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...

Convective boundary mixing is one of the major uncertainties in stellar evolution. In order to study its dependence on boundary properties and turbulence strength in a controlled way, we computed a series of 3D hydrodynamical simulations of stellar convection during carbon burning with a varying boosting factor of the driving luminosity. Our 3D implicit large eddy simulations were computed with the prompi code. We performed a mean field analysis of the simulations within the Reynolds-averaged Navier-Stokes framework. Both the vertical RMS velocity within the convective region and the bulk Richardson number of the boundaries are found to scale with the driving luminosity as expected from theory: ∝ 1/3 and Ri B ∝ −2/3 , respectively. The positions of the convective boundaries were estimated through the composition profiles across them, and the strength of convective boundary mixing was determined by analysing the boundaries within the framework of the entrainment law. We find that the entrainment is approximately inversely proportional to the bulk Richardson number, Ri B (∝ Ri − B , ∼ 0.75). Although the entrainment law does not encompass all the processes occurring at boundaries, our results support the use of the entrainment law to describe convective boundary mixing in 1D models, at least for the advanced phases. The next steps and challenges ahead are also discussed.

ABSTRACT In this work, we investigate the impact of uncertainties due to convective boundary mixing (CBM), commonly called ‘overshoot’, namely the boundary location and the amount of mixing at the convective boundary, on stellar structure and evolution. For this we calculated two grids of stellar evolution models with the MESA code, each with the Ledoux and the Schwarzschild boundary criterion, and vary the amount of CBM. We calculate each grid with the initial masses of 15, 20, and $25\, \rm {M}_\odot$. We present the stellar structure of the models during the hydrogen and helium burning phases. In the latter, we examine the impact on the nucleosynthesis. We find a broadening of the main sequence with more CBM, which is more in agreement with observations. Furthermore, during the core hydrogen burning phase there is a convergence of the convective boundary location due to CBM. The uncertainties of the intermediate convective zone remove this convergence. The behaviour of this convective zone strongly affects the surface evolution of the model, i.e. how fast it evolves redwards. The amount of CBM impacts the size of the convective cores and the nucleosynthesis, e.g. the 12C to 16O ratio and the weak s-process. Lastly, we determine the uncertainty that the range of parameter values investigated introduces and we find differences of up to $70{{\ \rm per\ cent}}$ for the core masses and the total mass of the star.

Stellar evolution models of massive stars are important for many areas of astrophysics, for example nucleosynthesis yields, supernova progenitor models and understanding physics under extreme conditions. Turbulence occurs in stars primarily due to nuclear burning at different mass coordinates within the star.The understanding and correct treatment of turbulence and turbulent mixing at convective boundaries in stellar models has been studied for decades but still lacks a definitive solution. This paper presents initial results of a study on convective boundary mixing (CBM) in massive stars. The 'stiffness' of a convective boundary can be quantified using the bulk Richardson number (RiB), the ratio of the potential energy for restoration of the boundary to the kinetic energy of turbulent eddies. A 'stiff' boundary (RiB ∼ 10 4 ) will suppress CBM, whereas in the opposite case a 'soft' boundary (RiB ∼ 10) will be more susceptible to CBM. One of the key results obtained so far is that lower convective boundaries (closer to the centre) of nuclear burning shells are 'stiffer' than the corresponding upper boundaries, implying limited CBM at lower shell boundaries. This is in agreement with 3D hydrodynamic simulations carried out by Meakin and Arnett (2007). This result also has implications for new CBM prescriptions in massive stars as well as for nuclear burning flame front propagation in Super-Asymptotic Giant Branch (S-AGB) stars and also the onset of novae.