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
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.
Characterizing the Evolution of the Coronal Magnetic
Field --- Principal Challenges:
►
There are no in situ measures of the state of the solar atmosphere.
►
Measurements of the vector magnetic field in the corona are
extremely challenging; as of yet, no routinely available source of
such data exists.
All data are obtained via remote sensing.
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.
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:
1. 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.
3. 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.
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:
A high-cadence sequence of MDI vector magnetograms of
CME producing AR-8210 on May 1,1998 (S. Regnier, R.
Canfield)
• Extremely complex active region
• Global trans-equatorial connection
to another active region
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.
“Algebraic Method” applied to NOAA AR-8210
►
Algebraic method applied to AR8210. Apparent velocities
determined by G. Fisher’s LCT code; shown are the “true”
flows as determined by B. Welsch’s application of the
algebraic method.
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:
I+LCT method applied to NOAA AR-8210 (Welsch & Fisher)
Demoulin & Berger’s 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 Welsch’s poster:
SH22A-0177 (Tuesday
afternoon)
►
I+LCT method applied to AR8210.
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.
Testing and Validation of the New Inversion Techniques
►
ANMHD simulations of W. Abbett
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
I+LCT and Algebraic Method applied to ANMHD simulations
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
FFF extrapolation of 8210 (Regnier)
field must match those specified by the vector
magnetogram at the lower boundary.
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.
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).
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 <J|B> 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.
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.