Is the mm/sub-mm dust polarization a robust tracer of the magnetic field
  topology in protostellar envelopes ? A model exploration
  High resolution (sub-)millimeter polarization observations have opened a new
era in the understanding of how B-fields are organized in star forming regions,
unveiling an intricate interplay between the B-fields and the gas in
protostellar cores. However, to assess the role of the B-field in the process
of solar-type star formation, it is key to be able to understand to what extent
these polarized dust emission are good tracers of the B-field in the youngest
protostellar objects. We present a thorough investigation of the fidelity and
limitations of using dust polarized emission to map the B-field topologies in
low-mass protostars. To assess the importance of these effects, we performed
the analysis of B-field properties in 27 realizations of MHD models of
star-forming cores. Assuming a uniform population of dust grains which sizes
follow the standard MRN, we analyze the synthetic polarized dust emission maps
produced if these grains align with the local B-field thanks to B-RATs. We find
that (sub-)millimeter polarized dust emission is a robust tracer of the B-field
topologies in inner protostellar envelopes and is successful at capturing the
details of the B-field spatial distribution down to radii ~100 au. Measurements
of the los averaged B-field orientation using the polarized dust emission are
precise to < 15{\deg} in about 75 - 95% of the independent lines of sight
peering through protostellar envelopes. Large discrepancies between the
integrated B-field mean orientation and the orientation reconstructed from the
polarized dust emission are mostly observed in (i) lines of sight where the
B-field is highly disorganized and (ii) lines of sight probing large column
densities. Our analysis shows that high opacity of the thermal dust emission
and low polarization fractions could be used to avoid utilizing the small
fraction of measurements affected by large errors.
