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Astron. Astrophys. 334, 239-246 (1998)

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1. Introduction

The interacting stellar winds (ISW) model (Kwok et al., 1978; Kahn, 1983; Kwok, 1983) is nowadays widely accepted as a basic theory for the formation of the planetary nebulae (PNe). This seems to be so since: first, it is a natural consequence of the evolution of the central stars of the PNe (CSPN); second, it solves the problem with the 'sharpness' of the inner edge of the PNe, third, the ISW model is very successful in explaining the variety of shapes (symmetric as well as asymmetric) of the PNe. On the other hand, the ISW theory received much support from the observed fast winds in the central stars of PNe (CSPN), recognized to be a quite common phenomenon (e.g., Perinotto, 1993). The high velocities (600-3500  km s-1) of the CSPN winds (Patriarchi & Perinotto, 1991), are, according to the ISW model, directly responsible for an high gas temperature in the hot bubble, which is then expected to be the source of an extended X-rays and extreme ultraviolet (EUV) radiation. The PNe should also emit infrared coronal lines (IRCL) of highly ionized species since the high temperature plasma of the hot bubble is in contact with the much colder outer shell (optical PN). As a result, the thermal conductivity is expected to play an important role for the physics of the hot bubble and an extended region of intermediate temperatures (5 [FORMULA] 105 - 106  K) must exist, much suited for the production of IRCL radiation (e.g., Greenhouse et al., 1993). Having this in mind, it is starightforward to conclude that a direct observational evidence for the hot bubble existence is a keypoint in the ISW model. This is why modelling of the hot-bubble characteristics and comparing them with the corresponding observables is of a great importance in order to check the validity of the model.

In this study we make use of the two-winds PN model by Zhekov & Perinotto (1996, ZhP throughout this text) in order to describe the detailed structure of the hot bubble. This is a simple 1-D model based on a similarity solution which takes into account the time-dependent characteristics of the CSPN wind as well as the effects of thermal conductivity. The latter mechanism is capable of explaining why the temperature of the X-ray emitting gas in PNe has a lower value than what is suggested by the postshock temperature corresponding to the CSPN wind velocities. Thus, the thermal conductivity effects can explain the 'softness' of the PNe X-ray spectra. For example, the observed X-ray spectra of some PNe suggest a gas temperature of a few million degress (e.g., Kreysing et al., 1992, Arnaud et al., 1996) and the shape of the spectrum is hard to reconcile with a blackbody emission corresponding to the photospheric temperature of the CSPN in these objects. On the other hand, if even a weak magnetic field is present in the PN, the effect of the thermal conductivity will be strongly suppressed in direction perpendicular to the field lines. Soker (1994) was the first who pointed out that heat conduction fronts may play an important role for the PNe physics. He also discussed the interaction of the thermal conductivity with magnetic fields. Since there is no direct evidence for the magnetic fields in PNe, it is our impression that a 'pure' conductivity model can be used to try explaining some observables of the hot bubble in PNe. Also, one of the main advantages of such a model is its simplicity in geometry since introducing of magnetic fields in the PNe physics will have as a consequence an increase of the dimensions of the problem (from 1-D to 2-D or even 3-D). Moreover, up to now the hydrodynamic simulations have paid little attention to the hot-bubble observables and this is well understood since it is technically hard to follow the PN evolution for a relatively long period of time (e.g., for a few tousand years) and also to have enough spatial (grid) resolution over the whole nebula (the optical nebula [FORMULA] the hot bubble). For example, Mellema & Frank (1995) have discussed the hot-bubble structure in some details but only for relatively young PNe ([FORMULA]  years).

Another important item which should be addressed is whether the ISW model is consistent with the other theories which apply to the CSPN (e.g., the theory of stellar evolution, the radiation-driven winds model etc.), that is to have a general view of the complex object PN consisting of the nebula itself as well as of its central star. Namely, since acording to the ISW model, the formation of a PN is a consequence of its central star evolution, then, the global characteristics of the PN as well as the properties of its hot bubble, being of main interest in this study, should not be arbitrarily derived by simply fitting the hot-bubble observables but must be related to the physical parameters of the CSPN itself.

The aim of this work is to consider the ISW model in the frame of this so called 'general picture' for the PNe which is described in Sect. 2. Results of the application of the model to NGC  6543 and NGC  6826 are presented in Sect. 3. The conclusions follow in Sect.4.

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© European Southern Observatory (ESO) 1998

Online publication: May 12, 1998

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