We present polarization spectra near maximum light for the strongly subluminous Type Ia supernova SN 1999by that show that the supernova is intrinsically polarized. SN 1999by has an observed, overall level of polarization of approximate to0.3%-0.8%, a rise of the polarization P redward of 6500 Angstrom, and a change in polarization across the Si II lambda 6150 feature of about 0.4%. The presentation of the polarization at different wavelengths in the Q-U plane is shown to be a powerful tool to determine the overall geometry and the interstellar component. The distribution of points with wavelength using this empirical Q-U plane method reveals that SN 1999by has a well-defined axis of symmetry and suggests an interstellar polarization (ISP) vector with P-ISP = 0.3% and position angle Theta = 150 degrees with an error circle in the Q-U plane of radius about 0.1%. Synthetic non-LTE spectra for axisymmetric configurations based on delayed-detonation models have been computed assuming ellipsoidal geometry. The input ejecta structure and composition are based on a Chandrasekhar mass delayed-detonation model. The parameters of the explosion are chosen to reproduce the time evolution of IR spectra of SN 1999by without further adjustments. Spherical models are then mapped onto ellipsoidal geometries and the axis ratio, viewing angle, and ISP adjusted to provide the best agreement with the polarization spectra. Both flux and polarization spectra can be reasonably well reproduced by models with an asphericity of approximate to 20% observed equator-on. The general properties of the polarization can be understood as a consequence of the structure of subluminous models. Best fits are obtained for the theoretical models with P-ISP = 0.25% and Theta = 140 degrees, consistent with the empirical method. We discuss our results for this subluminous Type Ia in the context of "normally bright" Type Ia supernovae. For normally bright Type Ia, the photosphere is near the inner iron-rich layers at maximum light and the ubiquitous iron lines give a rapid variation to the model polarization spectra. In subluminous models, the photosphere near maximum is in the silicon layers with fewer lines and a smoother overall polarization spectrum, as observed for SN 1999by. Though data are sparse, the low upper limits for polarization determined for many normal events in contrast to the high polarization in SN 1999by may suggest a relation between the asymmetry we observed and the mechanism that produces a subluminous Type Ia. Among various mechanisms, rapid rotation of the progenitor white dwarf and/or an explosion during a binary white dwarf merger process are likely candidates to explain the asphericity in SN 1999by.
