Relative Importance of Convective Uncertainties in Massive Stars

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 15, 20 and $25\, \rm M_ødot$. 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 red-wards. 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 introduce and we find differences of up to $70$ for the core masses and the total mass of the star

Convective core entrainment in 1D main-sequence stellar models

3D hydrodynamics models of deep stellar convection exhibit turbulent entrainment at the convective-radiative boundary which follows the entrainment law, varying with boundary penetrability. We implement the entrainment law in the 1D Geneva stellar evolution code. We then calculate models between 1.5 and 60 M⊙ at solar metallicity (Z = 0.014) and compare them to previous generations of models and observations on the main sequence. The boundary penetrability, quantified by the bulk Richardson number, RiB, varies with mass and to a smaller extent with time. The variation of RiB with mass is due to the mass dependence of typical convective velocities in the core and hence the luminosity of the star. The chemical gradient above the convective core dominates the variation of RiB with time. An entrainment law method can therefore explain the apparent mass dependence of convective boundary mixing through RiB. New models including entrainment can better reproduce the mass dependence of the main-sequence width using entrainment law parameters A ∼ 2 × 10−4 and n = 1. We compare these empirically constrained values to the results of 3D hydrodynamics simulations and discuss implications

3D Simulations and MLT. I. Renzini’s Critique

Renzini wrote an influential critique of “overshooting” in mixing-length theory (MLT), as used in stellar evolution codes, and concluded that three-dimensional fluid dynamical simulations were needed. Such simulations are now well tested. Implicit large eddy simulations connect large-scale stellar flow to a turbulent cascade at the grid scale, and allow the simulation of turbulent boundary layers, with essentially no assumptions regarding flow except the number of computational cells. Buoyant driving balances turbulent dissipation for weak stratification, as in MLT, but with the dissipation length replacing the mixing length. The turbulent kinetic energy in our computational domain shows steady pulses after 30 turnovers, with no discernible diminution; these are caused by the necessary lag in turbulent dissipation behind acceleration. Interactions between coherent turbulent structures give multi-modal behavior, which drives intermittency and fluctuations. These cause mixing, which may justify use of the instability criterion of Schwarzschild rather than the Ledoux. Chaotic shear flow of turning material at convective boundaries causes instabilities that generate waves and sculpt the composition gradients and boundary layer structures. The flow is not anelastic; wave generation is necessary at boundaries. A self-consistent approach to boundary layers can remove the need for ad hoc procedures of “convective overshooting” and “semi-convection.” In Paper II, we quantify the adequacy of our numerical resolution in a novel way, determine the length scale of dissipation—the “mixing length”—without astronomical calibration, quantify agreement with the four-fifths law of Kolmogorov for weak stratification, and deal with strong stratification