Active Region Magnetic Fields in the Solar Interior

1
Active Region Magnetic Fields in the Solar
Interior

• W.P. Abbett
• UC Berkeley SSL

2
The Importance of Active Region Magnetic Fields
Jan 15, 1996 CME as captured by the LASCO C3
coronagraph
TRACE movie of the coronal response to a
rotating structure

• Active regions represent the largest
  concentrations of magnetic flux at the solar
  surface
• Many, if not all, space weather events (e.g., SEP
  events triggered by flares or CME shock fronts)
  are associated with active regions

3
The Importance of Active Region Magnetic Fields

• The magnetic field we observe at the visible
  surface of the Sun is ultimately governed by
  forces acting on magnetic structures at and below
  the photosphere, in the turbulent interior.
• The evolution of active region magnetic fields at
  the surface provide important constraints on
  theories and models of CME initiation, and
  ultimately provide the lower boundary conditions
  for large-scale coupled models of the
  Sun-to-earth system.

From V. Abramenko BBSO 2004 RHESSI Sonoma
workshop
4
Outline

• In this review, I will discuss
• what has been learned about the evolution of
  active region magnetic fields deep in the solar
  interior,
• what aspects of the observations can be explained
  in terms of theoretical and computational models,
  
• and what remains mysterious.

I will then suggest directions for future
research in this area.
5
Observational Characteristics of Active Region
Magnetic Fields
Left SOHO EIT image of coronal plasma at
1.3MK Right Timeseries of MDI LOS magnetograms
taken between Oct.22 and Nov 15 1998 (a time of
heightened solar activity)

• Roughly speaking, active regions are confined to
  symmetric latitudinal bands across the solar
  equator
• These bands move poleward as the 11-year solar
  cycle progresses, but on average do not venture
  farther than 35 degrees away from mid-latitude

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• Leading polarities of active regions in a given
  hemisphere are the same, and oppose those of the
  opposite hemisphere
• Active region bipoles are oriented nearly
  parallel to the E-W direction (Hales Law 1919)

MDI magnetogram from May 11, 2000

• On average, the leading polarity of an active
  region is positioned closer to the equator than
  the trailing polarity.
• The mean tilt angle of active regions increases
  with latitude (Joys Law)

Fisher et al. 1995
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Implications of the Observed Behavior of Active
Regions

• Hales Law implies that the underlying field
  geometry is torodial (aligned in the E-W
  direction)
• Since Hales Law persists over multiple solar
  cycles, the toroidal layer must lie deep in the
  interior in a region relatively free from
  convective turbulence.

• The natural place for active region magnetic
  fields to be stored is at or near the place where
  they are thought to be generated the
  tachocline, where the differentially rotating
  convection zone transitions into the stable
  radiative layers

8
Interpretations Based on Observations

• Many active regions emerge as simple bipoles.
  These structures can be interpreted as the tops
  of large Omega-shaped flux tubes anchored deep in
  the convection zone.
• Active regions exhibiting non-Hale configurations
  (e.g., delta spots) are often interpreted as
  twisted, or writhed flux tubes

From Fisher et al. 2000
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A Theoretical Interpretation

• Derive an equation of motion for a flux tube
  moving in a field-free background model
  convection zone given the following constraints
• As the tube moves, it retains its identity i.e.,
  the tube remains cohesive and does not disperse
  or fragment
• The tube is thin i.e., its cross-section is
  small relative to all other relevant length
  scales of the problem
• Quasi-static pressure balance is maintained
  across the diameter of the tube at all times

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The Thin Flux Tube Approximation

• Here, FB refers to the magnetic buoyancy force,
  FT the force due to magnetic tension, FC the
  Coriolis force, and FD the force resulting from
  aerodynamic drag (?e and ?i refer to the gas
  density external to the tube, and in the tubes
  interior respectively)

(Spruit 1981, Moreno-Insertis 1986, Ferriz-Mas
Schussler 1993, Caligari et al.1995)
11
Studies Using the Thin Flux Tube Model

• Coriolis force deflects tube toward the poles as
  it tries to rise radially

From Fan Fisher 1996
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Studies Using the Thin Flux Tube Model

• What is the magnetic field strength of the
  toroidal layer at the base of the solar
  convection zone?
• Thermally or magnetically unstable toroidal flux
  rings with field strengths between 3x104 and
  105 G at the base of a model convection zone
  (significantly higher than the equipartition
  value) give rise to buoyant Omega-loops that
  emerge at latitudes consistent with observations.
• What is the physical origin of Joys Law?
• Thin flux tube simulations have shown that active
  region tilts could be explained by the Coriolis
  force acting on rising, expanding flux ropes

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Since this work was done, Tian Liu (2003) have
updated these results with magnetic fluxes
instead of polarity separations.
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Studies Using the Thin Flux Tube Model

• What is the physical basis of asymmetric spot
  motions?

• Plasma entrained in an emerging flux rope will
  conserve its angular momentum, resulting in a
  distorted Omega-loop the leading leg is less
  vertically inclined than the trailing leg,
  resulting in a more rapid motion of the leading
  polarity away from the neutral line.

From Caligari et al. 1995
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Studies Using the Thin Flux Tube Model

• The dispersion of tilt versus AR size (Longcope
  Fisher 1996)
• Morphological asymmetries of active regions
  (leading polarity is generally more compact than
  the trailing polarity)
• Helicity distributions of active regions with
  latitude (Longcope et al. 1998)

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Beyond the Thin Flux Tube Model

• MHD simulations of magnetic flux tubes in the
  solar interior
• 2D results show that without substantial
  fieldline twist (far more than is, on average,
  observed), flux tubes fragment and are unable to
  reach the surface.

Boussinesq simulations of Longcope et al 1996
From Fan et al. 1998
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3D MHD Simulations of Flux Tubes

• Simulations of buoyant magnetic flux tubes in a
  stratified background model convection zone show
• The fragmentation problem is a result of the
  axisymmetric assumption in 3D only a modest
  amount of twist is required for the flux tube to
  remain cohesive

From Abbett et al. 2000
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3D MHD Simulations of Flux Tubes

• When Coriolis effects are considered, the amount
  of twist necessary for emergence is essentially
  negligible
• Asymmetries predicted by thin flux tube
  calculations are borne out by 3D MHD simulations
  in a rotating, stratified model convection zone

From Abbett et al. 2001
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Highly Twisted Flux Tubes

• Properties of delta-spot active regions (often
  the source of the strongest flares and CMEs)
• Sunspot umbrae of opposite polarity in a common
  penumbra
• Strong shear along the neutral line
• Rotates as it emerges
• Interpretation The geometry of a kinked flux
  rope can explain the rotation and shear observed
  in delta spot active regions

Tanaka 1991, Linton et al. 1999, Fan et al. 1999
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Active Region Fields in a Convectively Unstable
Background State

• Q What are the conditions for the tube to retain
  its cohesion?
• Fieldline twist is relatively unimportant what
  matters is the axial field strength relative to
  the kinetic energy density of strong downdrafts

From Fan et al. 2003
21
Active Region Fields in a Convectively Unstable
Background State
From Abbett et al. 2004

• Q Is an active region-scale magnetic flux tube
  susceptible to flux pumping?

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Turbulent Pumping

• A robust property of compressible, penetrative
  convection magnetic flux is preferentially
  transported to the base of the convection zone at
  timescales characteristic of convective turnover

Images from Tobias et al. 2001
Tobias et al. 1998, 2001, Dorch Nordlund 2001
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• Are relatively weak active region-scale magnetic
  flux tubes susceptible to turbulent pumping in
  the absence of an overshoot layer?

From Abbett et al. 2004
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(No Transcript)
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The Transport of Magnetic Flux

• Over the lifetime of an active region-scale
  magnetic structure, there seems to be no
  systematic tendency for a net transport of signed
  magnetic flux into either the upper or lower half
  of the model convection zone (in the absence of
  an overshoot layer)

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The Transport of Magnetic Flux
To qualitatively understand this behavior, lets
neglect the effects of Lorentz forces and
magnetic diffusion, and consider the ideal MHD
induction equation
Applying Stokes theorem gives
Since we are interested how signed flux is
redistributed through the domain, lets consider
a closed circuit encompassing the lower half of a
single vertical slice. Our horizontal boundaries
are periodic, and vz and Bz are assumed
anti-symmetric across the lower boundary. Thus,
the line integral becomes
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The Transport of Magnetic Flux
The initial horizontal magnetic field is constant
(of the form B B0x) thus, the only way the
total amount of magnetic flux above or below the
mid-plane of a vertical slice can change, is by
the interaction of vertical flows with the
horizontal layer of flux. Then the average time
rate of change of signed magnetic flux in the
lower half of the domain can initially be
expressed as
If there are no bulk flows, or net vertical
pulsations in the domain (as is the case in our
dynamically relaxed model convection zone), then
And we should expect no initial tendency for a
horizontal flux layer to be preferentially
transported in one direction over the other,
solely as a result of the presence of an
asymmetric vertical flow field.
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• There are two important time scales to keep in
  mind
• The convective time scale Hr / vc
• The flux expulsion timescale --- i.e., the
  amount of time necessary for the field to reach
  its equilibrium distribution

After the flux distribution becomes significantly
non-uniform, there is a net downward transport
of flux (a weak pumping mechanism uncorrelated
with vertical flow asymmetries) while the flux
is redistributed to its equilibrium
configuration
From Abbett et al. 2004
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The Effects of Spherical Geometry
Fan, Y., 2005 SHINE meeting
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Dynamic Disconnection
Understanding the transition between active
region evolution in terms of emerging flux tubes
versus active region decay as described by
passive flux transport models (Schüssler Rempel
2005)

• As magnetic flux breaks through the
  photosphere, sunspots form and the initial
  coronal magnetic field is established
• As the plasma in the spots cools and sinks, and
  the buoyant plasma from below emerges, the upper
  parts of these flux tubes are blown apart and are
  then controlled by convective motions. Passive
  flux transport models then describe the surface
  evolution of the active region field

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Closer to the Surface
From Abbett et al. 2003
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Closer to the Surface

• The emergence of active region magnetic fields
  into the solar atmosphere

From Magara 2004
From Fan 2001
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Successes of Sub-surface Models

• Equatorial zone of avoidance of active regions
• Hales law and Joys law (active region
  orientation)
• The dependence of active region tilt on AR size
• The dispersion of tilt versus AR size
• Asymmetric spot motions (leading vs. following)
• Morphological asymmetry
• Helicity distribution of active regions with
  latitude
• Stability of active region flux tubes (O-loops)
  in 3D
• The transition between active region flux tube
  dynamics and flux transport models (new result)
• d-spot active regions as highly twisted kinking
  flux tubes (maybe)

34
Open Questions

• What triggers the eruption of active regions from
  the base of the convection zone? Instability,
  secular heating, convective overshoot, or
  something else?
• Most active regions exhibit only small amounts of
  twist, and are consistent with a tube lying
  initially at the base of the convection zone with
  no twist. How then do the island d-spot regions
  acquire so much twist?
• How is the free energy from sub-surface fields
  transported into the corona?

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Open Questions

• What is the magnetic connection between different
  active regions? Are active regions magnetically
  connected to each other in the dynamo region, or
  are they all separate?
• How do we relate active longitudes and active
  nests to a magnetic picture of the large-scale
  dynamo region at the base of the convection zone?
• Is the magnetic flux that gives birth to active
  regions in a smooth, slab-like geometry, or is
  the flux already pre-existing in the form of
  tubes?

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Open Questions

• What happens when active region flux tubes
  collide in the solar interior? What happens when
  a new active region emerges into an old one?
• How do active region flux tubes interact with the
  small scale field in the Quiet Sun?
• What is the 3D analogue of the surface flux
  transport models? How does the following
  polarity from decaying, emerged active regions
  return to the dynamo regions? What happens to
  the magnetic roots of an emerged active region
  once the active region begins decaying?

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Open Questions

• Can we infer the sub-surface structure of an
  active region by studying its surface evolution?
  
• Can we predict the emergence of new active
  regions before it happens, either from
  helioseismic observation, or from a better
  knowledge of the physics of magnetic evolution
  below the photosphere?