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.
