Line-driven ablation of circumstellar discs: III. Accounting for and analyzing the effects of continuum optical depth
In studying the formation of massive stars, it is essential to consider the strong radiative feedback on the stars' natal environments from their high luminosities ($10^4 \sim 10^6 L_\odot$). Given that massive stars contract to main-sequence-like radii before accretion finishes, one form this feedback takes is UV line-acceleration, resulting in outflows much like those expected from main-sequence massive stars. As shown by the prior papers in this series, in addition to driving stellar winds, such line forces also ablate the surface layers off of circumstellar discs within a few stellar radii of the stellar photosphere. This removal of material from an accretion disc in turn results in a decreased accretion rate onto the forming star. Quantifying this, however, requires accounting for the continuum optical depth of the disc along the non-radial rays required for the three-dimensional line-acceleration prescription used in this paper series. We introduce the "thin disc approximation", allowing these continuum optical depths arising from an optically thick but geometrically thin disc to be dynamically treated in the context of radiation-hydrodynamics simulations. Using this approximation in full dynamical simulations, we show that such continuum optical depth effects only reduce the disc ablation by 30 percent or less relative to previous simulations that ignored continuum absorption.