B-FROST. MBM12 CO cubes and H2 map

We computed the relative orientation between column density structures and magnetic fields using Planck observations of dust polarisation. We identified four main regions based on velocities with H2 column densities ranging from 2x10^20^-1.3x10^22^cm^-2^. The CO integrated line intensity, W(CO), increases linearly with N(H_2_), providing an average X(CO) factor close to the Galactic average.

At a low N(H_2_), X(CO) varies below XGal due to the fall-off of collisional de-excitation in low-density gas, and above XGal due to the drop of CO abundances in poorly shielded cloud edges. The hierarchical structures follow a broken power law mass-size relation M=AR^alpha^. The values of alpha_vir_ ranged from 3-60, with the smallest values at 0.1pc scales.

The mass-size relations for the structures with the lowest alpha_vir_ have scaling factors, A, three times larger than those of high alpha_vir_ structures, indicating external pressure one order of magnitude larger than the former. We found a transition from parallel to perpendicular relative orientations between column density structures and the magnetic field at N(H_2_)=4.5x10^21^cm^-2^. We provide the first integrated chemical, dynamical, and magnetic field analysis of MBM12.

Further investigation into the scale dependence of the mass-size relation and virial parameter can highlight the role of external pressure in regulating the star-formation efficiency.