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Granules in the Quiet and Magnetic Sun Robert F. Stein, Michigan State University Valentyna Abramenko , Big Bear Solar Observatory Åke Nordlund , Niels Bohr Institute, University of Copenhagen. Simulation Results. Magneto-Hydrodynamic Equations Mass conservation 𝜕𝜌/𝜕t = −∇ · (𝜌 u )
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Robert F. Stein, Michigan State University
ValentynaAbramenko, Big Bear Solar Observatory
ÅkeNordlund, Niels Bohr Institute, University of Copenhagen
𝜕𝜌/𝜕t = −∇ · (𝜌u)
Momentum conservation𝜕(𝜌u)/𝜕t =−∇·(𝜌uu)−∇𝑃 −𝜌g+J×B−2𝜌Ω×u−∇·𝜏visc
Energy conservation𝜕𝑒/𝜕t =−∇·(𝑒u)−𝑃(∇·u)+𝑄rad +𝑄visc +𝜂J2
Induction equation𝜕B/𝜕t = −∇ × E, E=−u×B+𝜂J+ (1/ene) (J×B−∇𝑃e),
High resolution simulations and observations reveal
that granule properties are very different in quiet Sun
and plage regions. In the quiet Sun granules have
scalloped edges with turbulent vertical velocity at their
edges. In plage granules have swirlingvertical vortex
tubes at their edges. Diverging upflowsapproach the
downflowintergranular lanes, are deflected by the
strong magnetic field and flow around the field creating
vertical vortex tubes. The best solar observations
currently clearly show the scalloped edges of granules
in the quiet Sun intensity images. Small vortex tubes
in the intergranular lanes at the edges of strong fields
are borderline visible currently.
6th-order centered finite-differencestaggered
3rd order Runga-Kutta
Equation of state
Tabular including ionization H, He + abundant elements
3D, LTE 4 bin multi-group
Quiet Sun: (left) Vertical velocity image (light is down, gray and dark up) is turbulent at granule edges.
(right) Fluid streamlines with volume rendering of magnetic field strength. Horizontal vortex tubes are common, vertical vortex tubes occur at some granule lane vertices. Plasma reaching the surface originates from the centers of underlying larger cells a depth. Rising plasma diverges and turn sover like a fountain and heads back down.
Vertical velocity image at continuum optical depth 0.1
with magnetic field contours at 300 & 1000 G.
Granule boundaries are corrugated in quiet Sun, but
smoother with swirls at boundaries of magentic regions.
Weak (1 kG), minimally structured (horizontal, uniform, untwisted) magnetic field .
Magnetic Sun: vertical vortex tubes along intergranular lanes. Plasma turning over into intergranular lanes where there are strong magnetic field concentrations
wraps around the the magnetic field creating a vertical vortex tube.
Continuum intensity image from 12x12x6 Mm simulation,
convolved with an 1.5 m airy psf. The scale is not exactly
the same as in the observed snapshot.
TiOband intensity image from New Solar Telescope (Big Bear Observatory)
Granules in field free regions have scalloped edges, whereas in magnetic locations granule boundaries are smoother with swirly strings of bright points.
These are bright (as pointed out by HenkSpruit) because where the field is strong, the density is lower and radiation escapes from deeper layers where
the plasma gets heated by the deeper hotter walls of the ascending granules. Both the observations with NST and the degraded simulation intensity
show a very similar behavior in both the quiet and magnetic locations.