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Dust polarization in millimeter (and centimeter) has been mapped in disksaround an increasing number of young stellar objects. It is usually thought tocome from emission by magnetically aligned (non-spherical) grains, but can alsobe produced by dust scattering. We present a semi-analytic theory of diskpolarization that includes both the direction emission and scattering, with anemphasis on their relative importance and how they are affected by the diskinclination. For face-on disks, both emission and scattering tend to producepolarization in the radial direction, making them difficult to distinguish,although the scattering-induced polarization can switch to the azimuthaldirection if the incident radiation is beamed strongly enough in the radialdirection in the disk plane. Disk inclination affects the polarizations fromemission and scattering differently, especially on the major axis where, in theedge-on limit, the former vanishes while the latter reaches a polarizationfraction as large as 1/3. The polarizations from the two competing mechanismstend to cancel each other on the major axis, producing two low polarization"holes" (one on each side of the center) under certain conditions. We findtantalizing evidence for at least one such "hole" in NGC1333 IRAS4A1, whosepolarization observed at 8 mm on the 100 AU scale is indicative of a patterndominated by scattering close to the center and by direction emission in theouter region. If true, it would imply not only that a magnetic field exists onthe disk scale, but that it is strong enough to align large, possibly mm-sized,grains.

Disk Polarization From Both Emission and Scattering of Magnetically Aligned Grains: The Case of NGC 1333 IRAS4A1