  We statistically evaluate the relative orientation between gas column density
structures, inferred from Herschel submillimetre observations, and the magnetic
field projected on the plane of sky, inferred from polarized thermal emission
of Galactic dust observed by BLASTPol at 250, 350, and 500 micron, towards the
Vela C molecular complex. First, we find very good agreement between the
polarization orientations in the three wavelength-bands, suggesting that, at
the considered common angular resolution of 3.0 arcminutes that corresponds to
a physical scale of approximately 0.61 pc, the inferred magnetic field
orientation is not significantly affected by temperature or dust grain
alignment effects. Second, we find that the relative orientation between gas
column density structures and the magnetic field changes progressively with
increasing gas column density, from mostly parallel or having no preferred
orientation at low column densities to mostly perpendicular at the highest
column densities. This observation is in agreement with previous studies by the
Planck collaboration towards more nearby molecular clouds. Finally, we find a
correspondence between the trends in relative orientation and the shape of the
column density probability distribution functions. In the sub-regions of Vela C
dominated by one clear filamentary structure, or "ridges", we find a sharp
transition from preferentially parallel or having no preferred relative
orientation at low column densities to preferentially perpendicular at highest
column densities. In the sub-regions of Vela C dominated by several filamentary
structures with multiple orientations, or "nests", such a transition is also
present, but it is clearly less sharp than in the ridge-like sub-regions. Both
of these results suggest that the magnetic field is dynamically important for
the formation of density structures in this region.
