Magnetic Field of Molecular Gas Measured with the Velocity Gradient Technique I. Orion A

Magnetic fields play an important role in the evolution of molecular clouds and star formation. Using the velocity gradient technique (VGT) model, we measured the magnetic field in Orion A using the ¹²CO, ¹³CO, and C¹⁸O(1-0) emission lines at a scale of ~0.07 pc. The measured B field shows an east-west orientation that is perpendicular to the integral shaped filament of Orion A at large scale. The VGT magnetic fields obtained from ¹³CO and C¹⁸O are in agreement with the B field that is measured from the Planck 353 GHz dust polarization at a scale of ~0.55 pc. Removal of density effects by using a velocity decomposition algorithm can significantly improve the accuracy of the VGT in tracing magnetic fields with the ¹²CO(1-0) line. The magnetic field strengths of seven subclouds, OMC-1, OMC-2, OMC-3, OMC-4, OMC-5, L 1641-N, and NGC 1999, have also been estimated with the Davis-Chandrasekhar-Fermi and the Two Mach Numbers technique, and these are found to be in agreement with previous results obtained from dust polarization at far-infrared and submillimeter wavelengths. At smaller scales, the VGT prove a good method to measure magnetic fields.