Extensive Montecarlo simulations of Post-Asymptotic Giant Branch (P-AGB) populations have been constructed, exploring the effects of various assumptions on synthetic H-R diagrams, luminosity functions, and inferred mass distributions. Such assumptions include the IMF, the initial mass-final mass relation, the AGB to PN transition time, the duration of the planetary nebula (PN) stage, etc. We have also investigated how the observational errors in luminosity and temperature propagate into the inferred mass distribution of the P-AGB stars.

Four new calculations of planetary nebulae spectral evolution are presented, as in Volk (1992). These models use the 0.64 M⊙ central star evolution track of Schönberner (1983) but with the rate of evolution accelerated by a factor of 2, as the original models evolve to the planetary nebula phase too slowly to match the observations. Models were calculated for mass-loss rates of 2.1 × 10−5 and 5.2 × 10−5 MM⊙ yr−1 using solar composition and silicate dust, and using the average observed planetary nebula composition and graphite dust. An interacting winds shell was assumed to form. The model results were combined with an assumed Galactic distribution of 25000 planetary nebula to simulate a variety of observables including V magnitudes, Hβ fluxes, the IRAS colours, the 5 GHz radio flux densities, and the nebular radii.

Stars of mass 1–5 MM⊙ and composition Y=0.25 and Z=0.016 have been evolved from the main-sequence to the white dwarf stage with an empirical mass loss formula based on observations of mass loss rates in AGB stars. This mass loss formula (Wood 1990) causes the mass loss rate to rise exponentially with pulsation period on the AGB until superwind rates are achieved, where these rates correspond to radiation pressure driven mass loss rates. The formula was designed to reproduce the maximum periods observed for optically-visible LPVs and it also reproduces extremely well the maximum AGB luminosities observed in star clusters in the Magellanic Clouds (see Vassiliadis and Wood 1992 for details).

We investigated the question how the evolution of post-AGB models depends on their history, i.e. on their initial mass and AGB evolution. Therefore, we calculated the evolution of a 3 and 5M ⊙ star from the main sequence towards the stage of white dwarfs. These models suffered from 9 and 17 thermal pulses on the AGB, resp., and the common mass-loss law led to final masses of 0.61 and 0.84M ⊙, resp., which are consistent with reasonable initial-final mass relationships. It was found that more massive AGB remnants fade much more slower than hitherto assumed. Thus, we conclude that only a reliable combination of initial and final mass yields the right fading time scales for more massive post-AGB models. To prove that we have recalculated the evolution of the 3M ⊙ model with another mass-loss law leading to 86 thermal pulses and a remnant mass of 0.84M ⊙, a combination which, however, does not comply with initial-final mass relations. Comparing now the post-AGB evolution of the two massive models of equal remnant mass (0.84M ⊙) but different initial masses (3 and 5M ⊙, resp.) yields completely different fading time scales. Thus we confirm by direct calculations the suggestion of Blöcker and Schönberner (1990, A&A 240, L11) that not only the remnant mass but also the initial mass determines the time scales of more massive central stars.

Making use of the results from recent infrared and radio surveys of planetary nebulae, we have selected 431 nebulae to form a sample where a number of distance-independent parameters (e.g., Tb , Td , I60μm and IRE) can be constructed. In addition, we also made use of other distance-independent parameters ne and T∗ where recent measurements are available. We have investigated the relationships among these parameters in the context of a coupled evolution model of the nebula and the central star. We find that most of the observed data in fact lie within the area covered by the model tracks, therefore lending strong support to the correctness of the model. Most interestingly, we find that the evolutionary tracks for nebulae with central stars of different core masses can be separated in a Tb -T∗ plane. This implies that the core masses and ages of the central stars can be determined completely independent of distance assumptions. The core masses and ages have been obtained for 302 central stars with previously determined central-star temperatures. We find that the mass distribution of the central stars strongly peaks at 0.6 M⊙, with 66% of the sample having masses <0.64 MM⊙. The luminosities of the central stars are then derived from their positions in the HR diagram according to their core masses and central star temperatures. If this method of mass (and luminosity) determination turns out to be accurate, we can bypass the extremely unreliable estimates for distances, and will be able to derive other physical properties of planetary nebulae.

A principally new, quantitative system of the classification of spectra of planetary nebulae is proposed. The excitation class of a nebula, p, is determined according to the relative intensities of emission lines, N1+N2/4686 HeII and N1+N2/Hβ. The excitation classes are obtained for 177 PN with known distances and sizes of all classes – low (p=1–3), middle (p=4–8) and high (p=9–12+). An empirical relationship between the excitation class p and the mean radius of the nebulae Rn is discovered – the largest sizes occur for highly excited nebulae, and the smallest for low excitation ones. This relationship as well as excitation class p, as an independent parameter admit an evolutionary interpretation (Gurzadyan, Egikyan 1991).

A large set of narrow-band images of planetary nebulae (PNe) have been studied together with the location of their nuclei (PNNi) on the logT eff – logL/L ⊙ plane, in order to disclose possible correlations between the morphological class of the PNe and the evolutionary stage of their PNNi.

A grid of homogeneous models of evolution of hydrogen burning planetary nebulae nuclei, assuming different stellar winds and the zero points for the post-AGB evolution, have been constructed from original Schönberners tracks. Following a simplified line-driven wind theory the mass loss rate has been adopted to be

Ultraviolet spectra taken with the IUE satellite indicate that the central star of the planetary nebula, NGC 2392, has declined in brightness by 7% per decade. We interpret this fading as a consequence of evolution toward higher temperature. With this interpretation, the rate of optical fading suggests that the stellar mass is 0.73 M ⊙.

We derive estimates of the masses of planetary nebulae central stars (CSPN), based on their rate of optical-UV fading.

The central stars of the planetary nebulae He 2–131 and He 2–138 show variations in their visual magnitudes, with amplitudes of about 0.1 mag. and time scales of a few hours. This behavior appears to be very similar to that exhibited by the central stars of IC 418 and IC 4593. These four central stars have several other characteristics in common: a relatively low effective temperature, between 27000 and 40000 K; clear spectroscopic evidences of mass loss, both in the ultraviolet (IUE) and visible spectral regions; and short-term spectroscopic variability, in the form of radial velocity variations and/or of substantial changes in emission and P-Cygni-type line profiles. None of these central stars has shown convincing evidence of binarity; we attribute their behavior to variations in the stellar winds.

The enormous potential of direct imaging CCDs with respect to stellar photometry was soon discovered after these detectors became available for standard instrumentation at modern telescopes. Among favourable properties like high quantum efficiency, linearity, and large dynamic range the multiplexing advantage of the 2-dimensional detector has permitted to perform quantitative work that otherwise would have been impossible with classical photoelectric photometry. Striking examples for this are the progress in constructing colour magnitude diagrams for globular clusters (see e.g. Hesser et al. 1987, their Fig.9) or the high precision (down to the mmag level) achieved in differential photometry on ensembles of stars (Gilliland and Brown 1988). Several groups have also used CCDs for time series measurements employing specialized instruments and/or proper observing strategies (Dunham et al. 1985, Howell and Jacoby 1986, Stover and Allen 1987). If high time resolution (on the order of seconds or less) is required, however, the photoelectric method is still superior to CCDs mainly because of problems like data rates and readout time overhead (Barwig 1987).

Variability of the [OIII]4363/4340 H γ ratio in IC 4007 was established in 1956 by William Liller and L.H. Aller who attributed the changes to a gradual decrease of electron density with time. Subsequent 4363/4340 ratio fluctuations negated this explanation. Ferland pointed out that small changes in the radiative flux of the Planetary nebula nucleus (PNN) could explains the variations. Our pervious study emphasized IUE observations, here we compare high dispersion spectra obtained with the Hamilton Echelle Spectrograph with previous measurements to asses line intensity variations. Emission line variability in PNN spectra as noted by Mendez et al. (1988) and by other for HeII 4686 in NGC 6572 may offer significant clues. PNN 4686 appeared by 1990 in IC 4997. Possibly both of these PNN may be evolving into Wolf-Rayet objects, but this development does not necessarily imply that the nebular excitation will increase with time.

The first two pulsating central stars of planetary nebulae to be discovered were those of K 1–16 (Grauer & Bond 1984) and Lo 4 (Bond & Meakes 1990). They are nonradial, multiperiodic g-mode pulsators, with typical periods near 25–31 min. They are O VI nuclei or related objects, with extremely high temperatures (T eff ≳ 100,000 K), hydrogen deficiency, and high abundances of C and O.

As reported in a contributed paper at this symposium, six “O VI”-type planetary nuclei are known to be pulsating variables. Through the techniques of asteroseismology, it should be possible to explore the interior structures of these stars, determine their masses and rotation rates, and measure the stellar evolutionary timescales through observations of changes in the pulsation periods.

In September 1991 we started a photoelectric monitoring of O VI PNNi that are candidate to be non radial pulsators. The observations were obtained using the two head photometer described by Piccioni et al. (1979, Acta Astron. 29,463), mounted on the 1.5 m telescope of the Bologna Observatory. We generally used the B and sometimes the U filter; only BA 1 was always observed without filters because of its faintness. The reductions have been pursued by means of a program that yields the moving averages of the counts of the variable and comparison star. For the search of periodicities the methods of Deeming (Kurtz 1985, MNRAS 213,773) and Scargle (1982, Ap J 263,835) were principally used. The list of observations is reported in the following Table, where σ is the mean value of the standard deviations obtained by computing the moving averages.

We performed detailed spectral analysis of the planetary nebula NGC 2371 and its nucleus. The central star of NGC 2371 is a member of the 0 VI PNNi class, and it shows luminosity variations (Bond & Ciardullo 1990, ASP Conf. Ser. vol 11, Confrontation between Stellar Pulsation and Evolution, C. Cacciari & G. Clementini (eds.), p. 529) that could be associated to nonradial pulsations. From the spectrum of NGC 2371 we calculate the nebular parameters and the abundance of the most prominent ions. The nucleus is hot (Teff ≥ 120,000K) and luminous (V=15.4), it is probably close to the blue bend of the post-AGB evolutionary sequence, and shows prominent O VI emission with (so far) unique double narrow-broad feature, as shown in the Figures. This feature can not be related to the shock front of the fast wind into the planetary nebula. This star has been analyzed together with the other O VI PNNi known. A preliminary correlation between the stellar parameters and the total O VI strength have been derived, and the locus of NGC 2371 on the logT eff – logL/L ⊙ plane have been studied in relation to the locus of the post-AGB nonradial instability strips. These results, together with a study on the other O VI central stars of planetary nebulae, will be published in the near future.

The nonradially pulsating GW Vir (a.k.a. DOV, or pulsating PG1159) stars and the K1–16 type variable stars provide an unparalleled opportunity to probe the internal structure of planetary nebula central stars and their immediate descendants, hot pre-white dwarfs. Recent global photometry campaigns have provided data of sufficient quality to severely constrain evolutionary models of these stars.

The nucleus of the PN Lo4 is very hot and H-deficient and may be classified as a PG 1159 star (Werner 1992). Besides K 1–16, it is the second known pulsating central star. New spectra were taken between May 1991 and Febr. 1992. Within 18 days we witnessed a rapid decline of an emission line phase, which has begun less than 7 months ago. During this time Lo4 has changed its spectral type from PG 1159 to early WC (WC2 or WC3) and back to PG 1159. This phenomenon has never been observed before in hot post-AGB stars. The event is interpreted as an intrinsic phenomenon. Because of the short time scales, the variations are probably confined to the outermost stellar layers. It is known that the pulsation driving zones are close to the stellar surface and we speculate about a causal relation between enhanced mass-loss and possible variations in the pulsation behaviour. Spectral analysis was performed using NLTE model codes for spherically expanding atmospheres (Hamann et al. 1991) to analyze the WC-type spectrum and for plane-parallel static atmospheres (Werner 1992) to analyze the PG 1159 type spectrum. We find T eff=120kK and log g=5.5 during the PG 1159 phase. For the WC phase we obtain the same T eff and the mass-loss rate log (·/(M⊙/yr))=−7.3. The element abundances are typical for PG 1159 stars (He:C:O=46:43:ll, by mass) and v∞=:4000 km/s. More details can be found in Werner et al. (1992).

The search for old planetary nebulae around hot white dwarfs, PG 1159 stars, and sdO stars is subject of intensive studies (e.g. Kwitter et al. 1989). We report here on the discovery of such a nebula around the white dwarf GD 561.