On the extinction of planetary nebulae and the turbulent structure of the Galaxy

Fluctuations in the extinction of planetary nebulae provide strong support for the concept of a turbulent interstellar medium. The mean extinction and its variance as a function of height, z, above the galactic plane have been analyzed. The mean increases monotonically, and exponentially, to a saturation level. The variance increases as z-squared for small z and has damped oscillations for intermediate z, before levelling off at large z. The observed mean extinction and the observed variance are found to be in excellent agreement with these theoretical deductions. The spatial scale of the mean extinction is estimated to be 100 pc; the oscillation scale of the variance and the damping scale of the oscillations are estimated to be about 200 plus or minus 100 pc. The rms level of density fluctuations in the absorbing material causing the extinction is about equal to the mean value.