Modeling the Dynamic Evolution of the Solar Atmosphere:

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Modeling the Dynamic Evolution of the Solar
Atmosphere

• C4 HMI-AIA Team Meeting 2-14-06
• Bill Abbett
• SSL, UC Berkeley

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Among the AIAs stated objectives

• To understand the evolution of the coronal
  magnetic field toward unstable configurations by
  stresses induced at the solar surface

Ultimately, we must understand the dynamic
magnetic and energetic connection between the
photosphere and corona.
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• Available theoretical / computational tools
• Sequences of static / steady-state models
• Dynamic MHD models of the solar atmosphere

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• 1. Sequences of static/steady-state models
• Measure the magnetic field at the photosphere
  (and/or chromosphere)
• perform global (or local) potential field and/or
  non-constant-a force-free extrapolations
• construct steady-state solutions to the
  continuity, momentum, and energy equations along
  selected fieldlines
• generate synthetic images using known
  instrumental bandpasses
• directly compare with observations
• interpret the results (e.g., understand helicity
  transport, energetics, topological changes), and
  place further observational constraints on the
  models

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Example Lundquist 2006
AR 8210 (CME producing AR) Extrapolation
optimization technique (Wheatland et al. 2000)
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Lundquist 2006
AR 9714 (decayed active region) Extrapolation
optimization technique (Wheatland et al. 2000)
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Interpreting steady state models

• Suppose we wish to understand the buildup and
  release of free
• magnetic energy in the solar corona in and around
  a particular
• active region complex.
• Q When are dynamic models necessary, and when
  are static descriptions sufficient?
• Put another way
• Q When is the history of the magnetic field
  necessary to properly describe the magnetic
  topology of the corona?
• Is all the necessary information contained in the
  vector magnetic field along the boundaries?
• If we assume ideal MHD evolution, is there a
  unique topology associated with a given set of
  boundary conditions? What if changes in magnetic
  topology occur as a result of reconnection?
• When should we worry about the non-uniqueness of
  the non-linear force-free extrapolation?

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Consider the following
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2. Dynamic models 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)
• 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 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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Whats out there?

• A number of numerical codes are publicly
  available, each designed to efficiently describe
  the physics of a specific regime, at various
  spatial and temporal scales.
• Whats missing?
• Robust efficient codes that treat both the
  magnetic and energetic transition between the
  surface layers and corona over large spatial
  scales

Whats missing?
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Idealized attempts to couple disparate regimes
Sub-surface anelastic
Zero-ß corona
?
(Abbett, Mikic et al. 2004)
?
?
?
(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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A qualitative comparison
potential field
MHD
Non-linear force-free
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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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Parallel work
Model Corona
Active Boundary Layer
Observational Data
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Common themes running through the HMI-AIA
scientific goals and objectives

• Understanding the dynamic, energetic, and
  magnetic connectivity between sub-surface fields
  and flows and the solar atmosphere (at both large
  and small spatial scales).
• Using observations of sub-surface and surface
  magnetic fields and flows along with atmospheric
  emission to constrain theoretical models of
  active region formation and evolution
• With efficient, less-idealized, AR-scale MHD
  models we will soon be in a position to study (in
  a self-consistent way) the physics of
• flux emergence, cancellation, submergence
• active region decay, dynamic disconnection
• resistive dissipation and its role in coronal
  heating (in a non-stochastic sense)
• the role of the convective dynamo and the effect
  of small scale magnetic fields on the magnetic
  structure of both the Quiet Sun corona and
  mature, decaying AR complexes
• CME initiation
• coronal emission