  The progenitor stars of core-collapse supernovae (CCSNe) are asymmetrically
fluctuating due to turbulent convections in the late stages of their lives. The
progenitor asymmetry at the pre-supernova stage has recently caught the
attention as a new ingredient to facilitate shock revival in the delayed
neutrino-heating mechanism. In this paper, we investigate the importance of the
progenitor asymmetries to shock revival with a semi-analytical approach. Free
parameters were chosen such that the time evolution of shock radii and mass
accretion rates are compatible with the results of detailed numerical
simulations of CCSNe in spherical symmetry. We first estimate the amplitude of
asymmetries required for the shock revival by the impulsive change of pre-shock
flows in the context of neutrino heating mechanism, and then convert the
amplitude to the corresponding amplitude in the pre-supernova phase by taking
into account the growth of asymmetries during infall. We apply our model to
various types of progenitors and find that the requisite amplitude of
pre-supernova asymmetry is roughly three times larger than the prediction by
current stellar evolution models unless other additional physical ingredients
such as multi-dimensional fluid instabilities and turbulent convections in
post-shock flows aid shock revival. We thus conclude that progenitor
asymmetries can not trigger the shock revival by the impulsive way but rather
play a supplementary role in reality.
