Update: Incorporating Vector Magnetograms into Dynamic Models of the Solar Atmosphere

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Update Incorporating Vector Magnetograms into
Dynamic Models of the Solar Atmosphere

• CISM-AG Meeting March 2006
• Bill Abbett, Brian Welsch, George Fisher
• SSL, UC Berkeley

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The objective

• To directly incorporate observations of the
  vector magnetic field at the photosphere (or
  chromosphere) into physics-based dynamic models
  of the solar atmosphere

• The requirements
• Sequences of reduced, ambiguity-resolved vector
  magnetograms
• of sufficient quality to incorporate into an MHD
  code
• (2) A robust method of determining the electric
  field consistent with both
• the observed evolution of the photospheric field
  and Faradays Law
• (3) An MHD code (or set of coupled codes)
  capable of modeling a region
• encompassing the photosphere (where relatively
  reliable measurements
• of the magnetic field are available),
  chromosphere, transition region and
• corona
• (4) A physically self-consistent means of
  incorporating (1) and (2) into (3)

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• Understand sequences of reduced, high-quality,
  ambiguity-resolved vector magnetograms well
  enough to incorporate them into a numerical
  simulation
• What magnetic field data provide the most
  important information about
• the state of the solar atmosphere, and how
  do we prepare the data and
• make best use of it?
• What is the best way to generate the initial
  atmosphere of a
• time-dependent calculation one that is both
  physically meaningful,
• and consistent with the relevant
  observations of the corona?
• (current method the optimization
  technique, e.g., Wheatland et al. 2000)
• How do we best describe the evolution of a model
  photosphere
• given the evolution of, and noise in, the
  observed data and our best
• understanding of the most important physics?

We currently rely on our CISM colleagues, and our
SHINE-funded collaboration with CoRA and MSU to
obtain quality measurements of active region
vector magnetic fields, and to address each of
these questions prior to attempting to
incorporate a given dataset into a numerical
calculation. (e.g., IVM data AR8210, May
1998 AR9046, June 2000 AR10030, July 2002
AR10725, Feb 2005)
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• (2) A method of determining the electric field
  consistent with both the observed evolution of
  the photospheric field and the MHD induction
  equation e.g., ILCT (Welsch et al. 2004)
• Apply Fourier Local Correlation Tracking (FLCT,
  Welsch et al. 2004) to
• to obtain an approximation to the 2D flux
  transport velocity uf
• Note that uf does not represent the 3D flow field
  of the magnetized
• plasma, v. However, the two are
  geometrically related (Demoulin
• Berger 2003)

Note that FLCT and ILCT are CISM deliverables
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To demonstrate how ILCT relates the MHD induction
equation to the flux transport velocity, consider
the vertical component of the ideal MHD
induction equation (here, for clarity, we
neglect the resistive term --- in general, it
can be included)
Substituting the geometric relation of the
previous slide, we have
(1)
Now, simply define Bnuf in the following way
(2)
Substituting this expression into (1) yields
Since the LHS is known, we have a Poisson
equation for f that can be easily solved.
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Taking the curl of (2), we have
If we assume that u(FLCT) (our LCT approximation
of uf) represents a true flux transport velocity,
we again have a solvable Poisson equation.
With both scalar potentials known, we can
determine a flux transport velocity that is both
consistent with the observed evolution of the
photospheric field and the MHD induction
equation
Up to this point, the analysis only requires the
normal component of the magnetic field! The
vector field is necessary only when
extracting the 3D flow field from
Note that to obtain v, we must appeal to the fact
that field-aligned flows are unconstrained by the
induction equation (one way of closing the
system is to simply assume ).
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• Brian Welsch has recently implemented a
  preliminary, automated
• Magnetic Evolution Pipeline (MEP)
• New MDI magnetograms are automatically downloaded
  (cron
• checks for new magnetograms using wget),
  de-projected, and
• tracked using FLCT
• The output stream includes de-projected
  magnetograms, FLCT
• flows (.png graphics files and ASCII data
  files), and tracking parameters
• Full documentation and all codes (including
  possible bugs!) are
• currently online

http//solarmuri.ssl.berkeley.edu/welsch/public/d
ata/Pipeline/
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1. An MHD code (or set of coupled codes) capable of
   modeling a region encompassing the
   photosphere, chromosphere, transition region and
   corona

• Some realities
• Extreme spatial and temporal disparities
• small-scale, active region, and global features
  are fundamentally inter-connected
• magnetic features at the photosphere are
  long-lived (relative to the convective turnover
  time) while features in the magnetized corona can
  evolve rapidly (e.g., topological changes
  following reconnection events)
• Vastly different physical regimes
• photosphere and below relatively dense,
  turbulent (high-ß) plasma with strong magnetic
  fields organized in isolated structures
• corona field-filled, low-density, magnetically
  dominated plasma (at least around strong
  concentrations of magnetic flux!)
• flow speeds in CZ below the surface are typically
  below the characteristic sound and Alfven speeds,
  while the chromosphere, transition region and
  corona are often shock-dominated

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• different physical regimes (contd)
• corona energetics dominated by optically thin
  radiative cooling, anisotropic thermal
  conduction, and some form of coronal heating
  consistent with the empirical relationship of
  Pevtsov et al. 2003 (energy dissipation as
  measured by soft X-rays proportional to the
  measured unsigned magnetic flux at the
  photosphere)
• photosphere/chromosphere energetics dominated by
  optically thick radiative transitions
• Additional computational challenges
• A dynamic model atmosphere extending from at or
  below the photosphere
• to the corona must
• span a 10 order of magnitude change in gas
  density and a thermodynamic transition from the
  1MK corona to the optically thick, cooler layers
  of the low atmosphere, visible surface, and below
• resolve a 100km photospheric pressure scale
  height (energy scale height in the transition
  region can be as small as 1km!) while following
  large-scale evolution

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Idealized attempts to couple disparate regimes
Sub-surface anelastic
Zero-ß corona
?
(Abbett, Mikic et al. 2004)
?
?
?
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(Abbett et al. 2005)
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Idealized dynamic calculations (no explicit
coupling)
Left Magara (2004) ideal MHD AR flux emergence
simulation as shown in Abbett et al.
2005 Right Manchester et al. (2004) BATS-R-US
MHD simulation of AR flux emergence
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Toward more realistic AR models

• We must solve the following system

• Energy source terms (Q) include
• Optically thin radiative cooling
• Anisotropic thermal conduction
• An option for an empirically-based coronal
  heating mechanism --- must maintain a corona
  consistent with the empirical constraint of
  Pevtsov (2003)
• LTE optically thick cooling (options solve the
  grey transfer equation in the 3D Eddington
  approximation, or use a simple parameterization
  that maintains the super-adiabatic gradient
  necessary to initiate and maintain convective
  turbulence)

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Surmounting practical computational challenges

• The MHD system is solved semi-implicitly on a
  block adaptive mesh.
• The non-linear portion of the system is treated
  explicitly using the semi-discrete central method
  of Kurganov-Levy (2000) using a 3rd-order CWENO
  polynomial reconstruction
• Provides an efficient shock capture scheme, AMR
  is not required to resolve shocks
• The implicit portion of the system, the
  contributions of the energy source terms, and the
  resistive and viscous contributions to the
  induction and momentum equations respectively, is
  solved via a Jacobian-free Newton-Krylov
  technique
• Makes it possible to treat the system implicitly
  (thereby providing a means to deal with temporal
  disparities) without prohibitive memory
  constraints

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Quiet Sun relaxation run (serial test)
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Toward AR scale MPI-AMR relaxation run (test)

• The near-term plan
• Dynamically and energetically relax a 30Mm
  square Cartesian domain extending to 2.5Mm below
  the surface.
• Introduce a highly-twisted AR-scale magnetic
  flux rope (from the top of a sub-surface
  calculation) through the bottom boundary of the
  domain
• Reproduce (hopefully!) a highly sheared,
  d-spot type AR at the surface, and follow the
  evolution of the model corona as AR flux emerges
  into, reconnects and reconfigures coronal fields
• The long term plan
• global scales / spherical geometery

Q How do different treatments of the
coefficient of resistivity, or changes in
resolution affect the topological evolution of
the corona?
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• Towards a physically self-consistent means of
  incorporating
• (1) and (2) into (3) The Active
  Boundary Layer

• Use AMPS as essentially two, fully coupled codes
  a thin, dynamic photospheric layer actively
  coupled (internally i.e., not via a framework
• such as InterComm) to the AMPS domain
• Within the thin, photospheric boundary layer,
  the continuity, induction,
• and energy equations are solved given an ILCT
  flow field (assumed to
• permeate the entirety of the thin layer).
• This active boundary is dynamically coupled to
  AMPS, which solves
• the full MHD system in a domain that extends
  from the top of the
• model photosphere into the transition region
  and low corona
• Inherent physical assumption Coronal forces do
  not affect the photosphere
• This internally-coupled system could instead
  extend to the low
• transition region, and then be externally coupled
  (e.g., via InterComm) to existing Coronal models
  whose lower boundaries necessarily reside in
• the transition region.

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Data Driving --- The Strategy
Model Corona
Active Boundary Layer
Observational Data / ILCT
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• Summary (where were at)
• Sequences of reduced, ambiguity-resolved vector
  magnetograms of sufficient quality to incorporate
  into an MHD code
• ? --- we look forward to the increasing
  availability of sequences of quality vector
  magnetograms
• (2) A robust method of determining the electric
  field consistent with both
• the observed evolution of the photospheric
  magnetic field and
• Faradays Law
• ? --- complete
• (3) An MHD code (or set of coupled codes)
  capable of modeling a region
• encompassing the photosphere (where
  relatively reliable measurements
• of the magnetic field are available),
  chromosphere, transition region and
• low corona
• ? --- almost there.
• (4) A physically self-consistent means of
  incorporating (1) and (2) into (3)
• ? --- still working on it! Hope to have
  something to present at SHINE

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