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Stellar wind models of central stars of planetary nebulae

Fast line-driven stellar winds play an important role in the evolution of planetary nebulae. We provide global hot star wind models of central stars of planetary nebulae. The models predict wind structure including the mass-loss rates, terminal velocities, and emergent fluxes from basic stellar parameters. We applied our wind code for parameters corresponding to evolutionary stages between the asymptotic giant branch and white dwarf phases. We study the influence of metallicity and wind inhomogeneities (clumping) on the wind properties. Line-driven winds appear very early after the star leaves the asymptotic giant branch (at the latest for $T_\rm{eff}\approx10\,$kK) and fade away at the white dwarf cooling track (below $T_\rm{eff}=105\,$kK). Their mass-loss rate mostly scales with the stellar luminosity and, consequently, the mass-loss rate only varies slightly during the transition from the red to the blue part of the Hertzsprung-Russell diagram. There are the following two exceptions to the monotonic behavior: a bistability jump at around $20\,$kK, where the mass-loss rate decreases by a factor of a few (during evolution) due to a change in iron ionization, and an additional maximum at about $T_\rm{eff}=40-50\,$kK. On the other hand, the terminal velocity increases from about a few hundreds of $\rm{km}\,\rm{s}^{-1}$ to a few thousands of $\rm{km}\,\rm{s}^{-1}$ during the transition as a result of stellar radius decrease. The wind terminal velocity also significantly increases at the bistability jump. Derived wind parameters reasonably agree with observations. The effect of clumping is stronger at the hot side of the bistability jump than at the cool side. Derived fits to wind parameters can be used in evolutionary models and in studies of planetary nebula formation. A predicted bistability jump in mass-loss rates can cause the appearance of an additional shell of planetary nebula.