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Context. Planck observations demonstrated that the grain alignment efficiencyis almost constant in the diffuse ISM. Aims. We test if the Radiative Torque(RAT) theory is compatible with observational constraints on grain alignment.Methods. We combine a numerical simulation with the radiative transfer codePOLARIS that incorporates a physical dust model and the detailed grainalignment physics of RATs. A dust model is designed to reproduce the spectraldependence of extinction of the ISM. From a RAMSES simulation of interstellarturbulence, we extract a cube representative of the diffuse ISM. Wepost-process the cube with POLARIS to get the grain temperature and RATs tosimulate synthetic dust polarization maps. Results. In our simulation the grainalignment efficiency is correlated with gas pressure, but not with the RATintensity. Because of the low dust extinction, the magnitude of RATs varieslittle, decreasing only for high column densities $N_H$. Comparing our mapswith a uniform alignment efficiency, we find no systematic difference. Thedependence of polarization fraction $p$ with $N_H$ or polarization dispersion$S$ is similar. The drop of RATs in dense regions barely affects thepolarization pattern, the signal being dominated by the LOS and magnetic fieldgeometry. If a star is inserted, the polarization increases, with no specificpattern around the star. The angle-dependence of RATs is not observed in themaps, and is weak using a uniform magnetic field. Conclusions. RATs arecompatible with Planck data for the diffuse ISM such that both uniformalignment and RAT alignment lead to similar observations. To further test thepredictions of RATs where an important drop of grain alignment is expected,polarization observations of dense regions must be confronted to numericalsimulations sampling high column densities through dense clouds, with enoughstatistics.

A systematic study of radiative torque grain alignment in the diffuse interstellar medium