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Depending on mass and metallicity as well as evolutionary phase, stars occasionally experience convectivereactive nucleosynthesis episodes. We specifically investigate the situation when nucleosynthetically unprocessed, H-rich material is convectively mixed with a He-burning zone, for example in convectively unstable shell on top of electron-degenerate cores in AGB stars, young white dwarfs or X-ray bursting neutron stars. Such episodes are frequently encountered in stellar evolution models of stars of extremely low or zero metal content, such as the first stars. We have carried out detailed nucleosynthesis simulations based on stellar evolution models and informed by hydrodynamic simulations. We focus on the convective-reactive episode in the very-late thermal pulse star Sakurai's object (V4334 Sagittarii). Asplund et al. (1999) determined the abundances of 28 elements, many of which are highly non-solar, ranging from H, He and Li all the way to Ba and La, plus the C isotopic ratio. Our simulations show that the mixing evolution according to standard, one-dimensional stellar evolution models implies neutron densities in the He intershell ( few 10 11 cm −3 ) that are too low to obtain a significant neutron capture nucleosynthesis on the heavy elements. We have carried out 3D hydrodynamic He-shell flash convection simulations in 4π geometry to study the entrainment of H-rich material. Guided by these simulations we assume that the ingestion process of H into the He-shell convection zone leads only after some delay time to a sufficient entropy barrier that splits the convection zone into the original one driven by He-burning and a new one driven by the rapid burning of ingested H. By making such mixing assumptions that are motivated by our hydrodynamic simulations we obtain significantly higher neutron densities (∼ few 10 15 cm −3 ) and reproduce the key observed abundance trends found in Sakurai's object. These include an overproduction of Rb, Sr and Y by about 2 orders of magnitude higher than the overproduction of Ba and La. Such a peculiar nucleosynthesis signature is impossible to obtain with the mixing predictions in our one-dimensional stellar evolution models. The simulated Li abundance and the isotopic ratio 12 C/ 13 C are as well in agreement with observations. Details of the observed heavy element abundances can be used as a sensitive diagnostic tool for the neutron density, for the neutron exposure and, in general, for the physics of the convective-reactive phases in stellar evolution. For example, the high elemental ratio Sc/Ca and the high Sc production indicate high neutron densities. The diagnostic value of such abundance markers depends on uncertain nuclear physics input. We determine how our results depend on uncertainties of nuclear reaction rates, for example for the 13 C(α, n) 16 O reaction. 10 Although even in this case multi-dimensional effects of convection have to be taken into account eventually as simulations by indicate that the velocity profile at the bottom of the convective shell is ...

We performed 3-D simulations of proton-rich material entrainment into 12 C-rich He-shell flash convection and the subsequent H-ingestion flash that took place in the post-AGB star Sakurai's object. Observations of the transient nature and anomalous abundance features are available to validate our method and assumptions, with the aim to apply them to very low metallicity stars in the future. We include nuclear energy feedback from H burning and cover the full 4π geometry of the shell. Runs on 768 3 and 1536 3 grids agree well with each other and have been followed for 1500min and 1200min. After a 850min long quiescent entrainment phase the simulations enter into a global non-spherical oscillation that is launched and sustained by individual ignition events of H-rich fluid pockets. Fast circumferential flows collide at the antipode and cause the formation and localized ignition of the next H-overabundant pocket. The cycle repeats for more than a dozen times while its amplitude decreases. During the global oscillation the entrainment rate increases temporarily by a factor ≈ 100. Entrained entropy quenches convective motions in the upper layer until the burning of entrained H establishes a separate convection zone. The lower-resolution run hints at the possibility that another global oscillation, perhaps even more violent will follow. The location of the H-burning convection zone agrees with a 1-D model in which the mixing efficiency is calibrated to reproduce the light curve. The simulations have been performed at the NSF Blue Waters supercomputer at NCSA.

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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.

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