Velocity Gradient and Stellar Polarization: Magnetic Field Tomography towards the L1688 Cloud

Magnetic fields are a defining yet enigmatic aspect of the interstellar medium (ISM), with their three-dimensional mapping posing a substantial challenge. In this study, we harness the innovative Velocity Gradient Technique (VGT), underpinned by magnetohydrodynamic (MHD) turbulence theories, to elucidate the magnetic field structure by applying it to the atomic neutral hydrogen (HI) emission line and the molecular tracer $^{12}$CO. We construct the tomography of the magnetic field in the low-mass star-forming region L1688, utilizing two approaches: (1) VGT-HI combined with the Galactic rotational curve, and (2) stellar polarization paired with precise star parallax measurements. Our analysis reveals that the magnetic field orientations deduced from stellar polarization undergo a distinct directional change in the vicinity of L1688, providing evidence that the misalignment between VGT-HI and stellar polarization stems from the influence of the molecular cloud's magnetic field on the polarization of starlight. When comparing VGT-$^{12}$CO to stellar polarization and Planck polarization data, we observe that VGT-$^{12}$CO effectively reconciles the misalignment noted with VGT-HI, showing statistical alignment with Planck polarization measurements. This indicates that VGT-$^{12}$CO could be integrated with VGT-HI, offering vital insights into the magnetic fields of molecular clouds, thereby enhancing the accuracy of our 3D magnetic field reconstructions.