  The polarized dust emission observed in Class 0 protostellar cores at high
angular resolution with ALMA has raised several concerns about the grain
alignment conditions in these regions. We aim to study the role of the
radiation field on the grain alignment mechanisms occurring in the interior
(<1000 au) of Class 0 protostars. We produce synthetic observations of the
polarized dust emission from a MHD model of protostellar formation, using the
POLARIS dust radiative transfer tool, which includes dust alignment with
Radiative Torques Alignment (RATs). We test how the polarized dust emission
from the model core depends on the irradiation conditions in the protostellar
envelope, by varying the radiation due to accretion luminosity propagating from
the central protostellar embryo throughout the envelope. The level of grain
alignment efficiency obtained in the radiative transfer models is then compared
to (sub-) millimeter ALMA dust polarization observations of Class 0 protostars.
Our radiative transfer calculations have a central irradiation that reproduces
the protostellar luminosities typically observed towards low- to
intermediate-mass protostars, as well as super-paramagnetic grains, and grains
>10 micron, which are required to bring the dust grain alignment efficiencies
of the synthetic observations up to observed levels. Our radiative transfer
calculations show that irradiation plays an important role in the mechanisms
that dictate the size range of aligned grains in Class 0 protostars. Regions of
the envelope that are preferentially irradiated harbor strong polarized dust
emission but can be affected by the rotational disruption of dust grains.
Episodes of high luminosity could affect grain alignment and trigger grain
disruption mechanisms. [abridged]
