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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.