  We present convincing evidence of unburned carbon at photospheric velocities
in new observations of 5 Type Ia supernovae (SNe Ia) obtained by the Nearby
Supernova Factory. These SNe are identified by examining 346 spectra from 124
SNe obtained before +2.5 d relative to maximum. Detections are based on the
presence of relatively strong C II 6580 absorption "notches" in multiple
spectra of each SN, aided by automated fitting with the SYNAPPS code. Four of
the 5 SNe in question are otherwise spectroscopically unremarkable, with ions
and ejection velocities typical of SNe Ia, but spectra of the fifth exhibits
high-velocity (v > 20,000 km/s) Si II and Ca II features. On the other hand,
the light curve properties are preferentially grouped, strongly suggesting a
connection between carbon-positivity and broad band light curve/color behavior:
Three of the 5 have relatively narrow light curves but also blue colors, and a
fourth may be a dust-reddened member of this family. Accounting for
signal-to-noise and phase, we estimate that 22 +10/-6% of SNe Ia exhibit
spectroscopic C II signatures as late as -5 d with respect to maximum. We place
these new objects in the context of previously recognized carbon-positive SNe
Ia, and consider reasonable scenarios seeking to explain a physical connection
between light curve properties and the presence of photospheric carbon. We also
examine the detailed evolution of the detected carbon signatures and the
surrounding wavelength regions to shed light on the distribution of carbon in
the ejecta. Our ability to reconstruct the C II 6580 feature in detail under
the assumption of purely spherical symmetry casts doubt on a "carbon blobs"
hypothesis, but does not rule out all asymmetric models. A low volume filling
factor for carbon, combined with line-of-sight effects, seems unlikely to
explain the scarcity of detected carbon in SNe Ia by itself.
