Brightness and Temporal Variation of Radio Emission from Galactic OH

Abstract

THE recent interferometric observations of the angular sizes of OH radio sources^1–3, which imply minimum brightness temperatures of between 10⁶ and 10¹¹ °K, remove any theoretical difficulty in accepting the temporal variations of intensity that the radio astronomy group at Berkeley claim to have detected⁴. The time constant for a variation of intensity may, in the absence of a rigorous solution of the equations of transfer and population densities for even a simple model, be estimated in two ways that lead to the same result. A simplified equation of transfer for any one of the four radio frequency lines is where i denotes the upper level of the Λ-doublet as split by hyperfine interaction, j denotes the lower level, I_ij is the intensity of the radiation, v_ij is the difference of the number of densities in the two levels, c is the velocity of light and (A_ij is the Einstein coefficient for spontaneous emission and δv the width of the line.) This equation of transfer incorporates a number of approximations which seem entirely justified in view of the very high intensity of the radiation, namely, that the rates of spontaneous emission and of non-radiative creation and destruction of excited states can be ignored in comparison with the rate of stimulated emission, and that the radiation is propagating in one direction only. The four equations for the four radio frequency lines are coupled through four simultaneous equations for the rates of change of the populations. It has not so far been possible to solve the eight equations except for very artificial cases. If it can be assumed that there are circumstances in which ∂I_ij/∂x is dominated by the other two terms in the equation of transfer, the time constant τ would be