This work investigates the properties of convection in stars with particular emphasis on entrainment across the upper convective boundary (CB). Idealised simulations of turbulent convection in the O-burning shell of a massive star are performed in 4π geometry on 768 3 and 1536 3 grids, driven by a representative heating rate. A heating series is also performed on the 768 3 grid. The 1536 3 simulation exhibits an entrainment rate at the upper CB of 1.33 × 10 −6 M s −1 . The 768 3 simulation with the same heating rate agrees within 17 per cent. The entrainment rate at the upper convective boundary is found to scale linearly with the driving luminosity and with the cube of the shear velocity at the upper boundary, while the radial RMS fluid velocity scales with the cube root of the driving luminosity, as expected. The mixing is analysed in a 1D diffusion framework, resulting in a simple model for CB mixing. The analysis confirms previous findings that limiting the MLT mixing length to the distance to the CB in 1D simulations better represents the spherically-averaged radial velocity profiles from the 3D simulations and provides an improved determination of the reference diffusion coefficient D 0 for the exponential diffusion CB mixing model in 1D. From the 3D simulation data we adopt as the convective boundary the location of the maximum gradient in the horizontal velocity component which has 2σ spatial fluctuations of ≈ 0.17H P . The exponentially decaying diffusion CB mixing model with f = 0.03 reproduces the spherically-averaged 3D abundance profiles.

Convective boundary mixing (CBM) in the advanced evolutionary stages of massive stars is not well understood. Structural changes caused by convection have an impact on the evolution as well as the subsequent supernova, or lack thereof. The effects of convectively driven mixing across convective boundaries during the post He core burning evolution of 25M , solar-metallicity, non-rotating stellar models is studied using the MESA stellar evolution code. CBM is modelled using the exponentially decaying diffusion coefficient equation, the free parameter of which, f CBM , is varied systematically throughout the course of the stellar model's evolution with values of (0.002, 0.012, 0.022, 0.032). The effect of varying this parameter produces mass ranges at collapse in the ONe, Si, Fe cores of (1.82M , 4.36M ), (1.67M , 1.99M ) and (1.46M , 1.70M ) respectively, with percent differences from the model with minimal CBM as large as 86.3%. At the presupernova stage, the compactness of the stellar cores from O'Connor & Ott (2011), ξ M , exhibit a range of (0.120, 0.354), suggesting that the extent of CBM in the advanced burning stages of massive stars is an important consideration for the explodability and type of compact remnant. The nucleosynthetic yields from the models, most notably C, O, Ne, Mg and Si are also significantly affected by the CBM assumptions, showing non-linear trends with increased mixing. The simulations show that interactions between convective C, Ne and O shells produce significant nonlinear changes in the evolution, whereas from the end of Si burning, the structural changes attributed to the CBM are dominated by the growth of the convective C shell. Progenitor structures for all the models are available from HERE (link and DOI to appear) .

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