Modelling of stellar convection

Abstract

The review considers the modelling process for stellar convection rather than specific astrophysical results. For achieving reasonable depth and length we deal with hydrodynamics only, omitting MHD. A historically oriented introduction offers first glimpses on the physics of stellar convection. Examination of its basic properties shows that two very different kinds of modelling keep being needed: low dimensional models (mixing length, Reynolds stress, etc.) and "full" 3D simulations. A list of affordable and not affordable tasks for the latter is given. Various low dimensional modelling approaches are put in a hierarchy and basic principles which they should respect are formulated. In 3D simulations of low Mach number convection the inclusion of then unimportant sound waves with their rapid time variation is numerically impossible. We describe a number of approaches where the Navier-Stokes equations are modified for their elimination (anelastic approximation, etc.). We then turn to working with the full Navier-Stokes equations and deal with numerical principles for faithful and efficient numerics. Spatial differentiation as well as time marching aspects are considered. A list of codes allows assessing the state of the art. An important recent development is the treatment of even the low Mach number problem without prior modification of the basic equation (obviating side effects) by specifically designed

Convective boundary mixing in low- and intermediate-mass stars – I. Core properties from pressure-mode asteroseismology

“…On scales where Pé 1, i.e., where the convective turn-over timescale is shorter than the diffusion timescale, penetrating material can modify the entropy in the stably stratified region. Material in high Pé regimes, such as at the base of the solar convective envelope (where Pé is O(10 5 ), Kupka & Muthsam 2017), can continue to travel adiabatically with the overall effect of extending the convective region. As a consequence it weakens the stratification in stable zones, and thus gives rise to a thermal boundary or transition layer.…”

Stellar Evolution and Modelling Stars

“…In recent years, a new possibility has appeared for determining convective efficiency values from 3D simulations of stellar envelopes. These simulations solve the time-dependent hydrodynamic equations of mass, momentum, and energy conservation and are by design free from adjustable parameters such as the α MLT (e.g., [61,62], and references therein). Using suitable averages, it is possible to match the atmospheric stratification of the 3D model with the equivalent from one-dimensional calculations and extract a calibrated convective efficiency (e.g., [63,64]).…”

Can we detect the stellar differential rotation of WASP-7 through the Rossiter–McLaughlin observations?

“…Apart from the instrumental noise, the remaining sources of uncertainty have stellar origins. They are the center-tolimb variation of the convective blue-shift (Dravins et al 2017;Cegla et al 2016a;Shporer & Brown 2011), granulation, oscillations and the convective broadening due to granulation (Kupka & Muthsam 2017, and references therein). We then explored how well the stellar differential rotation could be characterized and the precision with which we can retrieve the projected spin-orbit angle.…”