Physical Processes in Gaseous Nebulae. III. The Balmer Decrement.

Abstract

This paper contains a numerical solution of the equations derived and formally solved in two earlier papers of the series. Various tables of general interest, including those of functions X n = hR/n 2 kT e and-[Ef(-X n)], for useful astrophysical ranges of n and T e are given. The Bahner decrement, computed under two alternative hypotheses-A for a nebula transparent to Lyman line radiation, and B for an opaque nebula-is tabulated. The latter hypothesis agrees better with the observed data. The conclusion is reached that the electron temperature, T e , of the nebular gas cannot be effectively determined from observed Balmer decrement data, because the decre-ment is insensitive to temperature. In view of the extreme physical conditions that exist in nebulae, the partition of atoms among the various excited levels approaches surprisingly close to the thermodynamic value. In papers I and II 2 of this series the fundamental equations for calculating the relative intensities of lines of the Balmer series were set up and formally solved. The present paper gives the numerical results and the comparison of theory with observation. For the benefit of those whose interest is chiefly in the final results, we shall briefly recapitulate the theory and fundamental hypotheses on which the calculations were based. The energy emitted in a given Balmer line, say in the transition from level n to level 2, is given by E n2-NnAfâhv , (1) where N n is the number of atoms per cubic centimeter in level n, A n2 is the Einstein spontaneous probability coefficient, and v is the frequency. Outside of thermodynamic equilibrium, N n must be calculated by balancing the number of atoms leaving a given quantum level against those entering, by all possible routes. We thus have an infinite set of simultaneous equations to solve, one equation for each level. The method of solving these equations, for certain specified physical conditions, was given in II. The results are most con