J. M. Vorster, J. Montillaud, M. Juvela, E. Falgarone, J. Oers, E. Mannfors, D. Alina, Q. Gu, H. Kang, C. W. Lee, S. Li, T. Liu, K. Pattle, V. -M. Pelkonen, I. Ristorcelli, A. Zavagno, L. V. Tóth

In our Galaxy, the average star formation efficiency is of the order of a few percent. 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 combine {\it Herschel}-based, locally $κ_ν$-calibrated $N$(H$_2$) estimates with $^{12}$CO and $^{13}$CO ($J=1-0$) observations (2.5$^\circ \times$3$^\circ$ at 48$''$) to map $N$(CO), $X$(CO), and [CO/H$_2$], compute multi-scale $α_{\rm vir}$ and mass-size scaling laws from dendrograms, and derive the histogram of relative orientations from {\it Planck} dust polarisation. We identify four main regions based on velocities that have H$_2$ column densities ranging from $2\times10^{20}$ cm$^{-2} - 1.3\times10^{22}$ cm$^{-2}$. The average $X$(CO) is close to the galactic average, with variations below $X_{\rm Gal}$ from collisional de-excitation in low-density gas, and above $X_{\rm Gal}$ from CO photodissociation at cloud edges. The hierarchical structures follow a broken power law mass-size relation $M=AR^α$. The values of $α_{\rm vir}$ ranged from $3-60$, with the smallest values at 0.1 pc scales. The mass-size relations for the structures with the lowest $α_{\rm vir}$ have scaling factors $A$ three times larger than those of high $α_{\rm vir}$ structures, indicating external pressure one order of magnitude larger. We found a transition of parallel to perpendicular between column density structures and magnetic field orientations at $N$(H$_2$) $= 4.5 \times 10^{21}$ cm$^{-2}$. We provide the first integrated chemical, dynamical, and magnetic field analysis of MBM12. Scale-dependent mass-size and virial analysis can further constrain the role of external pressure in regulating the star formation efficiency.