  For line-driven winds from hot, luminous OB stars, we examine the subtle but
important role of diffuse, scattered radiation in determining both the topology
of steady-state solutions and intrinsic variability in the transonic wind base.
We use a smooth source function formalism to obtain nonlocal, integral
expressions for the direct and diffuse components of the line-force that
account for deviations from the usual localized, Sobolev forms. As the
scattering source function is reduced, we find the solution topology in the
transonic region transitions from X-type, with a unique wind solution, to a
nodal type, characterized by a degenerate family of solutions.
  Specifically, in the idealized case of an optically thin source function and
a uniformly bright stellar disk, the unique X-type solution proves to be a
stable attractor to which time-dependent numerical radiation-hydrodynamical
simulations relax. But in models where the scattering strength is only modestly
reduced, the topology instead turns nodal, with the associated solution
degeneracy now manifest by intrinsic structure and variability that persist
down to the photospheric wind base. This highlights the potentially crucial
role of diffuse radiation for the dynamics and variability of line-driven
winds, and seriously challenges the use of Sobolev theory in the transonic wind
region. Since such Sobolev-based models are commonly used in broad applications
like stellar evolution and feedback, this prompts development of new wind
models, not only for further quantifying the intrinsic variability found here,
but also for computing new theoretical predictions of global properties like
velocity laws and mass-loss rates.
