B-Fields and Star Formation across Scales with TRAO (B-FROST): CO Abundances, Dynamics and Relative Orientations in the Translucent High Latitude Cloud MBM12

Technical Summary: CO Abundances, Dynamics, and Relative Orientations in the Translucent High Latitude Cloud MBM12

Problem and Context
The star formation efficiency (SFE) in the Galaxy is observed to be low (a few percent), falling short of theoretical predictions. To understand the factors limiting star formation, detailed studies of individual molecular clouds (MCs) are required. The high-latitude molecular cloud MBM12 presents a specific case: while previous studies suggest it is dispersing or pressure-bound with little ongoing star formation, it contains T Tauri stars and may harbor gas at the onset of triggered star formation. A comprehensive understanding of MBM12's chemical, dynamical, and magnetic properties is necessary to assess its gravitational stability and the role of external pressure in regulating its evolution.

Methodology
This study, part of the B-FROST (B-Fields and Star Formation across Scales with TRAO) survey, utilizes multi-wavelength observations to construct a spatially resolved analysis of MBM12:

• Observations: The authors used 12CO and 13CO (J = 1−0) line observations from the Taeduk Radio Astronomical Observatory (TRAO) covering a 2.5° × 3° area at 48″ resolution. These were combined with Herschel dust emission data (250, 350, and 500 µm) and Planck dust polarization data (353 GHz).
• Column Density Estimation: The H2 column density, N(H2), was derived from Herschel dust emission. Crucially, the dust opacity ($\kappa_\nu$) was not assumed constant but empirically calibrated against near-infrared (NIR) extinction (K-band) to account for spatial variations in the translucent cloud environment.
• CO Analysis: CO column densities, N(CO), were estimated using Large Velocity Gradient (LVG) or Local Thermodynamic Equilibrium (LTE) assumptions based on 12CO and 13CO intensities. This allowed for the calculation of the CO-to-H2 conversion factor, X(CO), and the relative CO abundance, [CO/H2].
• Dynamical Analysis: A dendrogram algorithm was applied to the Position-Position-Velocity (PPV) cubes to identify hierarchical structures. The virial parameter ($\alpha_{vir}$) was calculated for these structures across multiple scales to assess gravitational binding, accounting for velocity dispersion and mass.
• Magnetic Field Analysis: The relative orientation between column density structures (filaments) and the plane-of-sky magnetic field ($B_{PoS}$) was analyzed using the FilDReaMS algorithm on Herschel dust maps and Planck polarization data.

Key Results

• Chemical Properties: The study identified four main velocity-separated regions: the Horseshoe, Bow, North Compact, and North Diffuse.
  • The integrated CO line intensity, W(CO), shows a quasi-linear dependence on N(H2), yielding an average X(CO) factor close to the Galactic average ($X_{Gal} \approx 2 \times 10^{20}$ cm$^{-2}$ (K km s$^{-1}$)$^{-1}$).
  • Deviations from the average occur at low N(H2): X(CO) drops below $X_{Gal}$ due to reduced collisional de-excitation in low-density gas, and rises above $X_{Gal}$ at cloud edges due to the drop in CO abundance in poorly shielded regions.
  • The average CO abundance [CO/H2] is $5.9 \times 10^{-5}$.
• Dynamics and Virial Parameters:
  • The hierarchical structures follow a broken power-law mass-size relation ($M = A R^\alpha$).
  • Virial parameters ($\alpha_{vir}$) range from 3 to 60 across the cloud, with the smallest values (closest to gravitational binding) found at the 0.1 pc scale.
  • Structures with the lowest $\alpha_{vir}$ exhibit mass-size scaling factors ($A$) three times larger than those with high $\alpha_{vir}$, suggesting they are subject to external pressures an order of magnitude higher.
  • No structures in the Bow or North Diffuse regions show $\alpha_{vir} \approx 2$ at any scale, whereas the North Compact region contains some sub-structures with $\alpha_{vir} < 2$.
• Magnetic Field Orientations:
  • A transition in the relative orientation between column density structures and magnetic fields was identified. At low column densities ($N(H_2) \le 4.5 \times 10^{21}$ cm$^{-2}$), filaments tend to be parallel to the magnetic field.
  • At higher column densities, particularly in the southern part of the Horseshoe, structures become perpendicular to the magnetic field, a configuration often associated with magnetically regulated collapse.

Significance and Claims
The authors claim this work provides the first integrated chemical, dynamical, and magnetic field analysis of MBM12. By combining these tracers, the study highlights:

1. The utility of empirically calibrated dust opacity for deriving accurate N(H2) in translucent clouds where standard assumptions fail.
2. The scale dependence of the virial parameter and mass-size relations, suggesting that external pressure plays a significant role in regulating the stability of substructures within the cloud.
3. The correlation between magnetic field orientation and column density, supporting the hypothesis that magnetic fields influence cloud evolution, transitioning from parallel to perpendicular arrangements as density increases.

The paper concludes that while MBM12 largely appears to be dispersing, the presence of low-$\alpha_{vir}$ structures and specific magnetic field alignments indicates that external pressure and magnetic fields may be regulating the remaining gas, potentially allowing for triggered star formation in specific localized regions. Further investigation into the scale dependence of these parameters is recommended to fully elucidate the regulation of star formation efficiency.