LAUSR

The convection that takes place in the innermost shells of massive stars plays an important role in the formation of core-collapse supernova explosions. Upon encountering the supernova shock, additional turbulence is generated, amplifying the explosion. In this work, we study how the convective perturbations evolve during the stellar collapse. Our main aim is to establish their physical properties right before they reach the supernova shock. To this end, we solve the linearized hydrodynamics equations perturbed on a stationary background flow. The latter is given by the spherical transonic Bondi accretion, while the convective perturbations are modeled as a combination of entropy and vorticity waves. We follow their evolution from large radii, where convective shells are initially located, down to small radii, where they are expected to encounter the accretion shock above the proto-neutron star. Considering typical vorticity perturbations with a Mach number $\sim 0.1$ and entropy perturbations $\delta S\sim 0.05 k_\mathrm{b}/\mathrm{baryon}$ at a radius of $1,500\,\mathrm{km}$, we find that the advection of these perturbations down to the shock generates strong acoustic waves with a relative amplitude $\delta p/\gamma p\sim 10\%$, in agreement with numerical simulations. The velocity perturbations consist of comparable contributions from vorticity and acoustic waves with values reaching $10\%$ of the sound speed ahead of the shock.