What can we Learn from the Rising Light Curves of Radioactively Powered Supernovae?

The light curve of the explosion of a star with a radius <~ 10-100 R _⊙ is powered mostly by radioactive decay. Observationally, such events are dominated by hydrogen-deficient progenitors and classified as Type I supernovae (SNe I), i.e., white dwarf thermonuclear explosions (Type Ia), and core collapses of hydrogen-stripped massive stars (Type Ib/c). Current transient surveys are finding SNe I in increasing numbers and at earlier times, allowing their early emission to be studied in unprecedented detail. Motivated by these developments, we summarize the physics that produces their rising light curves and discuss ways in which observations can be utilized to study these exploding stars. The early radioactive-powered light curves probe the shallowest deposits of ⁵⁶Ni. If the amount of ⁵⁶Ni mixing in the outermost layers of the star can be deduced, then it places important constraints on the progenitor and properties of the explosive burning. In practice, we find that it is difficult to determine the level of mixing because it is hard to disentangle whether the explosion occurred recently and one is seeing radioactive heating near the surface or whether the explosion began in the past and the radioactive heating is deeper in the ejecta. In the latter case, there is a "dark phase" between the moment of explosion and the first observed light emitted once the shallowest layers of ⁵⁶Ni are exposed. Because of this, simply extrapolating a light curve from radioactive heating back in time is not a reliable method for estimating the explosion time. The best solution is to directly identify the moment of explosion, either through observing shock breakout (in X-ray/UV) or the cooling of the shock-heated surface (in UV/optical), so that the depth being probed by the rising light curve is known. However, since this is typically not available, we identify and discuss a number of other diagnostics that are helpful for deciphering how recently an explosion occurred. As an example, we apply these arguments to the recent SN Ic PTF 10vgv. We demonstrate that just a single measurement of the photospheric velocity and temperature during the rise places interesting constraints on its explosion time, radius, and level of ⁵⁶Ni mixing.