AN ALTERNATIVE DERIVATION OF SOBOLEV LARGE VELOCITY-GRADIENT LIMIT

Our concern is with the net radiative bracket for a constant source function ρ{variant}csf(r) and with the formula ρ{variant}csf(r) = γ {1 - exp[ - ( 1 γ)} derived by Sobolev for a differentially moving medium with constant velocity gradient in the large velocity gradient (LVG) limit. The usual derivation of this formula is based on the ab initio assumption γT → ∞, which thus becomes a sufficient (though not a necessary) condition for the formula to be valid. We present an alternative derivation, for a constant velocity gradient, which shows that the necessary (and sufficient) condition for ρ{variant}csf(r) to attain the LVG limit in the case of strong absorption is γT ≳ 1 for a Doppler profile and γT → ∞ for a Lorentzian profile, and in the case of velocity-induced, near optical transparency is γT → ∞ irrespective of the shape of the absorption profile. © 1990.