A three-dimensional hydrodynamics simulation of oxygen-shell burning in the final evolution of a fast-rotating massive star

We perform for the first time a 3D hydrodynamics simulation of the evolution of the last minutes pre-collapse of the oxygen shell of a fast-rotating massive star. This star has an initial mass of 38 M$_\odot$, a metallicity of $\sim$1/50 Z$_\odot$, an initial rotational velocity of 600 km s$^{-1}$, and experiences chemically homogeneous evolution. It has a silicon- and oxygen-rich (Si/O) convective layer at (4.7-17)$\times 10^{8}$ cm, where oxygen-shell burning takes place. The power spectrum analysis of the turbulent velocity indicates the dominance of the large-scale mode ($\ell \sim 3$), which has also been seen in non-rotating stars that have a wide Si/O layer. Spiral arm structures of density and silicon-enriched material produced by oxygen-shell burning appear in the equatorial plane of the Si/O shell. Non-axisymmetric, large-scale ($m \le 3$) modes are dominant in these structures. The spiral arm structures have not been identified in previous non-rotating 3D pre-supernova models. Governed by such a convection pattern, the angle-averaged specific angular momentum becomes constant in the Si/O convective layer, which is not considered in spherically symmetrical stellar evolution models. Such spiral arms and constant specific angular momentum might affect the ensuing explosion or implosion of the star.