Magnetoconvection in Stellar Interiors
I have recently become interested in several specific aspects of the theory of turbulent convection and magnetoconvection; namely, the process of magnetic flux transport in the solar convection zone, and the generation of magnetic fields via a local dynamo (a process independent of the presence or absence of an interface layer separating the differentially rotating, turbulent convection zone and the stable radiative layer) in both the Sun and other fully convective, magnetically active, rapidly rotating stars.
3D MHD simulations (in the anelastic approximation) of of solar convection using two different treatments of viscosity (from Abbett et al. 2004).
The Advective Transport of Magnetic Flux:
With George Fisher, Yuhong Fan, and Dave Bercik, I have performed a large number of numerical simulations of non-penetrative magnetoconvection in order to understand in detail the apparent net downward transport of signed magnetic flux that occurs as a result of the asymmetric flow pattern (broad slow moving upflows punctuated by strong, localized cool downdrafts) present in a stratified, convectively unstable medium.
We find that the rapid net downward transport of signed flux (referred to as "turbulent pumping" in the literature) evident in simulations of penetrative convection (i.e., a model convection zone bounded by a stable layer below) does not manifest itself in a closed domain despite the presence of strong, vertical flow asymmetries. Instead, for simulations initiated with an initially horizontal flux layer, we find only a weak, transient pumping mechanism that occurs only after the initial field becomes significantly non-uniform, during the time when the distribution of magnetic field relaxes to its equilibrium configuration. Thus, we suggest that the rapid pumping mechanism evident in simulations of penetrative convection is due to the presence of the convective overshoot layer, where flux entrained within the strong downdrafts penetrates into the stable layers where it remains for a timescale far exceeding that of convective turnover. The results of our numerical experiments, and the associated theoretical analyses that support our conclusions can be found in:
Stellar Dynamos:
At about spectral type M3, main sequence stars become fully convective. Recent theories suggest that such stars rotate essentially as a solid body, thus preventing the action of a solar-like interface dynamo (see "About the Sun II"). Nevertheless, measurements of magnetic fields in M3-M4.5 stars and the detection of traditional activity indicators (e.g., chromospheric H-alpha emission) in late M and L stars suggest that fully convective stars are quite active, and entirely capable of generating strong magnetic fields.
A 3D MHD simulation of magnetic field generation in a relatively slowly rotating star (from Bercik et al. 2003).
Our group is currently performing a large number of numerical simulations of magnetic field generation in fully convecting stratified plasmas of different rotation rates, Reynolds and Rayleigh numbers. In each case, We begin with a tiny seed field, and allow the magnetic field to to evolve and grow in a self-consistent way. The goal of our large parameter space survey is to better understand the physics of the local dynamo, to relate our findings to stars of different spectral types and rotation rates and to make predictions of the distribution of surface fields that can be observationally verified.
Comparing Simulations to Mixing Length Theory:
Mixing Length Theory enjoys widespread acceptance as a relatively simple means of determining the convective transport of heat in models of stellar structure. However, the theory does have a number of well known limitations; notably, it cannot reproduce dynamic phenomena important to stellar evolution calculations (e.g., the overshoot from thermonuclear fusion driven core convection zones and deep envelope convection zones in giant stars). A few years back, Bob Stein, Dali Georgobiani, Barry Davids, myself, and others in the Physics and Astronomy Department at Michigan State University compared the predictions of Mixing Length Theory with corresponding predictions obtained from a 3D numerical simulation of surface convection (in the absence of magnetic fields). The results of that investigation can be found in: