Starlight scintillation and atmospheric turbulence

Abstract

Analytic expressions are derived for the correlation function and the spectrum of the intensity fluctuations of starlight. A model of the atmosphere is used that accounts for turbulent motion and refractive-index fluctuations in the entire atmosphere rather than merely in thin "seeing layers." The shape of the refractive- index spectrum is assumed to be constant along a ray path, but the magnitude of the fluctuations is allowed to vary with altitude. A comparison of scintillation characteristics calculated in this fashion with observa- tions suggests that the viscous cutoff eddy size is of the order of 10 cm in those parts of the atmosphere that contribute most significantly to the scintillation. It is found that the magnitude of the refractive-index fluctuations required to account for the observed scintillation data is in good agreement with typical airborne measurements of refractive4ndex fluctuations. When the refractive-index fluctuations are assumed to be proportional to the average air density, an rms fluctuation of about 2.6X t0- N-unit at sea level and 7.5X tO- N-unit at an altitude of tO km is sufficient to produce the average observed scintillations. Under this condition, more than 70% of the amplitude of the intensity variations is due to perturbations of the incoming wavefront in the altitude range from 7 to 15 km. The associated temperature variations are of the order of 0?0t. These values take into account only those turbulent motions that have eddy sizes smaller than about 100 m. The calculated magnitude and spectrum of star scintillation and the predicted influence of the telescope aperture agree well with observations.