A Statistical Basis for the Theory of Stellar Scintillation

Current theories of stellar scintillation and astronomical seeing suppose that there is a disturbed region in the atmosphere at a height of about 4 km which corrugates a plane wave-front passing through it; and that the observed phenomena are to be accounted for in terms of such a corrugated wave-front. On the assumption that the disturbed region is a turbulent layer in which the refractive index, µ, is subject to irregular fluctuations, the auto-correlation, | (r₁) ({r₂) }/ ^{2 }|⁠, of the instantaneous fluctuations in the refractive index at two different points r1 and r2 is introduced; on the further assumption that the turbulence which prevails is homogeneous and isotropic, the autocorrelation so defined can be a function, M (r) (say), only of the distance r between the two points considered. It is then shown how the statistical properties of the corrugated emergent wave-front, such as the angular dispersion in the wave normals, can be expressed in terms of M (r). From the known facts concerning astronomical seeing it is concluded that we can satisfactorily account for the observed phenomena by postulating a turbulent layer of a thickness of the order of a hundred metres, a micro-scale of turbulence of the order of ten centimetres and a root mean square fluctuation in refractive index of the order of |410^-8|⁠.