Classification of planetary nebulae by their departure from axisymmetry

We propose a scheme to classify planetary nebulae (PNe) according to their departure from axisymmetric structure. We consider only departure along and near the equatorial plane, i.e. between the two sides perpendicular to the symmetry axis of the nebula. We consider six types of departure from axisymmetry: (1) PNe where the central star is not at the centre of the nebula; (2) PNe having one side brighter than the other; (3) PNe having unequal size or shape of the two sides; (4) PNe where the symmetry axis is bent, e.g. the two lobes in a bipolar PN are bent toward the same side; (5) PNe where the main departure from axisymmetry is in the outer regions, e.g. an outer arc; and (6) PNe that show no departure from axisymmetry, i.e. any departure, if it exists, is on scales smaller than the scale of blobs, filaments and other irregularities in the nebula. PNe that possess more than one type of departure are classified by the most prominent type. We discuss the connection between departure types and the physical mechanisms that may cause them, mainly resulting from the influence of a stellar binary companion. We find that ∼50 per cent of all PNe in the analysed sample possess large-scale departure from axisymmetry. This number is larger than that expected from the influence of binary companions, namely ∼25–30 per cent. We argue that this discrepancy comes from many PNe where the departure from axisymmetry, mainly unequal size, shape or intensity, results from the presence of long-lived and large (hot or cool) spots on the surface of their asymptotic giant branch progenitors. Such spots locally enhance the mass-loss rate, leading to a departure from axisymmetry, mainly near the equator, in the descendent PN.     

Dust formation and inhomogeneous mass-loss from asymptotic giant branch stars

We examine the flow from asymptotic giant branch (AGB) stars when along a small solid angle the optical depth resulting from dust is very large. We consider two types of flows. In the first, small cool spots are formed on the surface of slowly rotating AGB stars. Large quantities of dust are expected to be formed above the surface of these cool spots. We propose that if the dust formation occurs during the last AGB phase when the mass-loss rate is high, the dust shields the region above it from the stellar radiation. This leads to both further dust formation in the shaded region and, owing to lower temperature and pressure, the convergence of the stream toward the shaded region, and the formation of a flow having a higher density than its surroundings. This density contrast can be as high as ∼4. A concentration of magnetic cool spots toward the equator will lead to a density contrast of up to a few between the equatorial and polar directions. This process can explain the positive correlation between high mass-loss rate and a larger departure from sphericity in progenitors of elliptical planetary nebulae. In the second type of flow, the high density in the equatorial plane is formed by a binary interaction, where the secondary star is close to, but outside the AGB envelope. The shielding of the radiation by dust results in a very slow and dense flow in the equatorial plane. We suggest this flow as an alternative explanation for the equatorial dense matter found at several hundred astronomical units around several post-AGB binary systems.     

Turbulent dynamo in asymptotic giant branch stars

Using recent results on the operation of turbulent dynamos, we show that a turbulent dynamo may amplify a large-scale magnetic field in the envelopes of asymptotic giant branch (AGB) stars. We propose that a slow rotation of the AGB envelope can fix the symmetry axis, leading to the formation of an axisymmetric magnetic field structure. Unlike solar-type αω dynamos, the rotation has only a small role in amplifying the toroidal component of the magnetic field; instead of an αω dynamo we propose an α ² ω . The magnetic field may reach a value of     , where B _e is the equipartition (between the turbulent and magnetic energy densities) magnetic field. The large-scale magnetic field is strong enough for the formation of magnetic cool spots on the AGB stellar surface. The spots may regulate dust formation, and hence the mass-loss rate, leading to axisymmetric mass loss and the formation of elliptical planetary nebulae (PNe). Despite its role in forming cool spots, the large-scale magnetic field is too weak to play a dynamic role and directly influence the wind from the AGB star, as required by some models. We discuss other possible problems in models where the magnetic field plays a dynamic role in shaping the AGB winds, and argue that they cannot explain the formation of non-spherical PNe.     

Magnetic field, dust and axisymmetrical mass loss on the asymptotic giant branch

I propose a mechanism for axisymmetrical mass loss on the asymptotic giant branch (AGB) that may account for the axially symmetric structure of elliptical planetary nebulae. The proposed model operates for slowly rotating AGB stars, having angular velocities in the range of 10⁻⁴ω _Kep  ω  10⁻² ω_Kep, where ω_Kep is the equatorial Keplerian angular velocity. Such angular velocities could be gained from a planet companion of mass  0.1  M _Jupiter, which deposits its orbital angular momentum to the envelope at late stages, or even from single stars that are fast rotators on the main sequence. The model assumes that dynamo magnetic activity results in the formation of cool spots, above which dust forms much more easily. The enhanced magnetic activity towards the equator results in a higher dust formation rate there, and hence higher mass-loss rate. As the star ascends the AGB, both the mass-loss rate and magnetic activity increase rapidly, and hence the mass loss becomes more asymmetrical, with higher mass-loss rate closer to the equatorial plane.     

The determination of progenitor masses for planetary nebulae

We have evaluated the likely progenitor masses M _PG of nebulae having elliptical, circular and bipolar morphologies, using observed ratios between the populations of these sources, and deduced central star mass functions. We find that most bipolar nebulae (BPNe) are likely to arise from progenitors having mass M _PG>2.3 M_⊙ and spectral types earlier than A3.2, whilst circular sources are associated with progenitors of mass 1.0 M_⊙< M _PG<1.2 M_⊙ and spectral range G1.9–F7.8 . Elliptical sources arise from intermediate-mass progenitors. The procedures employed to determine these values are relatively insensitive to uncertainties in scaleheights and population ratios, and completely insensitive to uncertainties in the distance scale. They are, however, dependent upon the precise forms adopted for the initial–final and central star mass functions, and we discuss the sensitivity of M _PG to uncertainties in these functions.     

Stellar structure and mass loss on the upper asymptotic giant branch

We examine the envelope properties of asymptotic giant branch (AGB) stars as they evolve on the upper AGB and during the early post-AGB phase. Because of the high mass-loss rate, the envelope mass decreases by more than an order of magnitude. This makes the density profile below the photosphere much shallower, and the entropy profile much steeper. We discuss the possible role of these changes in the profiles in the onset of the high mass-loss rate (superwind) and the large deviation from spherical mass loss at the termination of the AGB. We concentrate on the idea that the shallower density profile and steeper entropy profile allow the formation of cool magnetic spots, above which dust forms much more easily.     

Backflow in post-asymptotic giant branch stars

We derive the conditions for a backflow toward the central star(s) of circumstellar material to occur during the post-asymptotic giant branch (post-AGB) phase. The backflowing material may be accreted by the post-AGB star and/or its companion, if such exists. Such a backflow may play a significant role in shaping the descendant planetary nebula, by, among other things, slowing down the post-AGB evolution, and by forming an accretion disc which may blow two jets. We consider three forces acting on a slowly moving mass element: the gravity of the central system, radiation pressure, and fast wind ram pressure. We find that for a significant backflow to occur, a slow dense flow should exist, such that the relation between the total mass in the slow flow, M _i , and the solid angle it covers Ω, is given by     , where     . The requirement for both a high mass-loss rate per unit solid angle and a very slow wind, such that it can be decelerated and flow back, probably requires close binary interaction, hence this process is rare.     

Radially aligned clumps and tails in planetary nebulae

We study the formation of radially aligned condensations and tails through the compression of material inside ionization shadows at early ionization phases of planetary nebulae. A dense clump, formed before ionization starts, forms an ionization shadow behind it. The surroundings, which are ionized before the shadow, have a higher temperature, and as a result compress the material in the shadow, forming a compressed tail. If the compressed tail crosses a dense shell, a dense condensation (clump) is formed there. At later stages this condensation is ionized and observed as a bright knot, radially aligned with the inner clump. We find that for the shadow to be effective, the clump should be already present as the ionization by the central star starts, and its density enhancement should be by a factor of ≳ 5. We propose this mechanism as an explanation for the radially aligned condensations recently found in the planetary nebula IC 4593.     

Detecting planets in planetary nebulae

We examine the possibility of detecting signatures of surviving Uranus/Neptune-like planets inside planetary nebulae. Planets that are not too close to the stars (orbital separation larger than ∼5 au) are likely to survive the entire evolution of the star. As the star turns into a planetary nebula, it has a fast wind and strong ionizing radiation. The interaction of the radiation and wind with a planet may lead to the formation of a compact condensation or tail inside the planetary nebula, which emits strongly in H α , but not in [O  iii ]. The position of the condensation (or tail) will change over a time-scale of ∼10 yr. Such condensations might be detected with currently existing telescopes.     

Low-mass binary-induced outflows from asymptotic giant branch stars

A significant fraction of planetary nebulae (PNe) and protoplanetary nebulae (PPNe) exhibit aspherical, axisymmetric structures, many of which are highly collimated. The origin of these structures is not entirely understood, however, recent evidence suggests that many observed PNe harbour binary systems, which may play a role in their shaping. In an effort to understand how binaries may produce such asymmetries, we study the effect of low-mass  (<0.3 M_⊙)  companions (planets, brown dwarfs and low-mass main-sequence stars) embedded into the envelope of a  3.0-M_⊙  star during three epochs of its evolution [red giant branch, asymptotic giant branch (AGB), interpulse AGB]. We find that common envelope evolution can lead to three qualitatively different consequences: (i) direct ejection of envelope material resulting in a predominately equatorial outflow, (ii) spin-up of the envelope resulting in the possibility of powering an explosive dynamo-driven jet and (iii) tidal shredding of the companion into a disc which facilitates a disc-driven jet. We study how these features depend on the secondary's mass and discuss observational consequences.     

Magnetic fields in planetary nebulae and post-AGB nebulae

Magnetic fields are an important but largely unknown ingredient of planetary nebulae. They have been detected in oxygen-rich asymptotic giant branch (AGB) and post-AGB stars, and may play a role in the shaping of their nebulae. Here we present SCUBA submillimetre polarimetric observations of four bipolar planetary nebulae and post-AGB stars, including two oxygen-rich and two carbon-rich nebulae, to determine the geometry of the magnetic field by dust alignment. Three of the four sources (NGC 7027, 6537 and 6302) present a well-defined toroidal magnetic field oriented along their equatorial torus or disc. NGC 6302 may also show field lines along the bipolar outflow. CRL 2688 shows a complex field structure, where part of the field aligns with the torus, whilst an other part approximately aligns with the polar outflow. It also presents marked asymmetries in its magnetic structure. NGC 7027 shows evidence for a disorganized field in the south-west corner, where the SCUBA shows an indication for an outflow. The findings show a clear correlation between field orientation and nebular structure.     

The low-excitation structures of planetary nebulae

The low excitation properties of the planetary nebula (PN) NGC 6720 are known to be unusual, and to imply large ring/core emission ratios. We point out that such characteristics are by no means confined to this source alone, and that high ratios may occur in a large fraction of elliptical and circular PNe. Such trends may arise because of the presence of thin low-excitation emission sheets 'wrapped' within and around the primary outflows. The widths of such shells are required to be exceedingly small, and may (for certain cases) be of order ≪10⁻² pc. Such a mechanism appears capable of explaining most of the observed emission properties, and may arise through shock interaction between differing envelopes. Alternative explanations in terms of bipolar or cylindrical outflows are shown to be implausible.     

Asymmetry and inhomogeneity in proto- and young planetary nebulae

I study some effects of aspherical mass loss during the last stages of the asymptotic giant branch (AGB) on the appearance of proto-planetary nebulae (proto-PNs) and young PNs. The aspherical mass loss can be small-scale inhomogeneities, and/or axially symmetric mass-loss geometry. I first examine the role of the dust opacity in the optical band on the appearance of proto-PNs. I conclude that large optical depths will be found in proto-PNs that are post-AGB stars having high equatorial mass-loss rates, which require a stellar binary companion for their existence. In these cases light from the central star will reach larger distances along and near the polar directions, leading to the appearance of an elongated reflection nebula. These proto-PNs will become bipolar PNs, i.e., PNs with two lobes and an equatorial waist between them, or extreme ellipticals, e.g., a ring but no lobes on the two sides of the equatorial plane. I then derive the conditions for the enhancement of non-radial density inhomogeneity by the propagation of the ionization front at the early PN stages. The ionization will proceed faster in the radial direction along low-density regions. The low-density regions will be heated earlier, and they will expand as a result of their higher pressures, reducing further their densities. The opposite occurs in high-density regions. The condition for this ionization instability to develop is that the ionization time difference between two directions at the same radius is longer than the sound crossing time between these two regions. This condition for the ionization front instability can be expressed as a condition on the mass-loss rate inhomogeneity, i.e., its dependence on direction.