1. GOAL:
To understand the physics of active region decay, and the Quiet Sun network
APPROACH:
Use physics-based numerical models to simulate the dynamic connection between magnetic fields embedded in the turbulent convection zone, and those observed in the solar atmosphere
THE DOMAIN:
Must extend below the visible surface into the turbulent layers of the convective interior, and above the surface out into the low-corona
THE CURRENT FOCUS:
Quiet Sun magnetic fields generated by a convective dynamo

2. THE MODEL:
A new 3D MHD solver capable of treating the essential physics of the combined convection zone/corona system in an efficient manner over large spatial scales
THE ESSENTIAL PHYSICS:
Radiative cooling (optically thin in the corona, optically thick near the visible surface) --- drives the convection and determines the stratification of the atmosphere --- anisotropic thermal conduction (corona) and an assumed coronal heating mechanism
These sources and sinks must be included in the energy equation in order to achieve the stratification necessary to maintain a hot, low-density corona, and to initiate and maintain solar-like convective turbulence.
A proper treatment of the thermodynamics allows for a physics-based study of e.g., small scale flux emergence and cancellation, the transport of magnetic helicity from below the surface into the atmosphere, the effects of photospheric fields and flows on Quiet Sun coronal topology etc.

3. THE TRADE-OFF’s:
Forego a numerical solution of the transfer equation, and approximate optically thick radiative cooling
Restrict the domain to include only the portion of the convective interior close to the visible surface
CORONAL HEATING:
An empirically based volumetric heating function consistent with Pevtsov’s Law:
From Pevtsov et al. (2003) ApJ 598, 1387
X-ray luminosity must be proportional to both the chosen volumetric heating rate integrated over the X-ray emitting portion of the volume, and the total unsigned magnetic flux at the visible surface at any time during a simulation
T-Tauri stars
G,K,M dwarfs
Active regions
Active Sun (disk avg)
X-ray bright points
Quiet Sun

4. Left: log(Temperature) in degrees Kelvin along a vertical slice positioned at the center of the domain. Right: log(Density) (cgs) along the same vertical slice. The background stratification (and fluctuations about that background level) are apparent. This stratification is not imposed, rather it is the natural result of the choice of boundary conditions, and the characterization of the radiative transfer.

5. Top row: Vertical momentum along horizontal slices at different depths in the 30x30x7.5 Mm3 domain. From left to right: ~1Mm below the visible surface, the photosphere, the upper chromosphere, and the low corona. Bottom row: the vertical component of the magnetic field along the same horizontal slices. The second and third frames can be thought of as a simulated LOS magnetogram at disk center --- note the difference between the photospheric and chromospheric magnetogram in the simulated Quiet Sun.

6. Visualizing the convective dynamo: Contours of the magnetic field strength along a horizontal slice ~1Mm below the surface (left), at the photosphere (right), and along a vertical slice through the portion of the domain representing the convective interior (below).

7. Along the limb: Vertical slices through the atmosphere from the photosphere out to the low corona (5 Mm above the visible surface). From top to bottom: 1. log |B| along the slice extending through the model chromosphere, transition region and low corona; bright regions represent relatively strong fields, dark regions represent weaker fields. 2. The magnetic flux piercing the vertical slice; light regions indicate flux directed toward the observer, dark regions indicate flux directed away from the observer. 3. The vertical component of the magnetic field along the same slice A visualization of the logarithm of the plasma β (the ratio of gas to magnetic pressure) along the same vertical slice. Blue regions correspond to magnetically dominated plasma, and green and orange regions correspond to areas where β>1.

8. Above: Another visualization of log(β), this time across the entire vertical extent of the domain. Again, blue regions represent low β regions in the atmosphere, and red orange and yellow regions represent high-β regions in both the interior and atmosphere.
Below: A contour of the logarithm of the current density, log |J| (from a different vertical slice). Blue and black shades represent weak or negligible current densities.

9. Above: |J| along horizontal slices from (left to right) ~1Mm below the visible surface, the photosphere, the upper chromosphere, and the corona. Middle: Contours of the gas density at those same heights. Below: The log of the gas density along a vertical slice just above the photosphere.

10. Magnetic fieldlines drawn from a horizontal slice positioned in the chromosphere