Ongoing transient surveys are presenting an unprecedented account of the rising lightcurves of Type Ia supernovae ( SNe Ia ) .
This early emission probes the shallowest layers of the exploding white dwarf , which can provide constraints on the progenitor star and the properties of the explosive burning .
We use semi-analytic models of radioactively-powered rising lightcurves to analyze these observations .
As we have summarized in previous work , the main limiting factor in determining the surface distribution of ^ { 56 } Ni is the lack of an unambiguously identified time of explosion , as would be provided by detection of shock breakout or shock-heated cooling .
Without this the SN may in principle exhibit a “ dark phase ” for a few hours to days , where the only emission is from shock-heated cooling that is too dim to be detected .
We show that by assuming a theoretically-motivated time-dependent velocity evolution , the explosion time can be better constrained , albeit with potential systematic uncertainties .
This technique is used to infer the surface ^ { 56 } Ni distributions of three recent SNe Ia that were caught especially early in their rise .
In all three we find fairly similar ^ { 56 } Ni distributions .
Observations of SN 2011fe and SN 2012cg probe shallower depths than SN 2009ig , and in these two cases ^ { 56 } Ni is present merely \sim 10 ^ { -2 } M _ { \odot } from the WDs ’ surfaces .
The uncertainty in this result is up to an order of magnitude given the difficulty of precisely constraining the explosion time .
We also use our conclusions about the explosion times to reassess radius constraints for the progenitor of SN 2011fe , as well as discuss the roughly t ^ { 2 } power law that is inferred for many observed rising lightcurves .