Radiation transfer in a cylinder. III. Spectrum of basic integral equation

We present a method for computing the spectrum of the integral equation for radiation transfer in a cylinder. This method, as in the previous articles in this series, is based on a Hankel transformation applied to the equation. Calculating the spectrum then reduces to solving the equation for the auxiliary function for each eigenvalue separately. The corresponding eigenfunction is then found by an additional integration. We find asymptotic expressions for the eigenvalues and the eigenfunctions for a cylinder with a large optical radius when there is scattering in a spectral line, with complete redistribution over frequency when the absorption coefficient obeys a power law. We also derive equations determining the quantities entering into these expressions. For the simplest kernel of the equation all quantities can be expressed in terms of Bessel functions and roots of a transcendental equation.Translated from Astrofizika, Vol. 38, No. 1, pp. 75–88, January–March, 1995.