Stellar occultations by turbulent planetary atmospheres: A heuristic scattering model

A model of ray refraction by an isothermal atmosphere with a scattering screen at the center of bending is used to generate analytic results which simulate the effects of real atmospheric turbulence on occultations. Calculations are carried through for scattering which is constant with height and for exponential height dependence. The effect of the scattering is to bias the the mean intensity of the occulted source, and hence systematically to distort bending angles and height differences obtained from inversion of the intensity data. However, the effect is of order 〈δε{lunate}²〉/ε{lunate}² for either model, where 〈δε{lunate}²〉 is the mean square scattering angle and ε{lunate} is the average bending angle. The effect turns out to be small for plausible turbulence, since 〈δε{lunate}²〉/gfe² is of approximately the same order as the relative mean square density fluctuation. Thus the random effects of turbulence are unlikely to be a source of large systematic error in occultations, provided that the data can be meaningfully averaged either temporally or over a number of occultation events.