What are we learning from the relative orientation between density structures and the magnetic field in molecular clouds?

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 (NH) structures and the projected magnetic field orientation (⟨B̂⊥⟩) 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 NH structures and ⟨B̂⊥⟩ towards MCs, from mostly parallel at low NH to mostly perpendicular at the highest NH, 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 NH and ⟨B̂⊥⟩ being mostly parallel at low NH to mostly perpendicular at the highest NH, 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