  Stars with an initial mass below ~ 8 Msun evolve through the asymptotic giant
branch (AGB) phase, during which they develop strong stellar winds. Recent
observations have revealed significant morphological complexities in their
outflows, most likely caused by a companion. We study the impact of the
radiation force on such companion-perturbed AGB outflows. We present the
implementation of a ray tracer for radiative transfer in smoothed particle
hydrodynamics (SPH) and compared four different descriptions of radiative
transfer: the free-wind, the geometrical, the Lucy, and the attenuation
approximation. For both low and high mass-loss rates, the velocity profile of
the outflow is modified when going from the free-wind to the geometrical
approximation, also resulting in a different morphology. In the case of a low
mass-loss rate, the effect of the Lucy and attenuation approximation is
negligible due to the low densities but morphological differences appear in the
high mass-loss rate regime. By comparing the radiative equilibrium temperature
and radiation force to full 3D radiative transfer, we show that the Lucy
approximation works best. Although, close to the companion, artificial heating
occurs and it fails to simulate the shadow cast by the companion. The
attenuation approximation produces a lower equilibrium temperature and weaker
radiation force, but it produces the shadow cast by the companion. From the
predictions of the 3D radiative transfer, we also conclude that a radially
directed radiation force is a reasonable assumption. The radiation force thus
plays a critical role in dust-driven AGB winds, impacting the velocity profile
and morphological structures. For low mass-loss rates, the geometrical
approximation suffices, while high mass-loss rates require a more rigorous
method, where the Lucy approximation provides the most accurate results
although not accounting for all effects.
