B-FROST: B-Fields and star formation across scales with TRAO. CO abundances, dynamics, and relative orientations in the translucent high latitude cloud MBM12

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. 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. 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 ^13CO (J=1-0) line observations, covering an area of 2.5^̧irc . We estimated the multi-scale virial parameterα_ 3^̧irc at 48'' resolution, we mapped the CO column density N(CO), CO-to-H_2 factor X(CO), and abundance CO/H_2 ̊m 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. We identified four main regions based on velocities with H_2 column densities ranging from 2 - 1.3 $ 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_̊m Gal due to the fall-off of collisional de-excitation in low-density gas, and above X_̊m 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_̊m 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_̊m vir have scaling factors, A, three times larger than those of high α_̊m 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 $ cm$^ cm -2 22 10^ 21 -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.