Owocki, Cranmer, & Blondin 1994): (i) there exists a
rotational threshold value that is
required for the compressed outflow to occur. In early-type stars
this value is about 
(where 
is the terminal wind velocity; Bjorkman & Cassinelli 1993). The
critical value depends on the wind acceleration process and it could
be lower for AGB stars (the essential physical parameter is the
distance between the sonic point and the point where centrifugal
support is lost). (ii) A high density contrast
(
) can be formed (at least at a
few stellar radii). (iii) The velocity of the material in the
equatorial plane is considerably smaller than in the polar
direction. This is particularly important in our case, since, for
the interacting winds model to work, the late, fast wind must be
able to catch-up and interact with the density contrast.
While this mechanism is very likely to have operated in some
luminous Blue Variables like 
Car (Nota et al. 1995),
the main question that arises is:
what can cause an AGB star's envelope to rotate so rapidly (at least
a few percent of the break-up speed)? The problem here is that due
to their large moments of inertia, even when the increase in central
condensation is taken into account, typically
--
(e.g., Eriguchi et al. 1992),
and for low mass main sequence stars
. It, therefore,
appears that for this mechanism to be viable for PNe, considerable spin-up
of the AGB star's envelope is required. Probably the best agent for
inducing such a spin-up is a binary companion. I shall discuss the
possible effects of a companion in .3; here I would like to note
that a rotating AGB star as the origin for the density contrast has
also been suggested by Asida & Tuchman (1995). In
their suggestion, they make use of the fact that pulsations tend to
generate in the AGB star's atmosphere a ``tail'' of material that
extends up to about five stellar radii. In this tail (for a
rotating star), the centrifugal force can become a non-negligible
fraction of the gravitational force, thus potentially leading to
non-spherical mass ejection. According to the calculations of Asida
& Tuchman this scenario can form a modest density contrast
(
--7), but again, it requires the
AGB star to rotate at a non-negligible fraction of its break-up
rate.
Binary companions to the star can generate a density contrast in a number of ways (see also Livio 1993,1994, Soker & Harpaz 1992):
), in which the primary can fill its Roche lobe
during the AGB phase, an unstable mass transfer is obtained (this is
due to the fact that mass is being transferred from the more massive
component, which also possesses a deep convective envelope). Thus,
a common envelope (CE) phase ensues (see Iben & Livio 1993 for a
comprehensive review) in which the core of the AGB star and the
secondary spiral-in, are engulfed by a common, extended envelope. The
final outcome of a CE phase can be a substantial reduction in the
binary separation (including perhaps a merger in some cases),
accompanied by the ejection of the envelope (e.g., Rasio & Livio 1996).
Multi-dimensional hydrodynamic simulations of the CE phase have shown that due to the
fact that the spiraling-in binary deposits also angular momentum
into the envelope, mass ejection is concentrated to the orbital plane
(Livio & Soker 1988, Taam, & Bodenheimer 1989, Terman, Taam &
Hernquist 1994). Thus, CE evolution generates a density contrast
naturally.
Irrespective of the spin-up mechanism, the observation that many post AGB stars and proto PNe already show deviations from spherical symmetry (see ), demonstrates that some mechanism, which deforms the extended envelope and the mass-loss pattern of AGB stars, operates at relatively early stages (e.g., Groenewegen 1996).
; see .1).
As already noted in the introduction, some PNe exhibit highly collimated outflows (``jets''; e.g., K1--2, NGC 7009). It is not yet clear if such outflows can be the consequence of merely the inertial confinement provided by the density contrast (e.g., Icke et al. 1992), or if they require the presence of an accretion disk (which is thought to be a necessary ingredient for the formation of the jets observed in Young Stellar Objects and in AGN; a jet emanating from the center of an accretion disk has been observed in HH 30, Burrows et al. 1996). If the latter is true, then for such an accretion disk to form, a binary companion is required, to transfer mass onto the hot AGB star's core. Such a configuration is a possible outcome of the CE phase, since when the binary emerges from the CE, the secondary star may be in a bloated state (due to the accretion of high entropy material from the CE; see Soker & Livio 1994, Hjellming & Taam 1991). Another possibility is that a low mass companion spirals all the way in and is entirely dissipated to form a disk around the core (Rasio & Shapiro 1995, Soker 1996, Livio & Pringle 1996).
It is presently not fully understood how point-symmetric PNe form. However, it has been suggested by Corradi & Schwarz (1993) and Livio (1994) that these may represent intermittent ejection episodes of a precessing jet. Three-dimensional numerical hydrodynamic calculations of such a precessing jet, show that point-symmetric configurations that are very similar to the observed PNe, can indeed be obtained (Cliffe et al. 1995). Livio & Pringle (1996) suggested that the precession of the disk is a consequence of a radiation-induced warp, caused by the irradiation of the disk by the source. If this indeed represents the true formation mechanism, then the presence of a binary companion at some stage is certainly essential (to form an accretion disk).
One of the main questions that arise in relation to the binary
companion hypothesis is the question of statistics. Namely, do all
axisymmetric PNe contain (or did they contain in the past) binary
central stars. Using a population synthesis code, Yungelson,
Tutukov & Livio (1993) were able to show that 
% of all PNe
are expected to contain close binary nuclei or single nuclei that
were obtained by mergers. This fraction agrees with the fraction of
observed bipolar PNe (Corradi & Schwarz 1995). If we remember
that even very low mass (brown dwarf) companions can cause
significant deviations from spherical symmetry, then it appears that
the binary star hypothesis is not in conflict with the observations
from the statistical point of view (see also Bond 1995).
Another important question is whether or not binary companions can
generate very high density contrasts (such as those required, for
example, to reproduce the observed morphology in 
Car, see .1).
Numerical hydro calculations of the CE phase, for example,
tend to produce
only moderate contrasts (e.g., Terman, Taam, & Hernquist 1994).
However, it is possible that as the ejected material cools down, it
will collapse to the orbital plane, thus generating higher
equatorial to polar density ratios.
On the basis of the discussion presented in the previous sections, the following (deliberately conservative) conclusions can be drawn:
Several critical observations can be suggested in order to test some of the ideas presented in this paper:
Asida, S. M. & Tuchman, Y. 1995, in Asymmetrical Planetary Nebulae, eds. A. Harpaz & N. Soker (Bristol: Institute of Physics Publishing), p. 108
Balick, B. 1987, AJ, 94, 671
Balick, B. & Preston, H. L. 1988, AJ, 94, 958
Barden, S. C. & Wade, R. A. 1988, in ASP Conf. Ser. 3, Fiber Optics Astronomy, ed. S. C. Barden (San Francisco: Astron. Soc. Pac.), p. 113
Bjorkman, J. E. & Cassinelli, J. P. 1993, ApJ, 409, 429
Bond, H. E. 1995, in Asymmetrical Planetary Nebulae, eds. A. Harpaz & N. Soker (Bristol: Institute of Physics Publishing), p. 61
Bond, H. E. & Livio, M. 1990, ApJ, 355, 568
Burrows, C. et al. 1995, ApJ, 452, 680
Burrows, C. et al. 1996, in preparation
Chevalier, R. A. & Luo, D. 1994, ApJ, 421, 225
Cliffe, A., Frank, A., Livio, M., & Jones, T. W. 1995, ApJ, 447, L49
Corradi, R. L. M. & Schwarz, H. E. 1993, A&A, 268, 714
Corradi, R. L. M. & Schwarz, H. E. 1995, A&A, 293, 871
Counselman, C. C. III 1973, ApJ, 180, 307
Darwin, G. H. 1879, Proc. Roy. Soc. London, 29, 168
Eriguchi, Y., Yamaoka, H., Nomoto, K., & Hashimoto, M. 1992, ApJ, 392, 243
Frank, A., Balick, B., & Davidson, K. 1995, ApJ, 441, L77
Frank, A., Balick, B., Icke, V., & Mellema, G. 1993, ApJ, 404, L25
Groenewegen, M. A. T. 1996, A&A, in press
Harrington, I. P. & Borkowski, K. J. 1995, presented at the 185th AAS, Tucson, Arizona
Hjellming, M. S. & Taam, R. E. 1991, ApJ, 370, 70
Icke, V., Balick, B., & Frank, A. 1992, A&A, 253, 224
Icke, V., Mellema, G., Balick, B., Eulderink, F., & Frank, A. 1992, Nature, 355, 524
Kahn, F. D. 1982, in IAU Symp. 103, Planetary Nebulae, ed. D. R. Flower (Dordrecht: Reidel), p. 305
Kwok, S. 1982, ApJ, 258, 280
Kwok, S. 1993, in Luminous High-Latitude Stars, ASP Conf. Ser. 45, (San Francisco: Astron. Soc. Pac.), p. 348
Livio, M. 1993, in Planetary Nebulae, eds. R. Weinberger & A. Acker (Dordrecht: Kluwer), p. 279
Livio, M. 1994, in Circumstellar Media in the Late Stages of Stellar Evolution, eds. R. Clegg et al. (Cambridge: Cambridge University Press), p. 35
Livio, M. & Soker, N. 1988, ApJ, 329, 764
Livio, M. & Pringle, J. E. 1996, in preparation
McCray, R. & Lin, D. N. C. 1994, Nature, 369, 378
Meixner, M. 1993, Ph.D. Thesis, Univ. of California, Berkeley
Mellema, G. 1993, Ph.D. Thesis, University of Leiden
Nota, A., Livio, M., Clampin, M., & Schulte-Ladbeck, R. 1995, ApJ, 448, 788
Owocki, S. P., Cranmer, S. R., & Blondin, J. M. 1994, ApJ, 424, 887
Panagia, N., Gilmozzi, R., Macchetto, F., Adorf, H.-M., & Kirshner, R. P. 1991, ApJ, 380, L23
Paresce, F., Livio, M., Hack, W., & Korista, K. 1995, A&A, 299, 823
Pascoli, G. 1987, A&A, 180, 191
Pascoli, G., Leclercq, J., & Poulain, B. 1992, PASP, 104, 182
Pringle, J. E. 1989, MNRAS, 238, 37 p
Rasio, F. A. & Shapiro, S. L. 1995, ApJ, 438, 887
Rasio, F. A. & Livio, M. 1996, ApJ, submitted
Schwarz, H. E., Corradi, R. L. M., & Melnick, J. 1992, A&AS, 96, 23
Soker, N. 1995, in preparation
Soker, N. 1996, preprint
Soker, N. & Harpaz, A. 1992, PASP, 104, 923
Soker, N. & Livio, M. 1989, ApJ, 339, 268
Soker, N. & Livio, M. 1994, ApJ, 421, 219
Taam, R. E. & Bodenheimer, P. 1989, ApJ, 337, 849
Terman, J. L., Taam, R. E., & Hernquist, L. 1994, ApJ, 422, 729
Trammell, S. R., Dinerstein, H. L., & Goodrich, R. W. 1994, AJ, in press
Webbink, R. F. 1988, in Critical Observations Versus Physical Models for Close Binary Systems, ed. K. C. Leung (New York: Gordon & Breach), p. 403
Yungelson, L. R., Tutukov, A. V., & Livio, M. 1993, ApJ, 418, 794
Zahn, J.-P. 1977, A&A, 57, 383