Magnetic Flux Pumping and the Structure of a Sunspot Penumbra

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SunspotsJohn H. Thomas Dept. of Mechanical
Engineering and Dept. of
Physics Astronomy,
University of Rochester

• Outline
• Introduction.
• Axisymmetric models of sunspots.
• Fine structure of the umbra and penumbra. The
  interlocking-comb magnetic field in the penumbra.
• The formation and maintenance of the penumbra.
  Magnetic flux pumping by turbulent granular
  convection in the moat.
• The Evershed flow. Siphon-flow models.
• Oscillations in sunspots umbral oscillations,
  penumbral waves, sunspot seismology.
• Summary of open questions.

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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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Drawing of a sunspot by Samuel P. Langley,
Allegheny Observatory, December 23-24, 1873.
Appears as the frontispiece in books on the Sun
by C. A. Young (1881) and C. G. Abbott (1929).
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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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Subsurface structure of a sunspot. Monolith or
cluster?
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Simple, round theoreticians sunspot
Axisymmetric, flaring magnetic flux tube in a
stratified atmosphere
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Magnetic field configuration
Axisymmetric sunspot static model Jahn
Schmidt (1994)
Heat flow diagram
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Axisymmetric sunspot dynamic model Hurlburt and
Rucklidge (2000)
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Fine structure in the penumbra Movie of penumbral
dynamics, Swedish 1-m Solar Telescope (courtesy
of G. Scharmer).
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• Movie showing
• Inward migration of small bright features
  (penumbral grains) along bright penumbral
  filaments.
• Outward migration of bright magnetic features
  (moving magnetic features) across the moat
  surrounding the sunspot.

Chromospheric Ca II H
Photospheric G-band
(Dutch Open Telescope, 9 August 2003, courtesy of
R. Rutten.)
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Motions of penumbral grains
Paths of inward moving (black lines) and outward
moving (white lines) penumbral grains. (Sobotka
and Sütterlin 2001, AA 380, 714)
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Images of umbral dots
(Rimmele 2004, ApJ, 606, 906)
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Small-scale magnetoconvection in magnetic fields
inclined at an angle f to the vertical. Left f
0, spatially modulated oscillations, fixed in
space. Middle f 22, modulated traveling wave,
pattern drifts to the left (away from the tilt of
B). Right f 67, almost roll-like modulated
traveling wave, pattern drifts to left.
(Hurlburt, Matthews, and Rucklidge 2000)
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The interlocking-comb structure of the penumbral
magnetic field.
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Measuring vector B Stokes I, Q, U, and V profiles
of the spectrum near 630 nm along the ASP slit at
one instant of time. The six visible absorption
lines are Fe I 630.15 telluric O2 630.20
Fe I 630.25 telluric O2 630.30 Fe I
630.35 Ti I 630.40 The bottom panels are the
same images of the I and V profiles, but scaled
to show the weak umbral molecular lines lying
between the stronger lines.
(Lites, Thomas, Bogdan, and Cally 1998, ApJ, 497,
464)
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(Stanchfield, Thomas, and Lites 1997, ApJ, 477,
485)
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Magnetic field strength (Gauss)
Zenith angle of magnetic field (degrees)
(Westendorp Plaza et al. 2001, ApJ, 547, 1130)
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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 these 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 and penumbral structure
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Isolated magnetic flux tube
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Formation 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
  hence are subject to downward pumping by the
  turbulent granular convection. Some fraction of
  this more horizontal flux will be pumped
  downward, forming the returning magnetic flux
  tubes, while the remainder will either stay above
  the surface or rise 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 can still keep fields in the dark
  filaments submerged when the total magnetic flux
  is less than that at which the transition from a
  pore to a sunspot occurs.

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Magnetic flux pumping by turbulent convection

• Flux expulsion is a common feature of cellular
  convection (Parker 1963 Clark 1965 Weiss 1966).

• Turbulent diamagnetism magnetic flux is pumped
  down a gradient in turbulent intensity (Rädler
  1968 Moffatt 1983).

• Topological pumping in a stratified, convecting
  fluid distinction between isolated rising plumes
  and network of sinking fluid leads to downward
  pumping (Drobyshevski Yuferev 1974).

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

• The Suns surface granulation layer (a shallow,
  highly unstable, strongly superadiabatic boundary
  layer) produces downward magnetic flux pumping
  into the underlying deep, weakly unstable, nearly
  adiabatic convection zone (Thomas, Weiss, Tobias,
  Brummell 2002 Weiss, Thomas, Brummell,
  Tobias 2004). This pumping mechanism submerges
  the returning flux tubes in the sunspot penumbra.

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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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Volume renderings of the instantaneous vertical
velocity w and the logarithm of the enstrophy
density w2 for fully developed, purely
hydrodynamical penetrative convection, for two
values of the stability parameter S 0.0
(lower layer neutrally stable) S 0.01
(lower layer slightly unstable)
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Gray-scale plots of the horizontal distribution
of vertically averaged values of the
instantaneous vertical velocity, w(x,y), in the
upper (granulation) layer and lower layers, for
purely hydrodynamical convection (B 0) with S
0.01 (slightly unstable lower layer). Light
tones indicate downflows, dark tones indicate
upflows. In the upper layer there is a network of
downflows surrounding upflows, with about seven
convection cells in the domain. In the lower
layer the pattern of convection reflects the
presence of a single, larger cell (mesogranule)
in the upper layer. Also shown are power spectra
of the velocities at different depths.
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More realistic simulation, with an umbra (to
cause magnetic curvature forces that oppose
downward pumping).
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• Movie showing
• Inward migration of small bright features
  (penumbral grains) along bright penumbral
  filaments.
• Outward migration of bright magnetic features
  (moving magnetic features) across the moat
  surrounding the sunspot.

Chromospheric Ca II H
Photospheric G-band
(Dutch Open Telescope, 9 August 2003, courtesy of
R. Rutten.)
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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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