The nonlinear evolution of magnetized Keplerian shear ows is simulated in a local, three-dimensional model, including the e ects of compressibility and strati cation. Supersonic ows are initially generated by the Balbus-Hawley magnetic shear instability. The resulting ows regenerate a turbulent magnetic eld which, in turn, reinforces the turbulence. Thus, the system acts like a dynamo that generates its own turbulence. However, unlike usual dynamos, the magnetic energy exceeds the kinetic energy of the turbulence by a factor of 3{10. By assuming the eld to be vertical on the outer (upper and lower) surfaces we do not constrain the horizontal magnetic ux. Indeed, a large scale toroidal magnetic eld is generated, mostly in the form of toroidal ux tubes with lengths comparable to the toroidal extent of the box. This large scale eld is mainly of Present address: Nordita, Blegdamsvej 17, DK-2100 Copenhagen , Denmark y The National Center for Atmospheric Research is sponsored by the National Science Foundation 1 even (i.e. quadrupolar) parity with respect to the midplane and changes direction on a timescale of about 30 orbits, in a possibly cyclic manner. The e ective Shakura-Sunyaev alpha viscosity parameter is between 0.001 and 0.005, and the contribution from the Maxwell stress is about 3-7 times larger than the contribution from the Reynolds stress.
Numerical simulations provide information on solar convection not available by direct observation. We present results of simulations of near surface solar convection with realistic physics : an equation of state including ionization and three-dimensional, LTE radiative transfer using a four-bin opacity distribution function. Solar convection is driven by radiative cooling in the surface thermal boundary layer, producing the familiar granulation pattern. In the interior of granules, warm plasma ascends with B10% ionized hydrogen. As it approaches and passes through the optical surface, the plasma cools, recombines, and loses entropy. It then turns over and converges into the dark intergranular lanes and further into the vertices between granulation cells. These vertices feed turbulent downdrafts below the solar surface, which are the sites of buoyancy work that drives the convection. Only a tiny fraction of the Ñuid ascending at depth reaches the surface to cool, lose entropy, and form the cores of these downdrafts. Granules evolve by pushing out against and being pushed in by their neighboring granules, and by being split by overlying Ñuid that cools and is pulled down by gravity. Convective energy transport properties that are closely related to integral constraints such as conservation of energy and mass are exceedingly robust. Other properties, which are less tightly constrained and/or involve higher order moments or derivatives, are found to depend more sensitively on the numerical resolution. At the highest numerical resolution, excellent agreement between simulated convection properties and observations is found. In interpreting observations it is crucial to remember that surfaces of constant optical depth are corrugated. The surface of unit optical depth in the continuum is higher above granules and lower in the intergranular lanes, while the surface of optical depth unity in a spectral line is corrugated in ways that are inÑuenced by both thermal and Doppler e †ects.
We review the properties of solar convection that are directly observable at the solar surface, and discuss the relevant underlying physics, concentrating mostly on a range of depths from the temperature minimum down to about 20 Mm below the visible solar surface.The properties of convection at the main energy carrying (granular) scales are tightly constrained by observations, in particular by the detailed shapes of photospheric spectral lines and the topology (time- and length-scales, flow velocities, etc.) of the up- and downflows. Current supercomputer models match these constraints very closely, which lends credence to the models, and allows robust conclusions to be drawn from analysis of the model properties.At larger scales the properties of the convective velocity field at the solar surface are strongly influenced by constraints from mass conservation, with amplitudes of larger scale horizontal motions decreasing roughly in inverse proportion to the scale of the motion. To a large extent, the apparent presence of distinct (meso- and supergranulation) scales is a result of the folding of this spectrum with the effective “filters” corresponding to various observational techniques. Convective motions on successively larger scales advect patterns created by convection on smaller scales; this includes patterns of magnetic field, which thus have an approximately self-similar structure at scales larger than granulation.Radiative-hydrodynamical simulations of solar surface convection can be used as 2D/3D time-dependent models of the solar atmosphere to predict the emergent spectrum. In general, the resulting detailed spectral line profiles agree spectacularly well with observations without invoking any micro- and macroturbulence parameters due to the presence of convective velocities and atmosphere inhomogeneities. One of the most noteworthy results has been a significant reduction in recent years in the derived solar C, N, and O abundances with far-reaching consequences, not the least for helioseismology.Convection in the solar surface layers is also of great importance for helioseismology in other ways; excitation of the wave spectrum occurs primarily in these layers, and convection influences the size of global wave cavity and, hence, the mode frequencies. On local scales convection modulates wave propagation, and supercomputer convection simulations may thus be used to test and calibrate local helioseismic methods.We also discuss the importance of near solar surface convection for the structure and evolution of magnetic patterns: faculae, pores, and sunspots, and briefly address the question of the importance or not of local dynamo action near the solar surface. Finally, we discuss the importance of near solar surface convection as a driver for chromospheric and coronal heating.Electronic Supplementary MaterialSupplementary material is available for this article at 10.12942/lrsp-2009-2.
Numerical simulations of wave propagation in a two-dimensional stratified magneto-atmosphere are presented for conditions that are representative of the solar photosphere and chromosphere. Both the emergent magnetic flux and the extent of the wave source are spatially localized at the lower photospheric boundary of the simulation. The calculations show that the coupling between the fast and slow magnetoacoustic-gravity (MAG) waves is confined to thin quasi-one-dimensional atmospheric layers where the sound speed and the Alfvén velocity are comparable in magnitude. Away from this wave conversion zone, which we call the magnetic canopy, the two MAG waves are effectively decoupled because either the magnetic pressure (B 2 =8) or the plasma pressure (p ¼ Nk B T) dominates over the other. The character of the fluctuations observed in the magneto-atmosphere depend sensitively on the relative location and orientation of the magnetic canopy with respect to the wave source and the observation point. Several distinct wave trains may converge on and simultaneously pass through a given location. Their coherent superposition presents a bewildering variety of Doppler and intensity time series because (1) some waves come directly from the source while others emerge from the magnetic canopy following mode conversion, (2) the propagation directions of the individual wave trains are neither co-aligned with each other nor with the observer's line of sight, and (3) the wave trains may be either fast or slow MAG waves that exhibit different characteristics depending on whether they are observed in high-or low-plasmas ( 8p=B 2 ). Through the analysis of four numerical experiments a coherent and physically intuitive picture emerges of how fast and slow MAG waves interact within two-dimensional magneto-atmospheres.
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