To study the evolution of an expanding PNe formed by non-spherical stellar (super) wind we have computed seven evolutionary sequences for the dusty envelopes with mass 0.05 M⊙ taking angular distribution of mass loss and of the outflow velocity as parameters. In the case described below the gas velocity on the inner boundary is assumed: Vz=25 (1–0.4 (3 cos2 θ−1)12) km s−1 (where θ is the polar angle) with the density of ejected matter independent on θ. The mass loss rate on the (super) wind phase is 6 10−5 M⊙/yr the structure of the model at the moment of ionization breaks through PN in the polar direction is illustrated in Fig. 1. The density distribution in a meridional plane is shown in Fig. 1a together with the ionization boundary (the dashed line). Contours of equal emission measure nebula model are shown in Fig. 1b. After complete ionization of PN hydrogen distributions become smoother. We found that some of double-shell PNe may be the product of single mass loss event.

The planetary nebulae formation in the detached binaries is considered.

We will present photographic and CCD images of planetary nebulae that are known, on the basis of photometric observations of the central stars, to possess close-binary nuclei. All of the orbital periods range from 2.7 to 16 hours, except for the 16-day binary nucleus of NGC 2346.

A 14, H 3-75 and K 1-2, three planetary nebulae with binary nuclei, were imaged with narrow-band [N II], Ha, [O III] and He II filters by using the TI CCD chip on the 0.9-m telescope at CTIO. The purpose of doing the observing was to see if planetaries with known binary nuclei exhibit particularly peculiar morphologies. In some cases (e.g., NGC 1514, NGC 3132), planetaries with binary nuclei have morphologies that are exhibited by a number of nebulae. In other cases (e.g., He 2-36, the nebulae with binary central stars have unique morphologies.

Our understanding of the evolution of Central Stars of Planetary Nebulae (CPN) has made considerable progress during the last years. This was possible since consistent computations through the asymptotic giant branch (AGB), with thermal pulses and (in some cases) mass loss taken into account, became available (Schönberner, 1979, 1983; Kovetz and Harpaz, 1981; Harpaz and Kovetz, 1981; Iben, 1982, 1984; Wood and Faulkner, 1986). It turned out that the evolution depends very sensitively on the inital conditions on the AGB. More precisely, the evolution of an AGB remnant is a function of the phase of the thermal-pulse cycle during which this remnant was created on the tip of the AGB by the planetary-nebula (PN) formation process (Iben, 1984, 1987). This was first shown by Schönberner (1979), and then fully explored by Iben (1984). In short, two major modes of PAGB evolution to the white dwarf stage are possible, according to the two main phases of a thermally pulsing AGB star: the hydrogen-burning or helium-burning mode. If, for instance, the PN formation, i.e. the removal of the stellar envelope by mass loss, happens during a luminosity peak that follows a thermal pulse of the helium-burning shell, the remnant leaves the AGB while still burning helium as the main energy supplier (Härm and Schwarzschild, 1975). On the other hand, PN formation may also occur during the quiescent hydrogen-burning phase on the AGB, and the remnant continues then to burn mainly hydrogen on its way to becoming a white dwarf.

The expected distribution of planetary nebula nuclei (PNNs) on the log L-log T plane is calculated based upon modern stellar evolutionary theory, the initial mass function (IMF), and various assumptions concerning mass loss during post-main sequence evolution. The distribution is found to be insensitive to the assumed range of main-sequence progenitor mass, and to reasonable variations in the age and the star forming history of the galactic disk. Rather, the distribution is determined primarily by the heavy dependence of the evolution rate upon core mass, and secondarily upon the steepness of the IMF and other factors. The distribution is rather different than any found from observations, and probably reveals strong observational selection effects.

Central stars can be placed on the HR diagram if their effective temperature (Teff) and radii are known. Knowledge of the radius can sometimes be replaced by another indication of the luminosity. The distance, which always plays an important, really critical role, is not well known. This is the essential reason that there is so much uncertainty about the position on the HR diagram.

Planetary nebulae represent a transitory stage in the life of the majority of stars as they proceed towards the end of their nuclear evolution and descend to the domain of white dwarfs. The immediate precursors of the central stars are probably red giants which populate a part of the HR diagram far removed from the region inhabited by the central stars of well recognised nebulae. The problem of determining the initial masses is complicated by the widespread occurrence of massloss on the red giant branch. The total amount of mass lost by a star must depend upon a number of stellar parameters including the initial mass, but the exact nature of this dependence remains to be discovered and a unique relation between the final masses and initial main sequence masses is not yet available. Thus even though the mass distribution of the nuclei of planetary nebulae (NPN) has been derived in the last few years, it has not been possible to deduce from this an unambiguous initial mass distribution of the progenitors. Further, an observed sample always suffers from selection effects and, in the particular case of NPN mass distribution, this has led to irretrievable loss of information.

A non-negligible (∼ 15–20%) fraction of planetary nebulae is expected to be formed in close binaries in which one component fills its Roche lobe after the exhaustion of hydrogen or helium at its center. The nebula is ejected as a consequence of a frictional interaction between the stellar cores and a common envelope; the ionizing component of the central binary star may be a relatively high luminosity contracting star with a degenerate CO core, burning hydrogen or helium in a shell, or it may be a lower luminosity shell hydrogen-burning star with a degenerate helium core or a core helium-burning star. Even more exotic ionizing central stars are possible. Once the initial primary has become a white dwarf or neutron star, the secondary, after exhausting central hydrogen, will also fill its Roche lobe and eject a nebular shell in a common envelope event. The secondary becomes the ionizing star in a tight orbit with its compact companion. In all, there are roughly twenty different possibilities for the make-up of binary central stars, with the ionizing component being a post asymptotic giant branch star with a hydrogen- or helium-burning shell, a CO dwarf, a core helium-burning star, a shell helium-burning star with a degenerate CO core, a shell hydrogen-burning star with a degenerate helium core, or a helium degenerate dwarf, while its companion is a main sequence star, a CO degenerate dwarf, a helium star, a helium degenerate dwarf, or a neutron star. We estimate the occurrence frequency of several of these types and comment on the prior evolutionary history of 4 observed binary central stars.

When we look at evolutionary aspects of PNe, we hope to test our ideas and understanding of the origin of PNe -i.e. why and how gas is expelled from the progenitor star - and of the processes relevant in the evolution of the nebula as well as the central star.

The paper discusses the problem of planetary nebulae with massive nuclei from the point of view of their theoretical evolution and observational appearances. The available data suggest that NGC 2440, 6302, and 7027 have central stars with masses greater than 0.8 M⊙.

Planetary nebulae (PNe) are very useful as a tool for testing the theory of stellar evolution. The most widely applied method in this respect is the Hertzsprung-Russell (H-R) diagram. However, the observed positions of planetary nebulae nuclei (PNNi) on the H-R diagram are subject to large uncertainties, mostly due to inaccurate distances to them. On the other hand, the (absolute visual magnitude, age)-diagram also is not free of this problem. Therefore, an attempt has been done to develop a new method which is distance-independent. For comparison between theory and observations we propose the I (Hell λ 4686) /I(H β) versus log [I(H β, PN)/IC (H β, PNN)] diagram. Both ratios reflect the evolutionary status of the central star and the surrounding nebula. Consequently, such diagram is a valuable tool for studying common evolution of the PNN-PN system.

The mass distribution of central stars (CPN) as derived by the Schönberner method (1981) M⊙ vs. age, v(exp) = const, for an enlarged local ensemble, as presented at the London Symposium, 1983, appears to be much narrower and more strongly peaked towards smaller masses than the one recently derived by Heap and Augensen (1987) (HA) using the same method, but IUE data and M⊙ (λ 1300) vs. age, corrected for individual v(exp). Whereas according to Schönberner 65% of all CPN have M < 0.64 M⊙, HA find only 44% below the same limit. We demonstrate that this discrepancy is entirely due to the fact, that HA use Daub and 0.9 × Cahn/Kaler distances, whereas Schönberner used 1.3 × CK. We list a number of arguments which favor the larger distances, especially the recent work by Méndez et al. (preprint, 1987) (Teff/g determinations) and investigations of Magellanic Cloud PN by Aller et al. (1987), Wood et al. (1987) and Barlow (1987) which all indicate a scale ≥. 1.4 × CK. If one uses Barlow's recalibration formula for optically thick PN, the distances for those - which mainly contribute to the massive CPN in the HA analysis - are increased so much as to remove most of them from the local ensemble. We thus obtain for the revised IUE ensemble 84% CPN with M < 0.64 M⊙, in better agreement with results for white dwarfs (70%) (cf. Weidemann, 1987).

The more massive component star evolves faster than the less massive one. When it fills its inner critical Roche lobe at the red-giant stage or at the asymptotic-giant-branch (AGB) star stage, the mass transfer begins from the more massive to the less massive component. Since the separation decreases with the mass being transferred, the more massive component star eventually overfills its outer critical Roche lobe. The mass outside the outer critical Roche lobe flows out of the system and the outgoing matter carries away the orbital angular momentum. As a result, the separation of the binary shrinks and the size of the outer critical Roche lobe drops. This shrinkage of the Roche lobe enhances the systemic mass outflow. This process is almost dynamically unstable because the deep convective envelope responses the loss of the envelope mass in an almost dynamical time scale. This dynamical process will stop when most of the hydrogen-rich envelope of the more massive component is lost and its radius becomes less than the radius of the outer critical Roche lobe.

We compare theoretical evolutionary tracks of planetary nebulae nuclei with observational data on over a hundred planetary nebulae in the (log L, log Teff, log texp) space. The simultaneous use of the three coordinates eliminates some interpretation that might be proposed when looking at the (log L, log Teff) plane and at the (Mv, log texp) only. The inconsistencies which we find between theory and observations could be partly removed by adopting a different distance scale.

We have constructed a series of model planetary nebulae along a sequence of evolutionary models for the central star, taking into account the expansion of the nebula. The calculations have been performed using the computer code PHOTO, which calculates the intensities of the emission lines emitted by a nebula in ionization and thermal equilibrium.

The relation between nebular excitation E(He II λ4686/Hβ-ratio) and absolute visual magnitude of the central star (CS) is compared with hydrodynamical models of planetary nebulae (PNe) from Schmidt-Voigt and Köppen (Astron. Astrophys., 174, 211 and 223) (see figure below, data from D. Schönberner, Astron. Astrophys., 169, 189). Models marked by drawn lines have a 0.644 M⊙ CS following a Schönberner track, an initially expelled PN of 0.1 M⊙, and different mass loss rates of the precursor star on the AGB, described by the Reimers parameter η;η = 1 corresponds to a mass loss rate of 1.55 × 10−6M⊙ α−1 the dashed line model has a higher initially expelled mass (0.3 M⊙), the dash-dotted line model a CS of 0.6 M⊙ which evolves more slowly. Model numbers refer to the above cited studies. Since MV increases with evolutionary time, the MV axis represents a (highly) nonlinear time axis: for MV < 4 the CS heats up towards its temperature maximum and the PN is optically thin. Differences for high excitation nebulae are most probably due to different helium abundances. When the rate of ionizing photons decreases as the nuclear energy sources extinguish (MV > 4), the excitation may decline, depending on the density in the nebula. For the so called “accreting models” (M > 10−6M⊙ α−1) the mass accretion from the AGB wind determines the density hence nebular excitation. For an AGB mass loss rate M < 10−5M⊙α−1 the numerical results approximately fit an exponential law E= E0exp (-M⊙) with E0 ≊ 1.1 and M⊙ ≊ 6.1 × 10−6M⊙ α−1. From the spread of the observed E(MV = 4) we conclude a mean AGB mass loss rate of 6.+3.3−2.3 10−6M⊙ α−1 within 1σ error bars. Obviously the model 11 reproduces the data best since most of the observed objects are found in the dark shadowed regions of the histogram. This is totally consistent with our previous results (cited above). The colliding-wind models, having no initially PN, behave quite similar as model 11.

Studies of hot white dwarf samples constrain the properties and evolution of planetary nuclei and the nebulae. In particular, the white dwarf and planetary nebulae formation rates are compared. I discuss the overlap of the sequences of white dwarfs having hydrogen (DA) and helium-rich (DO) atmospheres with known central stars of high surface gravity. There is evidence that the hydrogen atmosphere nuclei have “thick” outer hydrogen layers (≳ 10−4 M⊙), but that DA white dwarfs may have surface hydrogen layers orders of magnitude thinner. Finally, a DA planetary nucleus is discussed (0950+139) which has undergone a late nebular ejection; this object may be demonstrating that a hydrogen layer can be lost even after the star has entered the white dwarf cooling sequence.

This paper reviews the properties and evolutionary status of white dwarf stars, focusing most closely on those aspects which are likely to be of significance to understanding the ultimate fate of planetary nebulae and their central stars. White dwarf stars show a broad variety of chemical compositions. Broadly speaking, they are divided into the DA stars (with H-rich photospheres) and the non-DA stars (with He-rich photospheres), though there are a fairly large number of subtypes. The mass distribution of white dwarf stars is quite narrow, with a mean value near 0.6 and with extremes at 0.43 and 1.05. Different varieties of trace elements (such as C, N, 0, Si, Ca, and Mg) are quite common. I will review several recent proposals for explaining these abundance patterns. A particularly significant question is whether processes operating while the star cools as a white dwarf can account for their variety, or whether at least part of the white dwarf phenomenology is related to events which took place when the object was a planetary nebula or even earlier.

To review or attempt to summarize a conference such as this recalls the request our department office once received from a little fourth-grade schoolgirl: “I'm doing a science project on the stars. Tell me all about them on two pages.” We can only try to look at the broad picture and attempt to identify problems that require special emphasis or attention.