  The role played by magnetic field during star formation is an important topic
in astrophysics. We investigate the correlation between the orientation of
star-forming cores (as defined by the core major axes) and ambient magnetic
field directions in 1) a 3D MHD simulation, 2) synthetic observations generated
from the simulation at different viewing angles, and 3) observations of nearby
molecular clouds. We find that the results on relative alignment between cores
and background magnetic field in synthetic observations slightly disagree with
those measured in fully 3D simulation data, which is partly because cores
identified in projected 2D maps tend to coexist within filamentary structures,
while 3D cores are generally more rounded. In addition, we examine the
progression of magnetic field from pc- to core-scale in the simulation, which
is consistent with the anisotropic core formation model that gas preferably
flow along the magnetic field toward dense cores. When comparing the observed
cores identified from the GBT Ammonia Survey (GAS) and Planck
polarization-inferred magnetic field orientations, we find that the relative
core-field alignment has a regional dependence among different clouds. More
specifically, we find that dense cores in the Taurus molecular cloud tend to
align perpendicular to the background magnetic field, while those in Perseus
and Ophiuchus tend to have random (Perseus) or slightly parallel (Ophiuchus)
orientations with respect to the field. We argue that this feature of relative
core-field orientation could be used to probe the relative significance of the
magnetic field within the cloud.
