The Transition of Polarized Dust Thermal Emission from the Protostellar
  Envelope to the Disk Scale
  Polarized dust continuum emission has been observed with ALMA in an
increasing number of deeply embedded protostellar systems. It generally shows a
sharp transition going from the protostellar envelope to the disk scale, with
the polarization fraction typically dropping from ${\sim} 5\%$ to ${\sim} 1\%$
and the inferred magnetic field orientations becoming more aligned with the
major axis of the system. We quantitatively investigate these observational
trends using a sample of protostars in the Perseus molecular cloud and compare
these features with a non-ideal MHD disk formation simulation. We find that the
gas density increases faster than the magnetic field strength in the transition
from the envelope to the disk scale, which makes it more difficult to
magnetically align the grains on the disk scale. Specifically, to produce the
observed ${\sim} 1\%$ polarization at ${\sim} 100\,\mathrm{au}$ scale via
grains aligned with the B-field, even relatively small grains of
$1\,\mathrm{\mu m}$ in size need to have their magnetic susceptibilities
significantly enhanced (by a factor of ${\sim} 20$) over the standard value,
potentially through superparamagnetic inclusions. This requirement is more
stringent for larger grains, with the enhancement factor increasing linearly
with the grain size, reaching ${\sim} 2\times 10^4$ for millimeter-sized
grains. Even if the required enhancement can be achieved, the resulting
inferred magnetic field orientation in the simulation does not show a
preference for the major axis, which is inconsistent with the observed pattern.
We thus conclude that the observed trends are best described by the model where
the polarization on the envelope scale is dominated by magnetically aligned
grains and that on the disk scale by scattering.
