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. 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. The radiation hydrodynamical models show that 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. 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 $10^{-4}$ of 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. 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.
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