3D simulations of AGB stellar winds II. Ray-tracer implementation and impact of radiation on the outflow morphology

Context. Stars with an initial mass below similar to 8 M-circle dot evolve through the asymptotic giant branch (AGB) phase, during which they develop a strong stellar wind, due to radiation pressure on newly formed dust grains. Recent observations have revealed significant morphological complexities in AGB outflows, which are most probably caused by the interaction with a companion. Aims. We aim for a more accurate description of AGB wind morphologies by accounting for both the radiation force in dust-driven winds and the impact of a companion on the AGB wind morphology. Methods. We present the implementation of a ray tracer for radiative transfer in the smoothed particle hydrodynamics (SPH) code PHANTOM. Our method allows for the creation of a 3D map of the optical depth around the AGB star. The effects of four different descriptions of radiative transfer, with different degrees of complexity, are compared: the free-wind approximation, the geometrical approximation, the Lucy approximation, and the attenuation approximation. Finally, we compare the Lucy and attenuation approximation to predictions with the 3D radiative transfer code MAGRITTE. Results. The effects of the different radiative transfer treatments are analysed considering both a low and high mass-loss rate regime, and this both in the case of a single AGB star, as well as for an AGB binary system. 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 wind morphology for AGB binary systems. 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 the predictions from MAGRITTE, we show that for most of the models, 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 leads to stronger absorption of the radiation field, yielding 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 code MAGRITTE, we also conclude that a radially directed radiation force is a reasonable assumption. Conclusions. The radiation force 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, however for high mass-loss rates, a more rigorous method is required. Among the studied approaches, the Lucy approximation provides the most accurate results, although it does not account for all effects.