  We investigate a method to construct parametrized progenitor models for
core-collapse supernova simulations. Different from all modern core-collapse
supernova studies, which rely on progenitor models from stellar evolution
calculations, we follow the methodology of Baron & Cooperstein (1990) to
construct initial models. Choosing parametrized spatial distributions of
entropy and electron fraction as a function of mass coordinate and solving the
equation of hydrostatic equilibrium, we obtain the initial density structures
of our progenitor models. First, we calculate structures with parameters
fitting broadly the evolutionary model s11.2 of Woosley et al. (2002). We then
demonstrate the reliability of our method by performing general relativistic
hydrodynamic simulations in spherical symmetry with the isotropic diffusion
source approximation to solve the neutrino transport. Our comprehensive
parameter study shows that initial models with a small central entropy
($\lesssim 0.4\,k_B$ nucleon$^{-1}$) can explode even in spherically symmetric
simulations. Models with a large entropy ($\gtrsim 6\,k_B$ nucleon$^{-1}$) in
the Si/O layer have a rather large explosion energy ($\sim 4\times 10^{50}$
erg) at the end of the simulations, which is still rapidly increasing.

High Energy Astrophysical Phenomena