  A survey of Type II supernovae explosion models has been carried out to
determine how their light curves and spectra vary with their mass, metallicity,
and explosion energy. The presupernova models are taken from a recent survey of
massive stellar evolution at solar metallicity supplemented by new calculations
at subsolar metallicity. Explosions are simulated by the motion of a piston
near the edge of the iron core and the resulting light curves and spectra are
calculated using full multi-wavelength radiation transport. Formulae are
developed that describe approximately how the model observables (light curve
luminosity and duration) scale with the progenitor mass, explosion energy, and
radioactive nucleosynthesis. Comparison with observational data shows that the
explosion energy of typical supernovae (as measured by kinetic energy at
infinity) varies by nearly an order of magnitude -- from 0.5 to 4.0 x 10^51
ergs, with a typical value of ~0.9 x 10^51 ergs. Despite the large variation,
the models exhibit a tight relationship between luminosity and expansion
velocity, similar to that previously employed empirically to make SNe IIP
standardized candles. This relation is explained by the simple behavior of
hydrogen recombination in the supernova envelope, but we find a sensitivity to
progenitor metallicity and mass that could lead to systematic errors.
Additional correlations between light curve luminosity, duration, and color
might enable the use of SNe IIP to obtain distances accurate to ~20% using only
photometric data.
