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

No impact of core-scale magnetic field, turbulence, or velocity gradient on sizes of protostellar disks in Orion A