Constraints on shallow ⁵⁶ni from the early light curves of Type Ia supernovae

Ongoing transient surveys are presenting an unprecedented account of the rising light curves of Type Ia supernovae (SNe Ia). This early emission probes the shallowest layers of the exploding white dwarf (WD), which can provide constraints on the progenitor star and the properties of the explosive burning. We use semianalytic models of radioactively powered rising light curves to analyze these observations. As we have summarized in previous work, the main limiting factor in determining the surface distribution of ⁵⁶Ni 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 ⁵⁶Ni distributions of three recent SNe Ia that were caught especially early in their rise. In all three we find fairly similar ⁵⁶Ni distributions. Observations of SN 2011fe and SN 2012cg probe shallower depths than SN 2009ig, and in these two cases ⁵⁶Ni is present merely 10 ^-2 M 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 t² power law that is inferred for many observed rising light curves.