3D, Compressible, Stratified

Parameter free, except for
Resolution
numerical Viscosity and Resistivity
Boundary Conditions
Realistic Physics:
Equation of State, including ionization
Radiative energy transfer: LTE, non-gray, 4 bin ODF, Lines
Agree with observations:
  Granulation
  Line Profiles: weak atomic lines
  Convection Zone Depth
  P-Mode Frequencies
  P-Mode Excitation Rate
Details:
Stein & Nordlund, 1998, ApJ, 499, 914.
Stein & Nordlund, 2000, Solar Phys. 192, 91.

Model: horizontal field is advected into the compuational domain by fluid entering through the bottom boundary.

[movie (293 Mb)]

Emergence of magnetic flux tubes. Time sequence is across then down. Loops emerge through surface and open up (e.g. snapshots 8-11 center). One loop later closes and is pulled down (snapshots 8-11, left).

Model: Initially uniform vertical 400 G magnetic field is shuffled about by convective motions.

Magnetic field is swept into the intergranular lanes and then to the underlying mesogranule boundary downflow. Contours are surface vertical magnetic field. Image is vertical velocity at surface (left) and 2.5 Mm below surface (right).

Magnetic field has filamentary structure below surface.

Vertical magnetic field distribution is exponential for case of horizontal flux advection and has long tail with peak at near equality with surrounding gas pressure for case of imposed vertical field.

Strong magnetic field locations are darker, occur in downflows, suppress the velocity both vertical and horizontal, and the tau=1 surface lies deeper by several hundred kilometers. Strong field locations also have smaller density, lower temperature and smaller gas pressure than their surroundings.

Micropores form where the magnetic field get concentrated at the vertices of intergranular lanes.

Micropore: intensity image with vertical magnetic field contours at half kG intervals. Red contours are zero vertical surface velocity to outline granules.

Micropores cool by radiating vertically to space (blue & purple) and are heated from their hot sidewalls (red).

Temperature is lower in both the bright point and micropore and the unit optical depth level is depressed in both.

Temperature (black) and magnetic field (red) contours in bright point (left) and micropore (right). Blue line is optical depth unity.

The flow is suppressed in a micropore, but not in a bright point. Strong downflow occurs at edges of micropore.

Velocity vectors and magnetic field contours (red) in bright point (left) and micropore (right).

Images of vertical velocity with magnetic field contours at the surface (above) and 1.5 Mm below the surface (below). Positive velocity is down. Units are km/s.

FeI 6302 (Wavelength range is +- 0.5 Angstrom).

Micropores typically form where a small granule disappears.

Magnetic field (left), Intensity (center), mask showing only the strongest magnetic field (right).

Intensity vs. magnetic field strength during pore formation. The dark pore forms first where the field is weak and the field strength gradually increases over time.

Image of surface magnetic field (top) and emergent intensity (bottom) as a function of time (increasing upward). The field initially is separate flux tubes around the micropore.

Magnetic field structures are long lived. Micropores are generally short lived. They form and disappear on a granular time scale (10 min.). Magnetic field (left) and Emergent Intensity (right) as function of time (increasing upward in 30 s intervals). At top long lived micropore exists for over an hour.

Intensity image and magnetic field contours on horizontal line at surface, as a function of time (increasing upward). A small granule disappears (lower left), the magnetic field around it converges and a micropore forms. The micropore disappears as a new granule pokes up into the intergranular lane. Later a new micropore forms (top left).

Time evolution on vertical line through center of micropore:

Solar rotation Differential rotation Meridional circulation Coriolis tilt of emerging flux

Stratified convection Stretching Downward pumping Buoyant fluxtubes Intermittent magnetic fields Surface random walk

 Growth is due to large scale stretching

• e-folding times ~ a few (several) turn-over times
• growth rates similar for laminar and turbulent case
  • reflect the same mechanism at work: stretching

 Compute Joule work and Ohmic dissipation

• There is an almost perfect balance in the high dissipation regions
  • The volume with dissipation above 0.1% of the maximum fills 10%
  • The dissipation there is almost perfectly balanced by local work
    • More than 99.5% of the dissipation occurs there
    • Less than 0.2% of the work occurs there!
• There is almost pure work (very little total dissipation) in the rest of the volume
  • The low-dissipation region covers 90% of the volume
    • Less than 0.5% of the dissipation occurs there
    • 99.8% dynamo work occurs there

 Conclusion:

• Dynamo work occurs by passive ("pure") stretching
• Most of the dissipation is unrelated to the dynamo process
  • In detailed balance by local work
    • Local rate of convergence much larger than the dynamo growth rate

Saturation due to curvature force

Fast downflows, slow upflows

  Simple Model: Polytropic stratification, ~3 orders of magnitude in density, Ideal gas, Initially "poloidal" sheet, in mid CZ.

 Field structure

• Very fragmented magnetic field in the CZ
• Much smoother in the undershoot layer

Pumping by convection Flux peaks in the undershoot layer BUT: most flux is in the CZ even more so in the real Sun much thinner undershoot layer The pumping effect is robust kinematic effect surprisingly resilient against buoyancy

 Field brought to surface by passive advection

Horizontal field strength decreases with height as rho^4/9 because of spreading in the horizontal direction perpandicular to the field (rho^1/3) and divergence of the vertical velocity (KE flux = rho*V_z³ approx. constant, so V_z varies as rho^-1/3).

• Evidence
  • Emergence lattitude independent of flux
  • Tilt angle independent of flux
  • Flux emerges at same time as velocity divergence appears

Magnetic Field grows from seed field and saturates around 100 G.

Surface Magnetic Field (G). The magnetic field is confined to the intergranular lanes.

Surface Magnetic Flux Tubes

Magnetic Flux Tube Structure throughout simulation volume.
Concentrated at mesogranular boundary.

Dynamo Conclusions

 Dynamo growth is due to large scale stretching

• For cases where large scale flows dominate

 Occurs on (a factor times) the turn-over (or shearing) time scale

• Similar for laminar and turbulent flows
  • Provided they have similar large scale topologies

 Most magnetic dissipation occurs in small volume and is unrelated to dynamo action

 Growth rates and saturation levels are independent of R_m and Re

• When sufficiently large

 Large scale field organized by shear

• in Lattitude (differential rotation)

 Field brought to surface by passive advection

• from small patches in deep convection zone