On the neutral points in Rayleigh transfer

In this paper we consider the dependence of the existence and position of the neutral points on the albedo of single scattering and the optical thickness in a Rayleigh scattering plane-parallel homogeneous atmospheres. We use the Chandrasekhar method of discrete ordinates and the method of approximating the Sobolev resolvent function to solve the vector equation of transfer in l- and r-representation. On the basis of many different models of Rayleigh atmospheres we show the behaviour of the neutral points while the parallel incident flux can be both unpolarized or polarized. Our calculations show with high probability that the maximum number of neutral points in a Rayleigh atmosphere is four. - Highlights: • The equation of radiative transfer for a plane-parallel homogeneous Rayleigh scattering atmosphere is solved by the method of discrete ordinates. • The maximum number of neutral points in a set of model atmospheres with different physical parameters was four. • The presence and position of neutral points in the Rayleigh scattering atmosphere are most strongly influenced by the polarization state of the incident beam.