Characterizing three-dimensional magnetic field, turbulence, and self-gravity in the star-forming region L1688

Abstract

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 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 $\approx55^\circ$ on average, while that of the central dense clump is $\approx30^\circ$. We find the global mean value of total magnetic field strength is $B_{\rm tot}\approx135$ uG from DCF and $B_{\rm tot}\approx75$ uG 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 H$_2$ column density and VGT reveal that L1688 is potentially 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 results 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$^{-3}$.