Dust polarisation studies on MHD simulations of molecular clouds: methods comparison for the relative orientations analysis

Context. Polarized dust emission can be used as a probe for magnetic fields at different scales. In particular, the analysis of the relative orientation between the density structures and the magnetic field projected on the plane of the sky can provide information on the role of magnetic fields in shaping the structure of molecular clouds. Aims. The relative orientation has been investigated using different methods. Our goal is to explicitly compare two of them: the Rolling Hough Transform (RHT) and the gradient technique. Methods. We have applied the RHT method and the gradient technique to two regions, identified in surface brightness maps at 353 GHz generated via MHD simulations post-processed using radiative transfer modelling. For both methods we have derived the relative orientation between the magnetic field and the density structures, to which we have applied two different statistics, the histogram of relative orientation (HRO) statistic and the projected Rayleigh statistic (PRS). Results. The samples of pixels selected by each method are substantially different. When the methods are applied to the same pixel selection, the results in terms of relative orientation as a function of column density are consistent between each other. When each method is applied to its own pixel selection, the differences are apparent. In Region 1, the RHT method roughly reproduces the observed trend of the relative orientation becoming more perpendicular for increasing column density, while the gradient method, applied at the same resolution as RHT, gives the opposite trend, with the relative orientation moving towards a more parallel alignment. In Region 2, the situation is reversed. The inconsistent results, which are due to the different pixel selections operated by the methods and to the intrinsic differences between them, provide complementary valuable information. Abridged.