Anelastic and Compressible Simulations of Stellar Oxygen Burning

In this paper we compare fully compressible (Meakin & Arnett 2006a,b) andanelastic (Kuhlen, Woosley, & Glatzmaier 2003) simulations of stellar oxygenshell burning. It is found that the two models are in agreement in terms of thevelocity scale (v_c ~ 1e7 cm/s) and thermodynamic fluctuation amplitudes (e.g.,rho'/ ~ 2e-3) in the convective flow. Large fluctuations (~11%) arise inthe compressible model, localized to the convective boundaries, and are due tointernal waves excited in stable layers. Fluctuations on the several percentlevel are also present in the compressible model due to compositioninhomogeneities from ongoing entrainment events at the convective boundaries.Comparable fluctuations (with amplitudes greater than ~1%) are absent in theanelastic simulation because they are due to physics not included in thatmodel. We derive an analytic estimate for the expected density fluctuationamplitudes at convective boundaries by assuming that the pressure fluctuationsdue to internal waves at the boundary, p_w', balance the ram pressure of theconvective motions, rho*v_c2. The predicted amplitudes agree well with thesimulation data. The good agreement between the anelastic and the compressiblesolution within the convection zone and the agreement between the stable layerdynamics and analytic solutions to the non-radial wave equation indicate thatthe compressible hydrodynamic techniques used are robust for the simulatedstellar convection model, even at the low Mach n umbers found M~0.01.