In this thesis, I present the results using two methods to model the magnetic fields in protostellar cores with interferometric polarimetry. I compare high angular resolution observations of the submillimeter polarized emission of NGC 1333 IRAS 4A with empirical models of density profiles and magnetic fields in protostellar core. With the assumptions of uniform temperature distribution, constant dust property, and small dust alignment efficiency, the simulations of Stokes I, Q, and U maps are computed with integrals along the line-of-sight. The Stokes I, Q, and U maps are then convolved into visibilities of Stokes parameters to be compared with observations using two methods. The first method of modeling magnetic fields is based on the comparisons of modeled polarization angle and observed polarization angle. The second method is a direct analysis of Stokes parameter visibilities from models and observations. Three types of magnetic field configurations, poloidal magnetic fields, inclined poloidal magnetic fields, and polodial and toroidal magnetic fields, are used to model the polarization distribution in IRAS 4A. The results show that hourglass structures alone cannot reproduce the depolarization effect in IRAS 4A if the inclination angle is indeed as small as what have been inferred from the outflow line-of-sight velocity and proper motions. My analysis favors a morphology of inclined magnetic fields with an hourglass structure at scales of few hundred AU and a toroidal component with a maximum in a middle section of the disk around the protostars. Applications of the modeling magnetic fields in the visibility space to high quality interferometric polarization measurements and detail studies with magnetohydrodynamics (MHD) simulations would be feasible in the future.

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