Abstract
Context . On average, in our Galaxy, the star formation efficiency (SFE) is of the order of a few percent, which is lower than theoretical predictions. Detailed observational studies of individual molecular clouds may offer insight into the contributing factors to the low galactic SFE. Aims . We investigated the high-latitude molecular cloud MBM12 as part of the B-fields and star formation across scales (B-FROST) survey with the Taeduk Radio Astronomical Observatory (TRAO) to assess why star formation activity in MBM12 is low. Methods . We estimated N (H 2 ) with Herschel dust emission and a dust opacity κ ν derived from near-infrared extinction, 21 cm HI column densities, and far-infrared emission. With 12 CO and 13 CO ( J = 1-0) line observations, covering an area of 2.5° × 3° at 48″ resolution, we mapped the CO column density N (CO), CO-to-H 2 factor X (CO), and abundance [CO/H 2 ]. We estimated the multi-scale virial parameter α vir and constructed mass-size scaling laws of hierarchical structures with dendrograms. We computed the relative orientation between column density structures and magnetic fields using Planck observations of dust polarisation. Results . We identified four main regions based on velocities with H 2 column densities ranging from 2 × 10 20 −1.3 × 10 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 X Gal due to the fall-off of collisional de-excitation in low-density gas, and above X Gal 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 α . The values of α vir ranged from 3-60, with the smallest values at 0.1 pc scales. The mass-size relations for the structures with the lowest α vir have scaling factors, A , three times larger than those of high α 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 ) = 4.5 × 10 21 cm −2 . Conclusions . 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.