The role of heat conduction to the formation of [WC]-type planetary nebulae

Abstract

Abstract. X-ray observations of young Planetary Nebulae (PNe) have revealed diffuse emission in extended regions around both H-rich and H-deficient central stars. In order to also reproduce physical properties of H-deficient objects, we have, at first, extended our time-dependent radiation-hydrodynamic models with heat conduction for such conditions. Here we present some of the important physical concepts, which determine how and when a hot wind-blown bubble forms. In this study we have had to consider the, largely unknown, evolution of the CSPN, the slow (AGB) wind, the fast hot-CSPN wind, and the chemical composition. The main conclusion of our work is that heat conduction is needed to explain X-ray properties of wind-blown bubbles also in H-deficient objects. Keywords. conduction, hydrodynamics, planetary nebulae: generalIn Steffen et al. (2008) we present time-dependent radiation-hydrodynamic models of PNe that include heat conduction at a solar (H-rich) composition. Extending the models to work with H-deficient compositions, we note that the general Fokker-Planck-based plasma theory of Spitzer (1962), to good accuracy, applies to both pure hydrogen and other chemical compositions. Heat conduction is modeled through a heat-flux term q, which is written as a diffusion coefficient (D) multiplied with the temperature gradient, q = −D∇T . The charge-dependent factor in D -i.e. εδ T Z −1 , where ε(Z) and δ T (Z) are given in Spitzer & Härm (1953) -decreases modestly with increasing effective charge Z. Our more general tests with models that use typical H-deficient abundances show that Z 4.0; the highest values are reached inside the hot wind-blown bubble in the PNe. Figure 1a shows that D(Z), under H-deficient conditions, it is about a factor two smaller than in a pure hydrogen plasma of the same temperature, a rather insignificant decrease.The treatment of the stellar evolution is a crucial issue in time-dependent models of the ionization structure in PNe. The quality of the models increases with more accurate predictions of the history of the slow wind (of the previous asymptotic-giant-branch stage), the fast wind, the central star (CSPN), and the abundances. The winds are characterized by their mass-loss rate, outflow velocity, and abundances; and the CSPN by its effective temperature (T eff ), luminosity, and mass. For H-rich compositions Pauldrach et al. (1988Pauldrach et al. ( ,2004 find that the mass-loss rate of the fast wind decreases with time.