Magnetic Flux Pumping and the Structure of a Sunspot Penumbra

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The strange properties of sunspots (or The
intriguing structure of a sunspot penumbra) John
H. Thomas Dept. of Mechanical Engineering and
Dept. of
Physics Astronomy, University of
Rochester Isaac Newton Institute for Mathematical
Sciences, Cambridge Spitalfields Day, 6
December 2004
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Swedish 1-m Solar Telescope, La
Palma High-resolution G-band images of a sunspot
(2002, 2003 Courtesy of G. Scharmer and L.
Rouppe van der Voort)
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Dunn Solar Telescope, National Solar Observatory,
Sacramento Peak, New Mexico Adaptive optics (AO)
system (Courtesy of T. Rimmele, NSO)
AO off
AO on
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Simple, round theoreticians sunspot
Axisymmetric, flaring magnetic flux tube in a
stratified atmosphere
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Axisymmetric sunspot dynamic model Hurlburt and
Rucklidge (2000)
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Fine structure in the penumbra filamentary
structure, penumbral grains, etc. Movie of
penumbral dynamics, Swedish 1-m Solar Telescope
(courtesy of G. Scharmer).
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The interlocking-comb structure of the penumbral
magnetic field.
bright
dark
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The vector magnetic field in a sunspot as
measured by Stokes polarimetry Results from the
HAO/NSO Advanced Stokes Polarimeter (Stanchfield,
Thomas, and Lites 1997)
Note in the penumbra the spokes of more vertical
magnetic field (bright filaments) separated by
spokes of nearly horizontal magnetic field (dark
filaments).
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Coronal loops observed with the TRACE satellite
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EUV image of coronal loops connecting two
sunspots from the TRACE satellite, along with a
white-light image of the same sunspots. (Courtesy
of Lockheed Martin Solar and Astrophysics
Laboratory) The magnetic fields in the long loops
emerging from bright filaments in the penumbra
cannot interchange with the horizontal fields in
the dark penumbral filaments. The two components
of the interlocking-comb penumbral magnetic field
remain essentially distinct over the lifetime of
a sunspot.
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Magnetic flux pumping the formation and
maintenance of the penumbra
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Magnetic buoyancy
Isolated magnetic flux tube

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Scenario for the formation and maintenance of the
filamentary penumbra (Weiss, Thomas, Tobias, and
Brummell 2004, ApJ, 600, 1073)

• A sunspot forms by coalescence of pores into a
  growing pore with increasing total magnetic flux

• As the total magnetic flux increases, the
  inclination of the field (to the vertical) at the
  outer boundary of the flux tube increases

• At some critical angle the configuration becomes
  unstable to convectively driven filamentary
  (i.e., azimuthally periodic) perturbations.
  (Hurlburt et al. 2000 Tildesley 2003 Hurlburt
  and Alexander 2003).

• The nonlinear development of this instability
  leads to fluting at the boundary of the flux
  tube. (Tildesley and Weiss 2004) (Proto-penumbra)

• The more horizontal spokes of the magnetic field
  are brought into greater contact with the
  granular convective layer in the surroundings and
  are subjected to downward pumping by the
  turbulent granular convection. Some fraction of
  this more horizontal flux is pumped downward,
  forming the returning magnetic flux tubes, while
  the remainder either stays above the surface or
  rises buoyantly to the surface, forming the
  low-lying magnetic canopy. (Fully developed
  penumbra)

• The largest pores are bigger than the smallest
  sunspots. This hysteresis indicates that the
  instability is associated with a subcritical
  bifurcation (Rucklidge, Schmidt, and Weiss 1995).
  Magnetic flux pumping provides a physical
  mechanism for this hysteresis as a sunspot
  decays, pumping keeps fields in the dark
  filaments submerged even when the total magnetic
  flux is somewhat less than that at which the
  transition from a pore to a sunspot occurs.

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Magnetic flux pumping by turbulent convection

• Magnetic flux pumping is related to other
  effects
• Flux expulsion by convective eddies (Parker
  1963 Clark 1965 Weiss 1966).
• Turbulent diamagnetism in which magnetic flux is
  pumped down a gradient in turbulent intensity
  (Rädler 1968 Moffatt 1983).
• Topological pumping in a stratified convecting
  fluid, where the distinction between isolated
  rising plumes and the network of sinking fluid
  leads to downward pumping (Drobyshevski Yuferev
  1974).

• However, flux pumping in stratified compressible
  convection is mostly due to the strong contrast
  between broad, gently rising plumes and
  concentrated, rapidly falling plumes. Magnetic
  flux is pumped downward out of a convecting layer
  into a stably stratified layer below. (Nordlund
  et al. 1992 Brandenburg et al. 1996 Tobias et
  al. 1998, 2001 Dorch Nordlund 2001
  Ossendrijver et al. 2002).

• The Suns surface granulation layer is a
  shallow, strongly superadiabatic boundary layer
  of vigorous convection. It produces downward
  magnetic flux pumping into the underlying weakly
  unstable, nearly adiabatic convection zone. This
  pumping mechanism submerges the returning flux
  tubes just outside the penumbra and is a key
  feature in understanding the formation and
  maintenance of the penumbra. (Thomas, Weiss,
  Tobias, Brummell 2002 Weiss, Thomas, Brummell,
  Tobias 2004).

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The photospheric granulation
(Swedish Vacuum Solar Telescope)
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Numerical simulations of flux pumping by the
solar granulation. (N. H. Brummell, S. M. Tobias,
N. O Weiss, JHT)
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S 0.5 (lower layer slightly stable)
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Downward pumping of magnetic flux in the
simulation with S 0.5 (lower layer slightly
stable). Plots show the horizontal average of the
y-component of the magnetic field as a function
of depth z at evenly spaced times. Panel (a)
shows the rapid pumping phase in which the
magnetic field is redistributed by buoyancy and
convective motions. Panel (b) shows the later,
slow diffusive phase.
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More realistic simulation, with an umbra (to
cause magnetic curvature forces that oppose
downward pumping).
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Moving magnetic features (MMFs) in the sunspot
moat (longitudinal magnetograms).
(Courtesy of Alan Title, Lockheed-Martin Solar
and Astrophysical Laboratory)
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Flux pumping also helps explain the behavior of
moving magnetic features (MMFs) in the moat
around a sunspot
Sketch of the three types of MMFs (as defined by
Shine and Title 2001). Type I Bipolar pairs
of magnetic elements moving outward at 0.51.0
km s-1. Type II Single magnetic elements of
same polarity as the sunspot decay of sunspot.
Type III Single magnetic elements of opposite
polarity as the sunspot, moving rapidly outward
at speeds of 23 km s-1.

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