A Statistical Basis for the Theory of Stellar Scintillation

Abstract

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, $$\bar{\delta \mu ({r}_{1})\delta \mu ({r}_{2})}/\bar{{\delta }^{2}\mu }$$, 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 $$4\times{10}^{-8}$$.