Eddington limit for a gaseous stratus with finite optical depth

Abstract

Abstract The Eddington luminosity of a spherical source is usually defined for a uniformly extending normal plasma. We usually suppose that the gas can accrete to the central object at the sub-Eddington luminosity, while it would be blown off from the central luminous source in the super-Eddington case. We reconsider this central dogma of the Eddington limit under the radiative transfer effect for the purely scattering case, using analytical and numerical methods. For the translucent isolated gas cloud (stratus) with finite optical depth, the concept of the Eddington luminosity is drastically changed. In an heuristic way, we find that the critical condition is approximately expressed as Γ = (1 + μ* + τc)/2, where Γ (=L/LE) is the central luminosity L normalized by the Eddington luminosity LE, τc is the optical depth of the stratus, and μ* ($=\sqrt{1-R_*^2/R^2}$) is the direction cosine of the central object, R* being the radius of the central object, and R the distance from the central object. When the optical depth of the stratus is around unity, the classical Eddington limit roughly holds for the stratus; Γ ∼ 1. However, when the optical depth is greater than unity, the critical condition becomes roughly Γ ∼ τc/2, and the stratus would infall on to the central source even at the highly super-Eddington luminosity. When the optical depth is less than unity, on the other hand, the critical condition reduces to Γ ≳ (1 + μ*)/2, and the stratus could be blown off in some limited ranges, depending on μ*. This new concept of the Eddington limit for the isolated stratus could drastically change the accretion and outflow physics of highly inhomegeneous plasmas, with relevance for astrophysical jets and winds and supermassive black hole formation.