Curvature Mapping Method: Mapping Lorentz Force in Orion A

TL;DR

The paper addresses the challenge of quantifying the magnetic field's role in star formation, where traditional diagnostics like the mass-to-flux ratio lack information on magnetic force direction and magnitude. It introduces the Curvature Mapping Method, which maps the projected Lorentz force on the plane of the sky from polarization-derived magnetic field strength and curvature, parameterized by $f_{L,POS} \approx \frac{\Omega}{\mu_0} B_{tot}^2 \boldsymbol{\kappa}$. The method is validated against 3D MHD simulations, showing that the orientation is reliably captured in roughly half to two-thirds of cases and the strength is within about a factor of two, and then applied to the Orion A region (OMC-1) to produce a detailed Lorentz force map that reveals an hourglass-shaped magnetic field with magnetic tension counteracting gravity in lower-density zones. The study estimates $B_{tot}$ in OMC-1 to be near $0.5$ mG, finds the Lorentz force scales with column density as $f_L \propto \Sigma^{1.6}$, and demonstrates that the magnetic field can provide support in parts of the cloud but not in the densest regions, highlighting the method's potential to inform surveys on magnetic field influence in star formation.

Abstract

Magnetic force is a fundamental force in nature. Although widely believed to be important in counterbalancing against collapse in star formation, a clear evaluation of the role of the magnetic field in star formation remains hard to achieve. Past research attempts to evaluate the importance of magnetic forces using diagnostics such as the mass-to-flux ratio, which measures its strength but not how it functions. Since star formation is a complex process and the observed regions have complex structures, mapping the importance of the magnetic field is necessary. We propose a new technique, the Curvature Mapping Method, to evaluate the role of the magnetic force by providing maps of the magnetic force estimated using polarization observations. The Curvature Mapping Method provides maps with the contribution of the magnetic force clearly outlined. We apply the method to the star formation region of Orion A and provide a first quantitative result where the magnetic force arising from the pinched magnetic field does provide support against gravity. By comparing it against the gravitational force, we find that the magnetic force is enough to affect the low-density gas but is insufficient to support the dense region from collapse. The method effectively uses information contained in polarization maps and can be applied to data from surveys to understand the role of the B-field.

Figures (8)

• Figure 1: Curvature Mapping method: mapping the Lorentz force in molecular clouds. Magnetic field strength and the curvature of the field lines combined to derive the Lorentz force Previous studies estimate magnetic field strength using Zeeman splitting or the DCF method. In comparison, the Curvature Mapping Method can provide spatially resolved maps of the magnetic force.
• Figure 2: Distribution of offset angle between pseudo Lorentz force and Projected Lorentz force in MHD simulations. The three panels present the distribution of offset angle between pseudo Lorentz force and Projected Lorentz force in weak, middle, and strong magentic field states, respectively. The percentages of offset angle $<$ 30$^\circ$ (parallel aligned) are around 40$\%$, 50$\%$, and 50$\%$ in weak, middle, and strong magentic field states, respectively. That of offset angle $<$ 45$^\circ$ (close to parallel) are around 50$\%$, 60$\%$, and 60$\%$ in weak, middle, and strong magentic field states, respectively.
• Figure 3: Distribution of modified factors of curvature mapping method in various magnetic field states. The ratio between the projected Lorentz force and the pseudo Lorentz force presents the modified factor $\Omega$ of curvature mapping method. In three simulations (weak, middle, and strong magnetic state in left, middle, and right panel), the distribution of modified factor forms norm distributions, where the mean values are 1.5, 1.2, and 1.1 with the standard deviation around 0.3 at the log scale.
• Figure 4: Distribution of magnetic curvature and Lorentz force orientations. The left panel displays the magnetic curvature map (black arrows), where the arrow orientations represent the orientation of the Lorentz force. The background illustrates the 850$\mu$m continuum emission, while the streamlines depict the magnetic field structure derived from 850$\mu$m dust polarization observations. The contours show the column density as 10$^{23.4}$ cm$^{-2}$ and the triangle markers display the position of clumps Orion-KL and Orion South. The top-right panel shows the orientation distributions of the Lorentz force (blue) and the magnetic field (orange). The Lorentz force orientation peaks at angles perpendicular to those of the magnetic field, indicating the expected orthogonality between the two. The bottom-right panel presents the distribution of magnetic curvature magnitudes. The orange line represents a Gaussian fit to the distribution, and the red line indicates the average curvature value ($<\kappa>\sim 1.6{\rm pc}^{-1}$).
• Figure 5: Distribution of Lorentz force vector. The left panel displays the vector map of the Lorentz force (black arrows). The background illustrates the 850$\mu$m continuum emission, while the streamlines depict the magnetic field structure derived from 850$\mu$m dust polarization observations. Black contours show the H$_2$ column density from Herschel from 10$^{22}$ to 10$^{23.5}$ cm$^{-2}$ with step as 10$^{0.5}$. The bottom-right panel presents the 2D histogram between Lorentz force and H$_2$ column density. The red dot line fits a 'power law' relation between Lorentz force and H$_2$ column density. The top-right pane presents the distribution of Lorentz force weighted by column density, due to the Lorentz force strength related to column density. The orange line represents a Gaussian fit to the distribution, and the red line indicates the average curvature value ($<f_{\rm L}>\sim 2.5\times 10^{-26} {\rm G}^2{\rm cm}^{-1}$).