The radiative equilibrium of an expanding planetary Nebula. I. Radiation pressure in LYMAN-α

Abstract

In this paper the problem of the radiative equilibrium in Lyman-α of a differentially expanding planetary nebula is formulated de novo. Particular attention has been -given to the formulation of the. boundar>; condi.tion~. It is shown that the transfer problem reduces to a novel boundary-value problem in hyperbolic partial differential equations. Explicit solutions have been found for the case III which the line absorption coefficient σ(ν) has a rectangular form. On the basis of the solutions obtained, the question of the radiation pressure in Lyman-α has been re-examined. It is shown that when the Doppler shift due to the difference in velocities between the inner and the outer boundaries of the nebula exceeds the line width 2Δν of σ(ν) by a factor 2√3, the nebula can be divided into three parts: an inner, a central, and an outer part. In the central part the radiation pressure in Lyinan-α is of the same order as that in the continuum, while in the inner and the outer parts it is not inappreciable. The bearing of this manner in which the radiation pressure in Lyman-α operates in an expanding atmosphere on the dynamics of a planetary nebula and also on other astrophysical problems is briefly indicated.