Three-dimensional Hydrodynamics Simulations of Pre-collapse Shell Burning in the Si and O-rich Layers

We present three-dimensional (3D) hydrodynamics simulations of shell-burning in two progenitors with zero-age main sequence masses of 22 and 27 $M_{\odot}$ for $\sim$ 65 and 200 s up to the onset of gravitational collapse, respectively. The 22 and 27 $M_{\odot}$ stars are selected from a suite of one-dimensional (1D) progenitors. The former and the latter have an extended Si and O-rich layer with the width of $\sim 10^9$ cm and $\sim 5 \times 10^9$ cm, respectively. Our 3D results show that turbulent mixing occurs in both of the progenitors with the angle-averaged turbulent Mach number exceeding $\sim$ 0.1 at the maximum. We observe that an episodic burning of O and Ne, which takes place underneath the convection bases, enhances the turbulent mixing in the 22 and 27 $M_\odot$ models, respectively. The distribution of nucleosynthetic yields is significantly different from that in 1D simulations, namely in 3D more homogeneous and inhomogeneous in the radial and angular direction, respectively. By performing a spectrum analysis, we investigate the growth of turbulence and its role of material mixing in the convective layers. We also present a scalar spherical harmonics mode analysis of the turbulent Mach number. This analytical formula would be helpful for supernova modelers to implement the precollapse perturbations in core-collapse supernova simulations. Based on the results, we discuss implications for the possible onset of the perturbation-aided neutrino-driven supernova explosion.