On Milne-Barbier-Uns\"old relationships

TL;DR

This paper reviews the origins of the Milne-Barbier-Uns"old relationships, clarifying their historical development and the assumptions behind their derivation in the context of radiative transfer in stellar atmospheres.

Contribution

It clarifies the historical development and assumptions behind the Milne-Barbier-Uns"old relationships, highlighting earlier formulations by Milne in 1921.

Findings

The relationships relate emergent intensity and flux to the source function at specific optical depths.

Milne's earlier formulation in 1921 predates Barbier's derivation in 1943.

The paper clarifies assumptions behind the original derivation.

Abstract

This short review aims to clarify upon the origins of the so-called Eddington-Barbier relationships, which relate the emergent specific intensity and the flux to the photospheric source function at specific optical depths. Here we discuss about the assumptions behind the original derivation of Barbier (1943). We also point to the fact that Milne had already formulated these two relations in 1921.