  We compared the sizes and fluxes of a sample of protostellar disks in Orion A
measured with the ALMA 0.87 mm continuum data from the VANDAM survey with the
physical properties of their ambient environments on the core scale of 0.6 pc
estimated with the GBT GAS NH3 and JCMT SCUPOL polarimetric data. We did not
find any significant dependence of the disk radii and continuum fluxes on a
single parameter on the core scale, such as the non-thermal line width,
magnetic field orientation and strength, or magnitude and orientation of the
velocity gradient. Among these parameters, we only found a positive correlation
between the magnitude of the velocity gradient and the non-thermal line width.
Thus, the observed velocity gradients are more likely related to turbulent
motion but not large-scale rotation. Our results of no clear dependence of the
disk radii on these parameters are more consistent with the expectation from
non-ideal MHD simulations of disk formation in collapsing cores, where the disk
size is self-regulated by magnetic braking and diffusion, compared to other
simulations which only include turbulence and/or a magnetic field misaligned
with the rotational axis. Therefore, our results could hint that the non-ideal
MHD effects play a more important role in the disk formation. Nevertheless, we
cannot exclude the influences on the observed disk size distribution by
dynamical interaction in a stellar cluster or amounts of angular momentum on
the core scale, which cannot be probed with the current data.
