For many years we are witnessing a lively debate on the existence and extent of convective overshooting, mainly in the cores of main-sequence stars. This is an important issue, since even a small amount of overshooting increases considerably the mass of the finally hydrogen exhausted core and lenghthens the main-sequence lifetime correspondingly. The available evolutionary calculations assume either moderate overshooting, d/Hp = 0.25, (d = overshooting distance, Hp = pressure scale height; Maeder & Meynet 1988) or strong overshooting, d/Hp ≈ 0.50 (Bertelli et al. 1986). Presently theory is unable to quantify the exact amount of overshooting, and one has to resort to empirical determinations.Recently, Stothers (1991) collected all available information from the literature on stellar parameters and evolutionary calculations and concluded that, within the errors, d/Hp = 0 is an acceptable result, with a conservative upper limit of d/Hp < 0.2. However, such an approach is hampered by observational errors (like distance or temperature uncertainties, rotation) that are difficult to quantify and that may mask any definitive result. Detailed investigations of detached binaries may help in this matter (Andersen et al. 1990) but the number of suitable binary systems is probably not very large.

Abstract. We follow hydrodynamically the evolution of spherical model planetary nebulae subject to different initial conditions and with various central stars, investigating how combinations of central-star mass and asymptotic giant branch mass-loss rate determine the shape and kinematics of a planetary nebula. With this approach we aim at constituting a framework useful for the interpretation of the evolutionary status and previous mass-loss history of observed individual nebulae, making use of their kinematical properties and surface brightness characteristics. In particular, the models are compared with the observed morphologies and kinematics of double shell nebulae. The dynamical structure of all the models is characterized by a more or less complicated shock wave pattern set up by ionization and wind interaction whose combined action results in general in a typical double-shell structure. We have found that models with simple initial structures based on a constant AGB massloss rate fail to comply with observed shell morphologies and surface-brightness distributions. A reasonable agreement with the observations is only found for a model where the mass-loss rate is strongly increasing towards the end of the asymptotic giant-branch evolution. Depending on the central star's evolutionary speed and the density of the cool wind expelled along the asymptotic giant-branch, planetary nebulae may never get optically thin. This is primarily the case for the more massive central stars, and this fact offers a rather natural explanation for the long standing problem of the very existence of molecular hydrogen in the immediate vicinity of hot central stars. We also show that distances to planetary nebulae based on expansion parallaxes are systematically too small by a significant amount.

We present a comprehensive observational study of haloes around planetary nebulae (PNe). Deep Hα+[N ii] and/or [O iii] narrow‐band images have been obtained for 35 PNe, and faint extended haloes have been newly discovered in the following 10 objects: Cn 1‐5, IC 2165, IC 2553, NGC 2792, NGC 2867, NGC 3918, NGC 5979, NGC 6578, PB 4, and possibly IC 1747. New deep images have also been obtained of other known or suspected haloes, including the huge extended emission around NGC 3242 and Sh 2‐200. In addition, the literature was searched, and together with the new observations an improved data base containing some 50 PN haloes has been compiled. The halo sample is illustrated in an image atlas contained in this paper, and the original images are made available for use by the scientific community at http://www.ing. iac.es/∼rcorradi/HALOES/. The haloes have been classified following the predictions of modern radiation‐hydrodynamical simulations that describe the formation and evolution of ionized multiple shells and haloes around PNe. According to the models, the observed haloes have been divided into the following groups: (i) circular or slightly elliptical asymptotic giant branch (AGB) haloes, which contain the signature of the last thermal pulse on the AGB; (ii) highly asymmetrical AGB haloes; (iii) candidate recombination haloes, i.e. limb‐brightened extended shells that are expected to be produced by recombination during the late post‐AGB evolution, when the luminosity of the central star drops rapidly by a significant factor; (iv) uncertain cases which deserve further study for a reliable classification; (v) non‐detections, i.e. PNe in which no halo is found to a level of ≲10−3 the peak surface brightness of the inner nebulae. We discuss the properties of the haloes: detection rate, morphology, location of the central stars in the Hertzsprung–Russell diagram, sizes, surface brightness profiles, and kinematical ages. Among the most notable results, we find that, as predicted by models, ionized AGB haloes are a quite common phenomenon in PNe, having been found in 60 per cent of elliptical PNe for which adequately deep images exist. Another 10 per cent show possible recombination haloes. In addition, using the kinematical ages of the haloes and inner nebulae, we conclude that most of the PNe with observed AGB haloes have left the AGB far from a thermal pulse, at a phase when hydrogen burning is the dominant energy source. We find no significant differences between the AGB haloes of hydrogen‐poor and hydrogen‐rich central stars.

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Context. Observations with space-borne X-ray telescopes revealed the existence of soft, diffuse X-ray emission from the inner regions of planetary nebulae. Although the existing images support the idea that this emission arises from the hot shocked central-star wind which fills the inner cavity of a planetary nebula, existing models have difficulties to explain the observations consistently. Aims. We investigate how the inclusion of thermal conduction changes the physical parameters of the hot shocked wind gas and the amount of X-ray emission predicted by time-dependent hydrodynamical models of planetary nebulae with central stars of normal, hydrogen-rich surface composition. Methods. We upgraded our 1D hydrodynamics code NEBEL by to account for energy transfer due to heat conduction, which is of importance at the interface separating the hot shocked wind gas ("hot bubble") from the much cooler nebular material. With this new version of NEBEL we recomputed a selection of our already existing hydrodynamical sequences and obtained synthetic X-ray spectra for representative models along the evolutionary tracks by means of the freely available CHIANTI package. Results. Heat conduction leads to lower temperatures and higher densities within a bubble and brings the physical properties of the X-ray emitting domain into close agreement with the values derived from observations. The amount of X-rays emitted during the course of evolution depends on the energy dumped into the bubble by the fast stellar wind, on the efficiency of "evaporating" cool nebular gas via heat conduction, and on the bubble's expansion rate. We find from our models that the X-ray luminosity of a planetary nebula increases during its evolution across the HR diagram until stellar luminosity and wind power decline. Depending on the central-star mass and the evolutionary phase, our models predict X-ray [0.45−2.5 keV] luminosities between 10 −8 and 10of the stellar bolometric luminosities, in good agreement with the observations. Less than 1% of the wind power is radiated away in this X-ray band. Although temperature, density, and also the mass of the hot bubble is significantly altered by heat conduction, the dynamics of the whole system remains practically the same. Conclusions. Heat conduction allows the construction of nebular models which predict the correct amount of X-ray emission and at the same time are fully consistent with the observed mass-loss rate and wind speed. Thermal conduction must be considered as a viable physical process for explaining the diffuse X-ray emission from planetary nebulae with closed inner cavities. Magnetic fields must then be absent or extremely weak.