Comparing star formation models with interferometric observations of the
  protostar NGC 1333 IRAS 4A. I. Magnetohydrodynamic collapse models
  Observations of dust polarized emission toward star forming regions trace the
magnetic field component in the plane of the sky and provide constraints to
theoretical models of cloud collapse. We compare high-angular resolution
observations of the submillimeter polarized emission of the low-mass
protostellar source NGC 1333 IRAS 4A with the predictions of three different
models of collapse of magnetized molecular cloud cores. We compute the Stokes
parameters for the dust emission for the three models. We then convolve the
results with the instrumental response of the Submillimeter Array observation
toward IRAS 4A. Finally, we compare the synthetic maps with the data, varying
the model parameters and orientation, and we assess the quality of the fit by a
\chi^2 analysis. High-angular resolution observations of polarized dust
emission can constraint the physical properties of protostars. In the case of
IRAS 4A, the best agreements with the data is obtained for models of collapse
of clouds with mass-to-flux ratio >2 times the critical value, initial uniform
magnetic field of strength ~0.5 mG, and age of the order of a few 10^4 yr since
the onset of collapse. Magnetic dissipation, if present, is found to occur
below the resolution level of the observations. Including a previously measured
temperature profile of IRAS 4A leads to a more realistic morphology and
intensity distribution. We also show that ALMA has the capability of
distinguishing among the three different models adopted in this work. Our
results are consistent with the standard theoretical scenario for the formation
of low-mass stars, where clouds initially threaded by large-scale magnetic
fields become unstable and collapse, trapping the field in the nascent
protostar and the surrounding circumstellar disk. In the collapsing cloud, the
dynamics is dominated by gravitational and magnetic forces.
