Multi-scale physical properties of NGC 6334 as revealed by local relative orientations between magnetic fields, density gradients, velocity gradients, and gravity

We present ALMA dust polarization and molecular line observations toward 4 clumps (I(N), I, IV, and V) in the massive star-forming region NGC 6334. In conjunction with large-scale dust polarization and molecular line data from JCMT, Planck, and NANTEN2, we make a synergistic analysis of relative orientations between magnetic fields ($\theta_{\mathrm{B}}$), column density gradients ($\theta_{\mathrm{NG}}$), local gravity ($\theta_{\mathrm{LG}}$), and velocity gradients ($\theta_{\mathrm{VG}}$) to investigate the multi-scale (from $\sim$30 pc to 0.003 pc) physical properties in NGC 6334. We find that the relative orientation between $\theta_{\mathrm{B}}$ and $\theta_{\mathrm{NG}}$ changes from statistically more perpendicular to parallel as column density ($N_{\mathrm{H_2}}$) increases, which is a signature of trans-to-sub-Alfv\'{e}nic turbulence at complex/cloud scales as revealed by previous numerical studies. Because $\theta_{\mathrm{NG}}$ and $\theta_{\mathrm{LG}}$ are preferentially aligned within the NGC 6334 cloud, we suggest that the more parallel alignment between $\theta_{\mathrm{B}}$ and $\theta_{\mathrm{NG}}$ at higher $N_{\mathrm{H_2}}$ is because the magnetic field line is dragged by gravity. At even higher $N_{\mathrm{H_2}}$, the angle between $\theta_{\mathrm{B}}$ and $\theta_{\mathrm{NG}}$ or $\theta_{\mathrm{LG}}$ transits back to having no preferred orientation or statistically slightly more perpendicular, suggesting that the magnetic field structure is impacted by star formation activities. A statistically more perpendicular alignment is found between $\theta_{\mathrm{B}}$ and $\theta_{\mathrm{VG}}$ throughout our studied $N_{\mathrm{H_2}}$ range, which indicates a trans-to-sub-Alfv\'{e}nic state at small scales as well. The normalised mass-to-flux ratio derived from the polarization-intensity gradient (KTH) method increases with $N_{\mathrm{H_2}}$.