What Can We Learn from the Rising Lightcurves of Radioactively-Powered Supernovae?

The lightcurve of the explosion of a star with a radius <10-100Rsun is powered mostly by radioactive decay. Observationally such events are dominated by hydrogen deficient progenitors and classified as Type I supernovae: white dwarf thermonuclear explosions (Type Ia) and core collapses of hydrogen-stripped massive stars (Type Ibc). 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 lightcurves and discuss how observations can be utilized to study these exploding stars. The early radioactive-powered lightcurves probe the shallowest 56Ni deposits. If the amount of 56Ni mixing can be deduced, then it places constraints on the progenitor and properties of the explosive burning. In practice we find it is difficult to disentangle whether the explosion occurred recently and one is seeing 56Ni heating near the surface or whether the explosion began in the past and 56Ni heating is deeper. In the latter case there is a "dark phase" between the moment of explosion and the first light observed from the shallowest layers of 56Ni. Because of this, simply extrapolating a lightcurve from 56Ni back in time is not a reliable method for estimating the explosion time. The best solution is to directly identify the moment of explosion, by either observing shock breakout or shock-heated surface cooling, so the depth being probed by the rising lightcurve is known. Since this is typically not available, we identify other diagnostics that are helpful for deciphering how recently an explosion occurred. As an example we apply these arguments to the SN Ic PTF 10vgv. We demonstrate that just a single measurement of the photospheric velocity and temperature during the rise places constraints on its explosion time, radius, and 56Ni mixing.