Most of the information on supernovae comes from optical observations during the first weeks and months following the explosion. One of the challenges in understanding the explosions is to relate the observed features of the emitted light to the properties of the exploding star and the explosion mechanism. This is challenging due to the fact that the light can be absorbed and emitted by thousands of atomic transitions on its way out. We are working on detailed numerical radiation transfer calculations as well as analytic approximations in order to learn about the explosions from the observations.
The equation in the image is a new and useful relation we recently found between the injection of energy Q(t) in the expanding material from radioactive decay and the total bolometric luminosity L(t) of supernovae. This equation is a direct result of conservation of energy with the multiplication by t exactly correcting for the adiabatic losses. This equation allows us to directly and robustly measure several global properties of the explosion, bypassing the complications of radiation transfer.