We present the first 4π-3D simulation of the last minutes of oxygen shell burning in an 18M supernova progenitor up to the onset of core collapse. A moving inner boundary is used to accurately model the contraction of the silicon and iron core according to a 1D stellar evolution model with a self-consistent treatment of core deleptonization and nuclear quasi-equilibrium. The simulation covers the full solid angle to allow the emergence of large-scale convective modes. Due to core contraction and the concomitant acceleration of nuclear burning, the convective Mach number increases to ∼0.1 at collapse, and an = 2 mode emerges shortly before the end of the simulation. Aside from a growth of the oxygen shell from 0.51M to 0.56M due to entrainment from the carbon shell, the convective flow is reasonably well described by mixing length theory, and the dominant scales are compatible with estimates from linear stability analysis. We deduce that artificial changes in the physics, such as accelerated core contraction, can have precarious consequences for the state of convection at collapse. We argue that scaling laws for the convective velocities and eddy sizes furnish good estimates for the state of shell convection at collapse and develop a simple analytic theory for the impact of convective seed perturbations on shock revival in the ensuing supernova. We predict a reduction of the critical luminosity for explosion by 12 . . . 24% due to seed asphericities for our 3D progenitor model relative to the case without large seed perturbations.

We present three-dimensional implicit large eddy simulations of the turbulent convection in the envelope of a 5 M red giant star and in the oxygen-burning shell of a 23 M supernova progenitor. The numerical models are analyzed in the framework of one-dimensional Reynolds-Averaged Navier-Stokes equations. The effects of pressure fluctuations are more important in the red giant model, owing to larger stratification of the convective zone. We show how this impacts different terms in the mean-field equations. We clarify the driving sources of kinetic energy, and show that the rate of turbulent dissipation is comparable to the convective luminosity. Although our flows have low Mach numbers and are nearly adiabatic, our analysis is general and can be applied to photospheric convection as well. The robustness of our analysis of turbulent convection is supported by the insensitivity of the mean-field balances to linear mesh resolution. We find robust results for the turbulent convection zone and the stable layers in the oxygen-burning shell model, and robust results everywhere in the red giant model, but the mean fields are not well converged in the narrow boundary regions (which contain steep gradients) in the oxygen-burning shell model. This last result illustrates the importance of unresolved physics at the convective boundary, which governs the mixing there.

We examine the physical basis for algorithms to replace mixing-length theory (MLT) in stellar evolutionary computations. Our 321D procedure is based on numerical solutions of the Navier-Stokes equations. These implicit large eddy simulations (ILES) are three-dimensional (3D), time-dependent, and turbulent, including the Kolmogorov cascade. We use the Reynolds-averaged Navier-Stokes (RANS) formulation to make concise the 3D simulation data, and use the 3D simulations to give closure for the RANS equations. We further analyze this data set with a simple analytical model, which is non-local and time-dependent, and which contains both MLT and the Lorenz convective roll as particular subsets of solutions. A characteristic length (the damping length) again emerges in the simulations; it is determined by an observed balance between (1) the large-scale driving, and (2) small-scale damping.The nature of mixing and convective boundaries is analyzed, including dynamic, thermal and compositional effects, and compared to a simple model. We find that (1) braking regions (boundary layers in which mixing occurs) automatically appear beyond the edges of convection as defined by the Schwarzschild criterion, (2) dynamic (non-local) terms imply a non-zero turbulent kinetic energy flux (unlike MLT), (3) the effects of composition gradients on flow can be comparable to thermal effects, and (4) convective boundaries in neutrino-cooled stages differ in nature from those in photon-cooled stages (different Péclet numbers). The algorithms are based upon ILES solutions to the Navier-Stokes equations, so that, unlike MLT, they do not require any calibration to astronomical systems in order to predict stellar properties. Implications for solar abundances, helioseismology, asteroseismology, nucleosynthesis yields, supernova progenitors and core collapse are indicated.

We present the first detailed 3D hydrodynamic implicit large eddy simulations of turbulent convection of carbon burning in massive stars. Simulations begin with radial profiles mapped from a carbon-burning shell within a 15 M 1D stellar evolution model. We consider models with 128 3 , 256 3 , 512 3 , and 1024 3 zones. The turbulent flow properties of these carbon-burning simulations are very similar to the oxygen-burning case. We performed a mean field analysis of the kinetic energy budgets within the Reynolds-averaged Navier-Stokes framework. For the upper convective boundary region, we find that the numerical dissipation is insensitive to resolution for linear mesh resolutions above 512 grid points. For the stiffer, more stratified lower boundary, our highest resolution model still shows signs of decreasing sub-grid dissipation suggesting it is not yet numerically converged. We find that the widths of the upper and lower boundaries are roughly 30 per cent and 10 per cent of the local pressure scaleheights, respectively. The shape of the boundaries is significantly different from those used in stellar evolution models. As in past oxygen-shell-burning simulations, we observe entrainment at both boundaries in our carbon-shell-burning simulations. In the large Péclet number regime found in the advanced phases, the entrainment rate is roughly inversely proportional to the bulk Richardson number, Ri B (∝Ri B −α , 0.5 α 1.0). We thus suggest the use of Ri B as a means to take into account the results of 3D hydrodynamics simulations in new 1D prescriptions of convective boundary mixing.Key words: convection -hydrodynamics -turbulence -stars: evolution -stars: interiorsstars: massive. I N T RO D U C T I O N1D stellar evolution codes are currently the only way to simulate the entire lifespan of a star. This comes at the cost of having to replace complex, inherently 3D processes, such as convection, rotation, and magnetic activity, with generally simplified mean-field models. An essential question is 'how well do these 1D models represent reality?' Answers can be found both in empirical and theoretical works. On the empirical front, we can investigate full star models, by comparing them to observations of stars under a range of conditions, as well as testing the basic physics that goes into models of multidimensional phenomena by studying relevant laboratory work and E-mail: a.j.cristini@keele.ac.uk (AC); r.hirschi@keele.ac.uk (RH); wdarnett@gmail.com (DA) data from meteorology and oceanography (remembering that stars are much bigger than planets, and are composed of high-energy density plasma). On the theoretical side, multidimensional simulations can be used to test 1D models under astrophysical conditions that can be recreated in terrestrial laboratories only in small volumes, e.g. in National Ignition Facility (NIF) (Kuranz et al. 2011) and z-pinch device (Miernik et al. 2013) experiments. Astronomical testsThe results from the astronomical validation studies are mixed. Observations of stars confirm the gener...