Radiative Equilibrium: Classical Theory

Abstract

Planetary nebulae are transparent for radiation in forbidden lines and in lines of subordinate series of atoms and ions. They are transparent even in all resonance lines of atoms and ions — 1 550 CIV, 1 240 NV, 1 400 SiIV, 1909 CIII, 2 800 MgII etc. — with the exception of hydrogen and helium. Under these conditions the problem of the radiation field at the frequencies of emission lines can be solved quite easily. The density of radiation ε λ , e.g. in the lines of the Balmer series of hydrogen, is proportional to the square of the electron concentration in it: ε λ ~ n 2e . Therefore, the distribution of density of the radiation in these lines within the nebula will be proportional to the distribution of the electron concentration itself. Then, the intensity of radiation emerging from a nebula in any line of this series can be determined simply by summing the radiation from each unit volume along the line of sight. In the same way one can find the intensity of radiation emerging from a nebula in forbidden lines, with the only difference that in this case the volume emission coefficient is proportional to the product of the electron and atom (ion) concentrations of n(A), exciting the given line: ε λ ~ n e n(A). Nothing else is required to solve the radiative transfer problem at the frequencies of these categories of lines in the visible part of the spectrum.KeywordsVelocity GradientOptical DepthOptical ThicknessExpansion VelocityCentral StarThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.