Generalized Semi-Analytical Models Of Supernova Light Curves
We present generalized supernova (SN) light curve (LC) models for a variety of power inputs including the previously proposed ideas of radioactive decay of Ni-56 and Co-56 and magnetar spin-down. We extend those solutions to include finite progenitor radius and stationary photospheres as might be the case for SN that are powered by interaction of the ejecta with circumstellar matter (CSM). We provide an expression for the power input that is produced by self-similar forward and reverse shocks that efficiently convert their kinetic energy into radiation. We find that this ejecta-CSM interaction luminosity that we derive is in agreement with results from multi-dimensional radiation hydrodynamics simulations in the case of an optically thin CSM. We develop a semi-analytical model for the case of an optically thick CSM by invoking an approximation for the effects of radiative diffusion similar to that adopted by Arnett for SN II and compare this model to the results of numerical radiation hydrodynamics models. This model can give complex LCs, but for monotonically declining shock input, the LCs have a smooth rise, peak, and decline. In the context of this model, we provide predictions of the shock breakout of the forward shock from the optically thick part of the CSM envelope. We also introduce a hybrid LC model that incorporates ejecta-CSM interaction plus Ni-56 and Co-56 radioactive decay input. We fit this hybrid model to the LC of the super-luminous supernova (SLSN) 2006gy. We find that shock heating produced by ejecta-CSM interaction plus some contribution from radioactive decay provides a better fit to the LC of this event than previously presented models. We also address the relation between SN IIL and SN IIn with ejecta-CSM interaction models. The faster decline of SN IIL can be reproduced by the diffusion of previously deposited shock power if the shock power input to the diffusive component vanishes when the reverse shock sweeps up the whole ejecta and/or the forward shock propagates through the optically thick CSM. A CSM interaction with forward and reverse shock power input can produce the LCs of SN IIn in terms of duration, shape, and decline rate, depending on the properties of the CSM envelope and the progenitor star. This model can also produce LCs that are symmetric in shape around peak luminosity, which is the case for the observed LCs of some recently discovered peculiar transient events. We conclude that the observed LC variety of SN IIn and of some SLSNe is likely to be a byproduct of the large range of conditions relevant to significant ejecta-CSM interaction as a power source.