2017A&A...607A...2S

We investigate the conditions of ideal magnetohydrodynamic (MHD) turbulence responsible for the relative orientation between density gradients (∇ρ) and magnetic fields (B) in molecular clouds (MCs). For that purpose, we construct an expression for the time evolution of the angle (φ) between ∇ρ and B based on the transport equations of MHD turbulence. Using this expression, we find that the configuration where ∇ρ and B are mostly parallel, cosφ=±1, and where ∇ρ and B are mostly perpendicular, cosφ=0, constitute equilibrium points, that is, the system tends to evolve towards either of these configurations and they are more represented than others. This would explain the predominant alignment or anti-alignment between column density (N_H) structures and the projected magnetic field orientation (<B_⊥> ) reported in observations. Additionally, we find that departures from the cosφ=0 configurations are related to convergent flows, quantified by the divergence of the velocity field (∇*v) in the presence of a relatively strong magnetic field. This would explain the observed change in relative orientation between N_H structures and <B_⊥> towards MCs, from mostly parallel at low N_H to mostly perpendicular at the highest N_H, as the result of the gravitational collapse and/or convergence of flows. Finally, we show that the density threshold that marks the observed change in relative orientation towards MCs, from N_H and <B_⊥> being mostly parallel at low N_H to mostly perpendicular at the highest N_H, is related to the magnetic field strength and constitutes a crucial piece of information for determining the role of the magnetic field in the dynamics of MCs.