Impact of gravity on changing magnetic field orientations in a sample of massive protostellar clusters observed with ALMA

The magnetic field is integral to our understanding of the formation and dynamical evolution of molecular clouds and star formation within. We present a polarimetric survey of 17 massive protostellar cluster forming clumps, covered in 34 pointings in the 230-GHz window using the Atacama Large Millimeter/submillimeter Array (ALMA). The two array configurations, C43-1 and C43-4, probe linearly polarized dust emission, hence the plane-of-the-sky orientation of magnetic fields, at resolutions of 1\arcsec\ and 0\arcsec.4 that correspond to approximately 0.01pc core and $10^3$ au envelope scales, respectively. The relative orientations (ROs) of the magnetic field probed at two spatial scales are analyzed for the entire protostellar cluster sample and for a subset of objects in NGC 6334. We found a bimodal distribution of ROs with peaks at 0\deg\ (parallel) and 90\deg (orthogonal) for the entire sample combined as well as for NGC 6334. We investigate the physical origin of this bimodal distribution through a projected Rayleigh statistic (PRS) analysis in relation to column densities and local gravity in NGC 6334. We found an excess of parallel magnetic fields at column densities $> 10^{23}$ \cmm. The underlying cause of the RO distribution of the magnetic field is gravitational collapse at higher gas densities, which drags and reorients the magnetic field as shown in the alignment between the magnetic field and the direction of gravitational forces. The distribution of ROs observed here is consistent with the evolution of relative orientations of an initially sub-Alv\'enic cloud that becomes magnetically super-critical and super-Alv\'enic as the cloud collapses to form stars.