On Emission Lines in Stellar Spectra

Abstract

Conditions are investigated for the formation of absorption lines when the fraction ξ of the line absorption coefficient lν is due to absorption and the fraction 1 – ξ is due to scattering, continuous absorption and continuous isotropic scattering being taken into account when estimating the flux of continuous radiation. It is shown that if |$\xi \lt{\lambda }_{c}={k}_{\nu }/({k}_{\nu }+\sigma )$| the line must be dark, but that if |$\xi \gt{\lambda }_{c}$| the line may be bright. The case ξ = 1, in which the line is formed by pure absorption, is considered in detail. It is shown that the line will be bright if |$f({\lambda }_{\nu },\,{\beta }_{\nu })\gt f({\lambda }_{c},\,{\beta }_{\nu })$|⁠, where |$f(\lambda ,\,\beta )$| is a certain function, |${\lambda }_{\nu }=({k}_{\nu }+{l}_{\nu })/({k}_{\nu }+\sigma +{l}_{\nu }),\,\text{and}\,{\beta }_{\nu }$|⁠, is a constant depending on the constitution of the star and the frequency ν considered. Some numerical examples are discussed.