  The rising luminosity of the recent, nearby supernova 2011fe shows a
quadratic dependence with time during the first 0.5-4 days. In addition, the
composite lightcurves formed from stacking together many Type Ia supernovae
(SNe Ia) show a similar power-law index of 1.8+-0.2 with time. I explore what
range of power-law rises are possible due to the presence of radioactive
material near the surface of the exploding white dwarf (WD). I summarize what
constraints such a model places on the structure of the progenitor and the
distribution and velocity of ejecta. My main conclusion is that the rise of SN
2011fe requires a mass fraction 0.03 of 56Ni (or some other heating source like
48Cr) distributed between a depth of ~0.004-0.1Msun below the WD's surface.
Radioactive elements this shallow are not found in simulations of a single C/O
detonation. Scenarios that may produce this material include helium-shell
burning during a double-detonation ignition, a gravitationally confined
detonation, and a subset of deflagration to detonation transition models. In
general, the power-law rise can differ from quadratic depending on the details
of the event, so comparisons of this work with observed bolometric rises of SNe
Ia would place strong constraints on the distribution of shallow radioactive
material, providing important clues for identifying the elusive progenitors of
SNe Ia.
