50 pages, 12 figures; accepted to ApJ. Note: online abstract is abbreviated - SnovaeWe report Nearby Supernova Factory observations of SN 2005gj, the second confirmed case of a "hybrid" Type Ia/IIn supernova. Our early-phase photometry of SN 2005gj shows that the interaction is much stronger than for the prototype, SN 2002ic. Our first spectrum shows a hot continuum with broad and narrow H-alpha emission. Later spectra, spanning over 4 months from outburst, show clear Type Ia features combined with broad and narrow H-gamma, H-beta, H-alpha and HeI 5876,7065 in emission. At higher resolution, P Cygni profiles are apparent. Surprisingly, we also observe an inverted P Cygni profile for [OIII] 5007. We find that the lightcurve and measured velocity of the unshocked circumstellar material imply mass loss as recently as 8 years ago. The early lightcurve is well-described by a flat radial density profile for the circumstellar material. However, our decomposition of the spectra into Type Ia and shock emission components allows for little obscuration of the supernova, suggesting an aspherical or clumpy distribution for the circumstellar material. We suggest that the emission line velocity profiles arise from electron scattering rather than the kinematics of the shock. This is supported by the inferred high densities, and the lack of evidence for evolution in the line widths. Ground- and space-based photometry, and Keck spectroscopy, of the host galaxy are used to ascertain that the host galaxy has low metallicity Z/Zsun < 0.3; (95% confidence) and that this galaxy is undergoing a significant star formation event that began roughly 200+/-70 Myr ago. We discuss the implications of these observations for progenitor models and cosmology using Type Ia supernovae
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