This work investigates the properties of convection in stars with particular emphasis on entrainment across the upper convective boundary (CB). Idealized simulations of turbulent convection in the O-burning shell of a massive star are performed in 4π geometry on 7683 and 15363 grids, driven by a representative heating rate. A heating series is also performed on the 7683 grid. The 15363 simulation exhibits an entrainment rate at the upper CB of 1.33 × 10-6M⊙ s-1. The 7683 simulation with the same heating rate agrees within 17 per cent. The entrainment rate at the upper CB 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 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 provide an improved determination of the reference diffusion coefficient D0 for the exponential diffusion CB mixing model in 1D. From the 3D simulation data, we adopt as the CB the location of the maximum gradient in the horizontal velocity component which has 2σ spatial fluctuations of ≈0.17HP. The exponentially decaying diffusion CB mixing model with f = 0.03 reproduces the spherically averaged 3D abundance profiles.
Bibliographical noteFunding Information:
SJ is a fellow of the Alexander von Humboldt Foundation and acknowledges support from the Klaus Tschira Stiftung (KTS). RA, a CITA national fellow, acknowledges support from the Canadian Institute for Theoretical Astrophysics. This work has been supported by NSF grant PHY-1430152 (JINA Center for the Evolution of the Elements). The 3D hydrodynamical simulations reported here were carried out in part on the Compute CanadaWestGridOrcinus cluster at UBC, Canada and in part on the Blue Waters machine at NCSA under the support of NSF PRAC awards 0832618 and 1440025 and CDS&E award 1413548 to the University of Minnesota. FH acknowledges support from an NSERC Discovery grant. The development of the PPM code used in this work has also been supported by contracts with the Los Alamos National Laboratory and the Sandia National Laboratory through the University of Minnesota. FH would like to thank Roman Baranowski from UBC/WestGrid for his kind support and SJ and FH thank Michael Bennett for his preliminary work on the diffusion analysis presented in this paper. We would like to thank Bernhard M?ller for several helpful comments.
- Stars: evolution
- Stars: interior
- Stars: massive