  The Standing Accretion Shock Instability (SASI) is commonly believed to be
responsible for large amplitude dipolar oscillations of the stalled shock
during core collapse, potentially leading to an asymmetric supernovae
explosion. The degree of asymmetry depends on the amplitude of SASI, which
nonlinear saturation mechanism has never been elucidated. We investigate the
role of parasitic instabilities as a possible cause of nonlinear SASI
saturation. As the shock oscillations create both vorticity and entropy
gradients, we show that both Kelvin-Helmholtz and Rayleigh-Taylor types of
instabilities are able to grow on a SASI mode if its amplitude is large enough.
We obtain simple estimates of their growth rates, taking into account the
effects of advection and entropy stratification. In the context of the
advective-acoustic cycle, we use numerical simulations to demonstrate how the
acoustic feedback can be decreased if a parasitic instability distorts the
advected structure. The amplitude of the shock deformation is estimated
analytically in this scenario. When applied to the set up of Fernandez &
Thompson (2009a), this saturation mechanism is able to explain the dramatic
decrease of the SASI power when both the nuclear dissociation energy and the
cooling rate are varied. Our results open new perspectives for anticipating the
effect, on the SASI amplitude, of the physical ingredients involved in the
modeling of the collapsing star.
