Incorporating%20Vector%20Magnetic%20Field%20Measurements%20into%20MHD%20models%20of%20the%20Solar%20Atmosphere

1
Incorporating Vector Magnetic Field Measurements
into MHD models of the Solar Atmosphere

• W.P. Abbett
• Space Sciences Laboratory, UC Berkeley
• and
• B.T. Welsch, G.H. Fisher, T. Magara
• SSL UC Berkeley, NRL

2
Coupling the Photosphere to Coronal Models ---
Relevance to Sun-to-Mud Modeling

• The least understood component of the Sun-earth
  system is the solar atmosphere --- where eruptive
  events and solar storms originate.

• To progress beyond idealized calculations, an
  end-to-end coupled model of the Sun-Earth system
  ultimately will require validated models of
  solar eruptions that can provide the real time,
  observationally-based boundary conditions needed
  for successful physics-based space weather
  forecasting tools.

• CMEs, among the primary drivers of space
  weather, are magnetically driven and originate in
  the low corona. Central to our understanding of
  magnetic field evolution in the solar atmosphere
  is the strong topological coupling of the coronal
  field to magnetic field in the photosphere.

3
Characterizing the Evolution of the Coronal
Magnetic Field --- Principal Challenges

• There are no in situ measures of the state of the
  solar atmosphere. All data are obtained via
  remote sensing.

• Measurements of the vector magnetic field in the
  corona are extremely challenging as of yet, no
  routinely available source of such data exists.

Non-linear Force Free Field Extrapolation (Y. Liu)
PFSS models of Y. Li J. Luhmann

• A common approach Extrapolate a force-free or
  potential field from a series of photospheric
  magnetograms.

4
Coupling Photospheric Fields to a MHD Model Corona

• Computationally inexpensive, static methods may
  not adequately describe the continuous
  topological evolution of the corona near strong
  active region magnetic fields. MHD models
  provide a means to follow this dynamic evolution,
  however

• To drive an MHD model corona, one must first
  overcome a set of
• challenges
• Data-driven MHD models require an accurate
  time-series of vector
• magnetic field measurements at the
  photosphere.
• 2. Unlike PFSS and FFF extrapolations, MHD
  models require information
• about the flow field (electric field) at the
  photospheric boundary ---
• and that information is generally not
  available.
• MHD models require specification of an initial
  atmosphere (all
• components of the magnetic field throughout
  the volume) consistent
• with the observed vector field at the lower
  boundary.

5
The Photospheric Magnetic Field NOAA AR-8210

• Advantages of AR-8210 as a case study for
  numerical simulations
• There exists quality vector data
• AR-8210 produced multiple CMEs
• Candidate event for MURI project

• Disadvantages
• Extremely complex active region
• Global trans-equatorial connection
• to another active region

A high-cadence sequence of MDI vector
magnetograms of CME producing AR-8210 on May
1,1998 (S. Regnier, R. Canfield)
6
Using Observations to Obtain a Photospheric
Velocity Field
A new twist on Local Correlation Tracking
(Demoulin Berger 2003) LCT is a technique
that infers the transverse velocity of magnetized
plasma from the motion of magnetic features at
the visible surface by finding the shift that
maximizes the local correlation function between
successive images.
However, LCT determines only apparent transverse
flows --- consider the emergence of a tilted
magnetic structure.
uLCT vt Bt (vn/Bn)
Assuming ideal MHD, flows parallel to the
magnetic field cannot affect the evolution of
magnetic structures --- Welsch Fisher (2003)
point out that this closes the Demoulin Berger
equations, and allows for an algebraic solution
for all three components of the velocity field
given a time series of vector magnetograms.
7
Algebraic Method applied to NOAA AR-8210

• The results are very promising! However, to
  incorporate this data into MHD simulations, we
  must also ensure that the flow-field we obtain is
  consistent with the observed evolution of
  magnetic field, as specified by the z-component
  of the induction equation

Algebraic method applied to AR8210. Apparent
velocities determined by G. Fishers LCT code
shown are the true flows as determined by B.
Welschs application of the algebraic method.
8
ILCT method applied to NOAA AR-8210 (Welsch
Fisher)

• Demoulin Bergers hypothesis simplifies the
  z-component of the induction equation, making it
  possible to determine a velocity field consistent
  with both LCT and the MHD induction equation.
• This method returns such a flow field given
  vector magnetic field measurements and an
  apparent flow determined by LCT on resolved
  magnetic features.
• This method is described in detail in Brian
  Welschs poster
• SH22A-0177 (Tuesday afternoon)

ILCT method applied to AR8210.
9
MEF Method Applied to NOAA AR-8210 (Longcope
Klapper)

• Can we obtain a flow field that is consistent
  with the observed evolution of the magnetic field
  without obtaining apparent velocities via LCT?

• MEF Method
• By itself, the z-component
• of the MHD induction
• equation is under-determined.
• MEF constrains the system
• by minimizing the spatially
• integrated square of the
• velocity

MEF method applied to AR8210.
10
Testing and Validation of the New Inversion
Techniques

• A velocity field that satisfies the MHD induction
  equation in the photospheric layers (at the lower
  boundary of a coronal simulation) is not
  necessarily unique

ANMHD simulations of W. Abbett
ILCT and Algebraic Method applied to ANMHD
simulations
11
Obtaining an Initial Atmosphere from a Vector
Magnetogram
Data-driven MHD simulations of the corona require
an initial specification of the vector magnetic
field at all points in the computational
domain. Techniques are available to extrapolate
the structure of the magnetic field given a
photospheric vector magnetogram (e.g. PFSS, FFF).
However, two conditions must be met if a
given extrapolation is to provide a suitable
initial state 1. It must adequately describe
the coronal topology above the active region of
interest, and 2. The transverse components of
the magnetic field must match those specified by
the vector magnetogram at the lower boundary.
FFF extrapolation of 8210 (Regnier)
Unfortunately, potential field extrapolations
fail to meet condition 1 in and around strong,
dynamic active regions, and (depending on the
method used) certain force-free extrapolations
can fail to meet condition 2, particularly if the
magnetic field of an active region deviates
significantly from a force-free configuration.
12
How Force-Free is the Photosphere?

• T. Magara has recently simulated the emergence of
  a twisted flux rope through a computational
  domain that includes the transition layers from
  the photosphere to the low corona (see SH42B-0512
  -- Thursday)

Left Fieldline traces from the final timestep of
a run where a twisted flux tube has emerged into
the corona. Above The vertical component of the
magnetic field for slices at different heights
(from top left the photosphere, chromosphere,
transition region and low corona).
13
How Force-Free is the Photosphere?
Above A measure of how force-free a model solar
atmosphere is after a twisted flux system has
emerged into the model corona Shown is the value
of ltJBgt along field lines --- blue indicates
that currents flow along the fieldlines
(force-free), and red indicates regions where
currents are anti-parallel to the field (not
force-free). Thus, current simulations
suggest (Magara 2003, Abbett Fisher 2003) that
the atmosphere becomes force-free at and above
the chromosphere, and not below.
14
Other Issues Relevant to the Coupling of
Photospheric Observations to Data-driven Coronal
Models

• Measurements of the vector magnetic field at the
  photosphere arise from model dependent inversions
  of polarization observations, and suffer from
  ambiguities.

• Since observations provide no information about
  the depth dependence of the magnetic field in the
  photosphere, the new velocity inversion
  techniques can only prescribe flows on a plane
  consistent with the z-component of the induction
  equation. MHD codes in general require the
  specification of magnetic fields below the
  surface to self consistently update all
  components of the induction equation.

• A non-uniform mesh is required to model the
  dynamic evolution of the global corona while
  maintaining sufficient resolution in the
  photosphere in and around active regions to
  resolve a local pressure scale height (of order
  100km).

Conclusion Steady progress is being made toward
developing the machinery necessary to drive
models of the solar corona with photospheric
vector magnetograms.