The rising luminosity of the recent , nearby supernova 2011fe shows a quadratic dependence with time during the first \approx 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 \pm 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 X _ { 56 } \approx 3 \times 10 ^ { -2 } of ^ { 56 } Ni ( or some other heating source like ^ { 48 } Cr ) distributed between a depth of \approx 4 \times 10 ^ { -3 } -0.1 M _ { \odot } 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 .