The evolution of planetary nebulae. V. The diffuse X-ray emission

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 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.
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.

Dedicated to the memory of M. Perinotto, a dear friend and esteemed colleague who died unexpectedly and much too

early on August 15, 2007.