Modeling Active Region Magnetic Fields on the Sun

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Modeling Active Region Magnetic Fields on the Sun

• W.P. Abbett
• Space Sciences Laboratory
• University of California, Berkeley

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Motivation for Detailed Studies of Active Region
Evolution

• The ability to predict space weather is
  becoming increasingly important as our
• society becomes more reliant on ground and
  space-based technologies that are
• susceptible to a flux of energetic particles,
  or fluctuating ionospheric currents.

• Examples of activities disrupted by solar and
  geomagnetic events satellite
• operations, navigation (GPS), manned space
  flight, polar flights, power
• distribution networks, HF radio and long-line
  telephone communication, and
• pipeline operations.

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Motivation for Detailed Studies of Active Region
Evolution

• Coronal Mass Ejections (CMEs) are among the
  primary drivers of space
• weather.

• CMEs are magnetically driven and many are
  believed to originate in the
• low solar corona in and around active region
  magnetic fields.

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LASCO C3 Coronagraph CME of Jan. 15, 1996
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And now, a bit closer to the Sun

• In the low corona (where the CME is initiated),
  magnetic flux is frozen
• into the plasma, and the field is essentially
  line-tied to the photosphere
• as such, it evolves in response to changes to
  the Suns photospheric
• magnetic field .

TRACE 171 Movie of the X-class flare producing
NOAA active region 9906 on April 21, 2002.
TRACE 171 Movie of the corona over a rotating
sunspot in NOAA active region 9114 on August 9,
2000.

• Thus, understanding the evolution of the vector
  magnetic field at the
• photosphere is a crucial component of the
  effort to forecast and
• interpret space weather events.

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Active Region Magnetic Fields at the Photosphere

• Active regions appear as bipoles, which implies
  they are the tops of large
• Omega-shaped loops which have risen through the
  solar convection zone
• and emerged into the photosphere.
• 
  

• On average, bipoles are oriented nearly
• parallel to the E-W direction (Hales law
• 1919) indicating that the underlying field
• geometry is nearly toroidal.

Cauzzi et. al. (1996)

• Hales law persists for years
• through a given solar cycle,
• thus the toroidal layer must
• lie deep in the interior in a
• region relatively free from
• convective turbulence.

Full disk MDI magnetogram courtesy of Y. Liu
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A Simple Picture of Active Region Magnetic Flux

• A toroidal flux layer persists near the
  tachocline --- where the turbulent
• convection zone transitions into the stable
  radiative zone.

• Portions of the toroidal layer succumb to a
  dynamic or magnetic instability
• causing a magnetically buoyant flux rope to rise
  through the convection zone.

• The top of the loop emerges from the high-beta
  plasma of the convection zone, through the many
  pressure scale heights of the photosphere,
  chromosphere and transition region, into the
  low-beta, tenuous, energetic corona.

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Testing this Simple Picture Using Numerical Models

• Only recently has it become possible to
  routinely run 3D numerical
• simulations of the sub-surface evolution of
  active region-scale magnetic fields.

• In particular, a numerical solution of the
  system of MHD equations in the
• anelastic approximation allows for an exploration
  of the physics of active region
• magnetic fields in the solar interior. We can
  address questions such as

What is the role of fieldline twist, solar
rotation, and field strength on the dynamics of
flux emergence? Can simple models accurately
represent the physics of sub-surface magnetic
structures?
From Abbett et. al. (2000)
MDI Magnetogram from Cauzzi et al (1996)
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Modeling Magnetic Fields in the Solar Convection
Zone
Is an interface dynamo necessary to generate
active region-strength fields, and can magnetic
flux be transported back to the base of the
convection zone in the absence of an
interface layer?
From Abbett et al. 2003
Can magnetic flux tubes remain cohesive during
their ascent through the turbulent convection
zone? Can we determine how strong the
magnetic field must be at the base of the
convection zone to be consistent with the 1000G
fields observed at the photosphere?
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Coupling Photospheric Fields to a Model Corona
PFSS
Given a representation of the magnetic field at
or below the photosphere, can we characterize the
magnetic topology of the corona?

• One method is to assume that the vector
  magnetic field can be derived
• from a scalar potential --- this assumption
  coupled with the requirement
• that the field be radial far from the photosphere
  (at the source surface),
• is the basis of the potential field source
  surface (PFSS) extrapolation.

PFSS models of Li Luhmann
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Coupling Photospheric Fields to a Model Corona
FFF

• Another method is to assume that the magnetic
  field is in a force-free
• equilibrium (i.e. j X B 0). This type of
  extrapolation may provide
• an improved representation over the potential
  field model, particularly
• near dynamic active regions.

FFF calculations from Y. Liu (2003)
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Coupling Photospheric Fields to a Model Corona
MHD

• Another method --- the most computationally
  expensive technique so
• far --- is to numerically solve the system of
  ideal MHD equations.

• To drive an MHD model corona, on must first
  overcome a set of
• unique challenges
• 1. Unlike PFSS and FFF extrapolations, MHD
  models require information
• about the flow field at the photospheric boundary
  --- and that information
• is generally not available.
• To resolve individual active regions while
  simultaneously following the
• global evolution of the corona requires the
  implementation of an adaptive,
• non-uniform mesh.

Why go to all that trouble? MHD models are able
to describe the continuous topological evolution
of the corona, thus providing a means to e.g.
follow the dynamic evolution of the open field,
and to investigate proposed CME initiation
mechanisms.
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A First Attempt
From Abbett Fisher (2003)
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How Force-free are Emerging Structures?
The emergence of modestly twisted magnetic flux
tubes into the model corona. The color table is
a measure of how force-free the atmosphere is
--- the bluer the color the more the current
density is aligned with the magnetic field
lines. The difference in tilt angle between
overlying field lines and those close to the
lower boundary reflects the distribution of
twist present in the flux rope below the surface
From Abbett Fisher (2003)
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Another approach
Magara Longcope (2003) and Fan (2001) simulate
the emergence of highly twisted flux tubes
positioned just below the photosphere ---
information resulting from the buoyant rise of
the tube through the entirety of the convective
envelope is lost however, there is no need to
implement an interface boundary.
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A Few Caveats
Since the goal is not to directly simulate
coronal emission, and since we must make the
problem computationally tractable at active
region spatial scales, we do not treat (in
detail) the physics of radiative transport and
thermal conduction along field lines. An
example of a more realistic calculation (Bercik,
Stein, Nordlund 2002)

• Note that treating the visible surface as a
  simple 2D layer or thin 3D slab
• clearly simplifies the physics of these layers.

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Using Observations to Drive a MHD Model Corona

• AR8210 is a very complex,
• CME producing active region.
• Though complex, AR8210 is
• a MURI candidate event ---
• mainly because the vector
• data at the photosphere is
• of high quality.
• Can we obtain a flow field
• that is consistent with the
• observed evolution of the
• Magnetic field?

A high-cadence sequence of MDI vector
magnetograms of AR8210 on May 1,1998 (S.
Regnier, R. Canfield)
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New Velocity Inversion Techniques
ILCT (Welsch Fisher) --- Uses a combination of
Local Correlation Tracking (LCT) on magnetic
elements along with the MHD induction equation
to obtain a self-consistent flow field.
MEF (Longcope Klapper) --- constrains the
system by minimizing the spatially integrated
square of the velocity field.

• A flow field that satisfies the vertical
  component of the induction equation is
• not necessarily unique!

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Testing Velocity Inversion Techniques
Examples of using ANMHD to test velocity
inversion techniques.
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Putting it all Together (A Work in Progress)

• ILCT and MEF provide means to generate
• velocity fields from a sequence of vector
• magnetograms that can be used to update
• the lower boundary layers of an MHD model
• corona.

• Additionally, MHD models require an initial
• state, one that
• Matches the transverse components of
• the magnetic field observed at the
• photosphere, and
• Accurately represents the magnetic
• topology of the initial atmosphere

Options PF and FFF extrapolations.
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The Global Topology of AR8210

• Local calculations can go only
• so far!
• If CME initiation mechanisms
• depend on the magnetic topology
• of the global corona, local
• calculations performed in
• isolation may not tell the whole
• story
• Modeling the evolution of open field
• in the global corona is a critical
• component in the effort to understand
• and predict space weather --- in fact,
• recent studies have shown that
• Active regions are a significant source
• of the open field in times of
• heightened solar activity.

Yohkoh SXT reverse image of a trans-equatorial
loop emanating from AR8210.
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Resolving Active Regions Embedded in a Global
Corona
Using the domain decomposition and adaptive mesh
refinement tool PARAMESH (MacNeice et. al. 2000)
to resolve active region magnetic fields in a
global environment
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Toward Tetrahedral MHD/AMR
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Conclusions
Sun to Mud Models

• There is community-wide interest in the
  development of end-to-end
• coupled numerical models to be used as
  operational, real-time space
• weather forecasting tools.

• The least understood component of the Sun-earth
  system is the solar
• atmosphere --- where solar storms originate. To
  be successful, and to
• progress beyond idealized calculations, each of
  the above multi-agency,
• coordinated efforts ultimately will require an
  observationally-based solar
• model that can routinely provide real time,
  physical boundary conditions
• for their models.