2015ApJ...806..225P

Hydrogen-rich Type II-Plateau supernovae (SNe) exhibit correlations between the plateau luminosity L_pl, the nickel mass M_Ni, the explosion energy E_exp, and the ejecta mass M_ej. Using our global, self-consistent, multi-band model of nearby well-observed SNe, we find that the covariances of these quantities are strong and that the confidence ellipsoids are oriented in the direction of the correlations, which reduces their significance. By proper treatment of the covariance matrix of the model, we discover a significant intrinsic width to the correlations between L_pl, E_exp and M_Ni, where the uncertainties due to the distance and the extinction dominate. For fixed E_exp, the spread in M_Ni is about 0.25 dex, which we attribute to the differences in the progenitor internal structure. We argue that the effects of incomplete γ-ray trapping are not important in our sample. Similarly, the physics of the Type II-Plateau SN light curves leads to inherently degenerate estimates of E_exp and M_ej, which makes their observed correlation weak. Ignoring the covariances of SN parameters or the intrinsic width of the correlations causes significant biases in the slopes of the fitted relations. Our results imply that Type II-Plateau SN explosions are not described by a single physical parameter or a simple one-dimensional trajectory through the parameter space, but instead reflect the diversity of the core and surface properties of their progenitors. We discuss the implications for the physics of the explosion mechanism and possible future observational constraints.