Radiances and equivalent widths of Lorentz lines for nonisothermal paths

Abstract

The Ladenburg-Reiche analysis of the growth of an isolated spectral line was extended to the case of a nonisothermal path with optical depths for which neither a weak line nor a strong line approximation is appropriate. The results, in terms of the total radiance and equivalent width of the line, are given byN = 2πγe∫0f(xLN*ν(f)df and W = 2πγef(xLwhere xL is the total nondimensional optical depth of the extended source,f = f(x) = x exp(-x)[J0(ix)−iJ1(ix)] is the Ladenburg-Reiche function, and N*v(f) is the Planck function of the local temperature in the emitting- absorbing gas. The nondimensional optical depth is defined by dx = S(X)F(X)dX/2πγe, where S(X) is the local value of the line strength corresponding to T = T(X), dX is the increment of standard optical depth, γe is an effective spectral line half-width, and F(X) is a function characterizing the temperature dependence of the line width. The expression of F(X) by unity and by γ(X)/γe specifies respectively the “nearly weak” and “nearly strong” line approximations for use at intermediate optical depths.