  HET Optical spectra covering the evolution from about 6 days before to about
5 weeks after maximum light and the ROTSE-IIIb unfiltered light curve of the
"Branch-normal" Type Ia Supernova SN 2005hj are presented. The host galaxy
shows HII region lines at redshift of z=0.0574, which puts the peak unfiltered
absolute magnitude at a somewhat over-luminous -19.6. The spectra show weak and
narrow SiII lines, and for a period of at least 10 days beginning around
maximum light these profiles do not change in width or depth and they indicate
a constant expansion velocity of ~10,600 km/s. We analyzed the observations
based on detailed radiation dynamical models in the literature. Whereas delayed
detonation and deflagration models have been used to explain the majority of
SNe Ia, they do not predict a long velocity plateau in the SiII minimum with an
unvarying line profile. Pulsating delayed detonations and merger scenarios form
shell-like density structures with properties mostly related to the mass of the
shell, M_shell, and we discuss how these models may explain the observed SiII
line evolution; however, these models are based on spherical calculations and
other possibilities may exist. SN 2005hj is consistent with respect to the
onset, duration, and velocity of the plateau, the peak luminosity and, within
the uncertainties, with the intrinsic colors for models with M_shell=0.2 M_sun.
Our analysis suggests a distinct class of events hidden within the
Branch-normal SNe Ia. If the predicted relations between observables are
confirmed, they may provide a way to separate these two groups. We discuss the
implications of two distinct progenitor classes on cosmological studies
employing SNe Ia, including possible differences in the peak luminosity to
light curve width relation.
