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, /x, is subject to irregular fluctuations, the auto-correlation, 8jLt(ri)S/x(r 2)/S 2 /x> instantaneous fluctuations in the refractive index at two different points r x and r 2 is introduced; on the further assumption that the turbulence which prevails is homogeneous and isotropic, the auto-correlation 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 4X 10-8. I. Introduction,-On examining the recent literature on the subject of stellar scintillation and astronomical seeing, it appeared to the writer that a proper statistical basis for discussing certain aspects of the phenomenon was lacking. In this paper an attempt will be made to provide such a basis. But it may be useful, first, to clarify the nature of the problem and to indicate the need for a theory along the Unes outlined in this paper. It would appear that in discussing the general problem of stellar scintillation we should distinguish between the phenomena which are observed near the horizon and at low altitudes and the phenomena which are observed near the zenith and at high altitudes. That such a distinction should be made is clear, already from Lord Rayleigh's (1) discussion of the problem in 1893. For, as Rayleigh showed, at low altitudes the rays of different colours coming from the same star and reaching the same point on the Earth are separated by quite appreciable distances in the upper atmosphere. Thus, the separation, A^, between two rays of different colours at a height z above the Earth is given by (Rayleigh (i), eq. (10))