摘要: 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 $^{12}$CO,
$^{13}$CO, C$^{18}$O, and H I, as well as polarized dust emissions. To obtain
the 3D direction of the magnetic field, we employ the polarization fraction
analysis developed in Hu & Lazarian (2022). 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 introduced in Lazarian et al. (2022), 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 $\approx55^\circ$ on average, while that of the central dense
clump is $\approx30^\circ$. We find the global mean value of total magnetic
field strength is $B_{\rm tot}\approx$ 135 uG from DCF and $B_{\rm tot}\approx$
75 uG from DMA. We use the velocity gradient technique (VGT) to separate the
magnetic fields' POS orientations associated with L1688 and its
foreground/background. The magnetic fields' orientations are statistically
coherent. The probability density function of H$_2$ column density and VGT
reveal that L1688 potentially is undergoing gravitational contraction at large
scale $\approx1.0$ pc and gravitational collapse at small scale $\approx0.2$
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 $n_{\rm H}$ is less than approximately $6.0\times10^3$
cm$^{-3}$.