2023MNRAS.524.4431H

Interaction of three-dimensional magnetic fields, turbulence, and self-gravity in the molecular cloud is crucial in understanding star formation but has not been addressed so far. In this work, we target the low-mass star-forming region L1688 and use the spectral emissions of ¹²CO, ¹³CO, C¹⁸O, and H I, as well as polarized dust emissions. To obtain the 3D direction of the magnetic field, we employ the novel polarization fraction analysis. In combining with the plane-of-the-sky (POS) magnetic field strength derived from the Davis-Chandrasekhar-Fermi (DCF) method and the new differential measure analysis (DMA) technique, we present the first measurement of L1688's three-dimensional magnetic field, including its orientation and strength. We find that L1688's magnetic field has two statistically different inclination angles. The low-intensity tail has an inclination angle ≈55° on average, while that of the central dense clump is ≈30°. We find the global mean value of total magnetic field strength is B_tot ≈ $135 \,\mathrm{\mu }{\rm G}$ from DCF and B_tot ≈ $75 \,\mathrm{\mu }{\rm G}$ from DMA. We use the velocity gradient technique (VGT) to separate the magnetic fields' POS orientation associated with L1688 and its foreground/background. The magnetic fields' orientations are statistically coherent. The probability density function of H₂ column density and VGT reveal that L1688 is potentially undergoing gravitational contraction at large scale ≈1.0 pc and gravitational collapse at small scale ≈0.2 pc. The gravitational contraction mainly along the magnetic field resulting in an approximate power-law relation $B_{\rm tot}\propto n_{\rm H}^{1/2}$ when volume density n_H is less than approximately 6.0 × 10³ cm^–3.