On the effective temperatures of extended photospheres

Abstract

For material stratified in parallel planes in local thermodynamical equilibrium we have Milne's well-known result that B(τ)=½F(1+3/2τ), where πF is the constant net integrated flux of radiation, τ is the optical depth and B is the "ergiebigkeit" which is related to the temperature T by the relation B=σ/πT⁴, σ being the Stefan-Boltzmann constant. If we define the effective temperature by the relation πF=σT⁴_e, we have from (1) T⁴_e=0.8T⁴₁, where T₁ is the temperature ar τ=1. In this note we establish a similar result for extended photospheres where the curvature of the outer layers is properly taken into account.