Magnetic field properties in star formation: A review of their analysis methods and interpretation

Abstract

Linearly polarized emission from dust grains and molecular spectroscopy is an effective probe of the magnetic field topology in the interstellar medium and molecular clouds. The longstanding Davis-Chandrasekhar-Fermi (DCF) method and the recently developed Histogram of Relative Orientations (HRO) analysis and the polarization-intensity gradient (KTH) method are widely used to assess the dynamic role of magnetic fields in star formation based on the plane-of-sky component of field orientations inferred from the observations. We review the advances and limitations of these methods and summarize their applications to observations. Numerical tests of the DCF method, including its various variants, indicate that its largest uncertainty may come from the assumption of energy equipartition, which should be further calibrated with simulations and observations. We suggest that the ordered and turbulent magnetic fields of particular observations are local properties of the considered region. An analysis of the polarization observations using DCF estimations suggests that magnetically trans-to-super-critical and averagely trans-to-super-Alfvénic clumps/cores form in sub-critical clouds. High-mass star-forming regions may be more gravity-dominant than their low-mass counterparts due to higher column density. The observational HRO studies clearly reveal that the preferential relative orientation between the magnetic field and density structures changes from parallel to perpendicular with increasing column densities, which, in conjunction with simulations, suggests that star formation is ongoing in trans-to-sub-Alfvénic clouds. There is a possible transition back from perpendicular to random alignment at higher column densities. Results from observational studies using the KTH method broadly agree with those of the HRO and DCF studies.

Multi-scale physical properties of NGC 6334 as revealed by local relative orientations between magnetic fields, density gradients, velocity gradients, and gravity

“…At the highest N H2 bin, the alignment measure of two angles transits back to AM N G B ∼ 0 (i.e., no preferred orientation), which might be due to insufficient resolution. The transition from AM N G B < 0 to AM N G B > 0 is in agreement with trans-to-sub-Alfvénic simulations in numerical HRO studies (see a review in Liu et al 2022b), which suggests the NGC 6334 is trans-to-sub-Alfvénic at complex/cloud scale. Similar trans-to-sub-Alfvénic states have been reported in the Gould Belt clouds from previous observational HRO and VGT studies (Planck Collaboration et al 2016;Hu et al 2019).…”

“…Similar trans-to-sub-Alfvénic states have been reported in the Gould Belt clouds from previous observational HRO and VGT studies (Planck Collaboration et al 2016;Hu et al 2019). The statistically more perpendicular alignment between magnetic field and column density gradient (i.e., more parallel alignment between magnetic field and column density contour) at low column densities may be due to the stretch of an initially super-Alfvénic turbulence or due to the intrinsic property of a large-scale sub-Alfvénic turbulence (see Liu et al 2022b, and references therein). The direct reason for the transition from AM N G B < 0 to AM N G B > 0 is still under debate (Liu et al 2022b).…”

“…The angle between magnetic field and column density gradient (φ N G B ) is complementary to the angle between magnetic field and column density contour (φ N B ) that has been extensively studied by the HRO analysis 5 (see a recent review in Liu et al 2022b). Figure 7 shows the RO-N relation for φ N G B from the Planck, JCMT, and ALMA 4 The number of pixels per bin varies for different relative orientations due to the different detection area for the total dust emission, polarized dust emission, and molecular line emission.…”

“…The Davis-Chandrasekhar-Fermi (DCF) method (Davis 1951;Chandrasekhar & Fermi 1953) and its modified forms have been the most widely used method to indirectly derive the magnetic field strength with statistics of field orientations. The compilation of previous DCF estimations suggests that magnetically trans-to-super-critical and averagely trans-to-super-Alfvénic clumps/cores form in sub-critical clouds (Liu et al 2022a), but the breakdown of the DCF assumptions in specific physical conditions could bring some uncertainties to the DCF estimations (see a review by Liu et al 2022b). Thus, it is essential to study the magnetic field properties with other statistical methods as well.…”

“…The observational HRO studies reveal that the magnetic field and column density contour changes from a preferential parallel alignment to a perpendicular alignment with increasing column densities (e.g., Planck Collaboration et al 2016), and may transit back to a random alignment at higher column densities (e.g., Beuther et al 2020;Kwon et al 2022). The observational trends suggest that star formation is ongoing in trans-to-sub-Alfvénic clouds and the magnetic field is likely affected by star formation activities in high-density regions, but the exact reason for the different alignment at different column densities is still under debate (see a review in Liu et al 2022b). On the other hand, the polarization-intensity gradient method (Koch-Tang-Ho or KTH method, Koch et al 2012a) proposes to determine the local magnetic field strength as well as the local normalized mass-to-flux ratio (λ KTH ) under the assumption of ideal magnetohydrodynamics (MHD) by comparing the local orientations of magnetic fields, intensity gradients, and local gravity.…”