By performing neutrino-radiation hydrodynamic simulations in spherical symmetry (1D) and axial symmetry (2D) with different progenitor models by Woosley & Heger from 12 to 100 Mo, we find that all 1D runs fail to produce an explosion and several 2D runs succeed. The difference in the shock evolutions for different progenitors can be interpreted by the difference in their mass accretion histories, which are in turn determined by the density structures of progenitors. The mass accretion history has two phases in the majority of the models: the earlier phase, in which the mass accretion rate is high and rapidly decreasing, and the later phase, with a low and almost constant accretion rate. They are separated by the so-called turning point, the origin of which is a change of the accreting layer. We argue that shock revival will most likely occur around the turning point and hence that its location in the plane will be a good measure for the possibility of shock revival: if the turning point lies above the critical curve and the system stays there for a long time, shock revival will obtain. In addition, we develop a phenomenological model to approximately evaluate the trajectories in the plane, which, after calibrating free parameters by a small number of 1D simulations, reproduces the location of the turning point reasonably well by using the initial density structure of progenitor alone. We suggest the application of the phenomenological model to a large collection of progenitors in order to infer without simulations which ones are more likely to explode.
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