Generalized Semi-Analytical Models Of Type II Supernova Light Curves

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We present generalized supernovae (SN) light curve (LC) models for a variety of power inputs including previously proposed mechanisms. We extend those solutions to include non-centrally located power sources and stationary photospheres as might be the case for SN that are powered by ejecta-circumstellar matter (CSM) interaction. To do so we provide an expression for the power input that is produced by a self-similar circumstellar (CS) shock that efficiently converts its kinetic energy into radiation. We find that the CS shock 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. We compare fits of our model and LC models for different power inputs introduced by other authors to the observed LCs of the recently-discovered Super Luminous Supernovae (SLSNe) 2005ap, 2006gy, 2006tf, 2007bi, 2008am and 2008es as well as to the strongly interacting SNe 2008iy, PTF09uj and to the peculiar transient SCP06F6. We find that CS shock heating produced by ejecta-CSM interaction provides a better fit to the LCs of most of those events. Some contribution from radioactive decay can improve the fits in some cases. We also address the relation between Type IIL and Type IIn SN with ejecta-CSM interaction models. A faster Type IIL decline can be reproduced by the diffusion of previously deposited shock power if the CS power input to the diffusive component vanishes when the shock breaks out of the optically-thick CSM. We conclude that the observed LC variety of Type IIL, Type IIn and of the SLSNe is likely to be a byproduct of the large range of conditions relevant to significant ejecta-CSM interaction as a power source.

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