Solar convection zone dynamics

A comprehensive understanding of the solar magnetic cycle requires detailed modeling of the solar interior including the maintenance and variation of large scale flows (differential rotation and meridional flow), the solar dynamo and the flux emergence process connecting the magnetic field in the solar convection zone with magnetic field in the photosphere and above. Due to the vast range of time and length scales encountered, a single model of the entire convection zone is still out of reach. However, a variety of aspects can be modeled through a combined approach of 3D MHD models and simplified descriptions. We will briefly review our current theoretical understanding of these processes based on numerical models of the solar interior.Comment: 12 pages, 1 figure, to appear in IAGA Special Sopron Book Series, "The Sun, the Solar Wind and the Heliosphere", eds. M. Paz Miralles & J. Sanchez Almeid

Interaction Vertex for Classical Spinning Particles

We consider a model of the classical spinning particle in which the coadjoint orbits of the Poincare group are parametrized by two pairs of canonically conjugate four vectors, one representing the standard position and momentum variables and the other which encodes the spinning degrees of freedom. This "Dual Phase Space Model" is shown to be a consistent theory of both massive and massless particles and allows for coupling to background fields such as electromagnetism. The on-shell action is derived and shown to be a sum of two terms, one associated with motion in spacetime and the other with motion in "spin space." Interactions between spinning particles are studied and a necessary and sufficient condition for consistency of a three-point vertex is established.Comment: 26 pages, 2 figure

Numerical sunspot models: Robustness of photospheric velocity and magnetic field structure

MHD simulations of sunspots have successfully reproduced many aspects of sunspot fine structure as consequence of magneto convection in inclined magnetic field. We study how global sunspot properties and penumbral fine structure depend on the magnetic top boundary condition as well as on grid spacing. The overall radial extent of the penumbra is subject to the magnetic top boundary condition. All other aspects of sunspot structure and penumbral fine structure are resolved at an acceptable level starting from a grid resolution of 48 [24] km (horizontal [vertical]). We find that the amount of inverse polarity flux and the overall amount of overturning convective motions in the penumbra are robust with regard to both, resolution and boundary conditions. At photospheric levels Evershed flow channels are strongly magnetized. We discuss in detail the relation between velocity and magnetic field structure in the photosphere and point out observational consequences.Comment: 23 pages, 22 figures, 2 movies, accepted for publication in Ap

Numerical simulations of sunspot decay: On the penumbra -- Evershed flow -- moat flow connection

We present a series of high-resolution sunspot simulations that cover a time span of up to 100 hours. The simulation domain extends about 18 Mm in depth beneath the photosphere and 98 Mm horizontally. We use open boundary conditions that do not maintain the initial field structure against decay driven by convective motions. We consider two setups: A sunspot simulation with penumbra, and a "naked-spot" simulation in which we removed the penumbra after 20 hours through a change in the magnetic top boundary condition. While the sunspot has an Evershed outflow of 3-4 km/s, the naked spot is surrounded by an inflow of 1-2 km/s in close proximity. However, both spots are surrounded by an outflow on larger scales with a few 100 m/s flow speed in the photosphere. While the sunspot has almost constant magnetic flux content for the simulated time span of 3-4 days, the naked spot decays steadily at a rate of $10^{21}$ Mx/day. A region with reduced downflow filling factor, which is more extended for the sunspot, surrounds both spots. The absence of downflows perturbs the upflow/downflow massflux balance and leads to a large-scale radially overturning flow system, the photospheric component of this flow is to the observable moat flow. The reduction of the downflow filling factor also inhibits submergence of magnetic field in the proximity of the spots, which stabilizes them against decay. While this effect is present for both spots, it is more pronounced for the sunspot and explains the almost stationary magnetic flux content.Comment: 14 pages, 11 figues, accepted for publication in Ap

Can overturning motions in penumbral filaments be detected?

Numerical simulations indicate that the filamentation of sunspot penumbrae and the associated systematic outflow (the Evershed effect) are due to convectively driven fluid motions constrained by the inclined magnetic field. We investigate whether these motions, in particular the upflows in the bright filaments and the downflows at their edges can be reliably observed with existing instrumentation. We use a snapshot from a sunspot simulation to calculate 2D maps of synthetic line profiles for the spectral lines Fe\sci 7090.4 \AA ~ and C\sci 5380.34 \AA. The maps are spatially and spectrally degraded according to typical instrument properties. Line-of-sight velocities are determined from line bisector shifts. We find that the detectability of the convective flows is strongly affected by spatial smearing, particularly so for the downflows. Furthermore, the line-of-sight velocities are dominated by the Evershed flow unless the observation is made very near to disk center. These problems may have compromised recent attempts to detect overturning penumbral convection. Lines with a low formation height are best suited to detect the convective flows.Comment: 8 pages, 12 figures, accepted for publication in ApJ on 28th Ju

Efficient small-scale dynamo in solar convection zone

We investigate small-scale dynamo action in the solar convection zone through a series of high resolution MHD simulations in a local Cartesian domain with 1$R_\odot$ (solar radius) of horizontal extent and a radial extent from 0.715 to 0.96$R_\odot$. The dependence of the solution on resolution and diffusivity is studied. For a grid spacing of less than 350 km, the root mean square magnetic field strength near the base of the convection zone reaches 95% of the equipartition field strength (i.e. magnetic and kinetic energy are comparable). For these solutions the Lorentz force feedback on the convection velocity is found to be significant. The velocity near the base of the convection zone is reduced to 50% of the hydrodynamic one. In spite of a significant decrease of the convection velocity, the reduction in the enthalpy flux is relatively small, since the magnetic field also suppresses the horizontal mixing of the entropy between up- and downflow regions. This effect increases the amplitude of the entropy perturbation and makes convective energy transport more efficient. We discuss potential implications of these results for solar global convection and dynamo simulations.Comment: 46 pages, 25 figures, 1 table, accepted by Ap