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Analytical Light Curve Models of Super-Luminous Supernovae: chi^2-Minimizations of Parameter Fits

We present fits of generalized semi-analytic supernova (SN) light curve (LC) models for a variety of power inputs including Ni-56 and Co-56 radioactive decay, magnetar spin-down, and forward and reverse shock heating due to supernova ejecta-circumstellar matter (CSM) interaction. We apply our models to the observed LCs of the H-rich Super Luminous Supernovae (SLSN-II) SN 2006gy, SN 2006tf, SN 2008am, SN 2008es, CSS100217, the H-poor SLSN-I SN 2005ap, SCP06F6, SN 2007bi, SN 2010gx and SN 2010kd as well as to the interacting SN 2008iy and PTF09uj. Our goal is to determine the dominant mechanism that powers the LCs of these extraordinary events and the physical conditions involved in each case. We also present a comparison of our semi-analytical results with recent results from numerical radiation hydrodynamics calculations in the particular case of SN 2006gy in order to explore the strengths and weaknesses of our models. We find that CS shock heating produced by ejecta-CSM interaction provides a better fit to the LCs of most of the events we examine. We discuss the possibility that collision of supernova ejecta with hydrogen-deficient CSM accounts for some of the hydrogen-deficient SLSNe (SLSN-I) and may be a plausible explanation for the explosion mechanism of SN 2007bi, the pair-instability supernova (PISN) candidate. We characterize and discuss issues of parameter degeneracy.