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Azimuth disambiguation of solar vector magnetograms
M. K. GeorgoulisM. K. Georgoulis
JHU/APL11100 Johns Hopkins Rd., Laurel, MD 20723, USA
Ambiguity Workshop
Boulder, Co, 26 Sep 2005
Outline
Boulder, 09/26/05
Azimuth disambiguation: a brief introduction
Techniques:
Examples and comparison
Conclusions
Structure minimization
Nonpotential magnetic field calculation
Introduction
BBlonglong
BBtrantranss
BBtrantranss
SunSun
Therefore:
is unambiguously measured
is unambiguously measured
The orientation of is ambiguous
with two equally likely -differing solutions
longB
transB
transB
Vector magnetic field measurements are performed across and perpendicular to the observer’s line of sight
The deduced quantities are ,
and the azimuth of
longB transB
transB
The properties of the transverse Zeeman effect remain invariant under the transformation πφφ
φ
Boulder, 09/26/05
The problem at hand
Any physically meaningful disambiguation technique should rely on the local, rather than the line-of-sight, magnetic field components
Therefore, the location of the target magnetic configuration is crucial
BB & BB transhlongz
If the target AR is close to disk center
everywhere πΔφ
If the target AR is far from disk center
BB & BB transhlongz variableand π Δφ
Boulder, 09/26/05
The structure minimization technique
Technique developed by Georgoulis, LaBonte, & Metcalf (2004)
Semi-analytical, relying on physical and geometrical arguments
Assumptions and analysis:
Consider Ampere’s law where :bBB
bB4π
cJ and b
4π
cBJ where; JJJ 2121
BJ 2 Notice that
zz 21 J and J Both can be readily calculated
The current density becomes fully known if is found zB/2J
The current density maximizes on the interface between flux tubes
2J
2J Minimizing the magnitude leads to the minimum possible interfaces (structure) between flux tubes, i.e. to space-filling magnetic fields This is the minimum structure approximation
Boulder, 09/26/05
The structure minimization technique (cont’d)
The magnitude becomes minimum when 2J
y
Bb
x
Bb
bb
b
z
Byx2
y2x
z
2J zB/Both and do not show inter-pixel dependences since the only differentiated quantity is the ambiguity-free B
There are only two possible values for and at each location
2J zB/
To perform azimuth disambiguation, we assume that
in sunspots (physical argument)
has to be minimum in plages, because there and
0 zB/
z2J zBB z BJ 2(geometrical argument)
Boulder, 09/26/05
Implementation - Analysis
Vertical magnetic field Normalized wl continuum We construct the following quantity:
1ω0 , ω1ω re wheJωz
BωF pps2ps z
pω Typical - profile pω
The function F is free of inter-pixel dependences and has only two values at any given location. We choose the azimuth solution that minimizes FThis azimuth solution is treated as a good initial guess
Boulder, 09/26/05
Implementation - Numerics
The final solution is reached numerically, assuming smoothness of the azimuth solution and eliminating artificial gradients in the vertical fieldClose to disk center
The two solutions for Bz are very similar; the two azimuth solutions are very different
Far from disk centerAzimuth solutions may be similar; the two solutions for Bz are very different
The initial azimuth solution is smoothed via an iterative Jacobi relaxation process
The initial solution of Bz is filtered by means of the Lee filtering technique
Boulder, 09/26/05
Synopsis of the structure minimization technique
Strengths:
Fast (average running time ~ 5 – 10 min) and fully automatic
Effective - Propagation of a local erroneous solution is precluded because there are no inter-pixel dependences
Applicable to ARs both close and far from disk center
Weaknesses:
Ambiguous - Different numerical treatment when the AR is “ far ” or “ close ” to disk center (How “ far ” is far and how “ close ” is close?)
Restrictive - Initial solution reached from assumptions regarding sunspots and plages – what about other types of magnetic structure (canopies, EFRs, etc.) ?
Too much power on smoothing – limited control during the numerical phase
Boulder, 09/26/05
Nonpotential magnetic field calculation
Technique developed by Georgoulis (2005)
Semi-analytical, self-consistent solution, no final smoothing
Analysis:
Any closed magnetic structure has a potential and a nonpotential component:
npp BBB Gauge conditions:
All three components above are divergence-free:
0B and , 0B , 0B npp
The total and potential component share the same boundary condition on Bz, so the nonpotential component is purely horizontal:
0nB so nBnBSnpSpS
The nonpotential component is responsible for any electric currents
J /c π4BB np Boulder, 09/26/05
Nonpotential magnetic field calculation (cont’d)
Assumption: Assume that the vertical electric current density is knownThen the definition of the nonpotential field is
zznpSnpnp Jc
4πB and , 0nB , 0B
From this definition, is fully-determined (Chae 2001): npB
y )(Jkk
ik x )(J
kk
ikB z2
y2x
x1z2
y2x
y1np
Therefore, if we know we can find the distribution of Bz whose potential extrapolation + best match the observed horizontal magnetic field
npB
npB
This can be done iteratively, starting from any random, but relatively smooth, initial configuration of Bz
The problem is how to find Jz, or some proxy of it, prior to the disambiguation
Boulder, 09/26/05
Finding a proxy vertical electric current density
Objective: Extract as much information on Jz as possible from the ambiguity-free longitudinal magnetic fieldBRelation between the heliographic and the line-of-sight magnetic field components:
zy,x,j ; 1,2i ; BγBβBαB z ji ηy ji ξ xjj i
Because of the azimuthal ambiguity we have
2 η1 η2 ξ1 ξ BB and BB
Therefore, the average of the two ambiguity solutions is fully known and ambiguity-free :
21 BB 1/2
B z γy γx γBB 1/2B zzzy zx 21av
From this we can find a proxy vertical current density
z avp B π4
cJ
z
Boulder, 09/26/05
Examples of the proxy vertical current
Longitudinal magnetic field Proxy vertical current densityThe used proxy generally underestimates the actual vertical current
density with the bias depending on the target’s position on the solar disk
1B
2B
avB
1B
2B
avB
Close to disk center
Far from disk centerTherefore, we are pursuing a minimum-current azimuth solution Boulder,
09/26/05
Examples and comparison
Structure minimization Nonpotential magnetic field calculation
AR 9026
IVM, NOAA AR 9026
Boulder, 09/26/05
Examples and comparison (cont’d)
Structure minimization Nonpotential magnetic field calculation
ASP, NOAA AR 7205, 06/24/92
AR 7205
Boulder, 09/26/05
The nonpotential field calculation in action
Nonpotential magnetic field vector
onB
Proxy vertical electric current density
zz 21 BB
2
1
z
21p hhzBB
2
1J
Boulder, 09/26/05
Limitations of the nonpotential field calculation
The nonpotential field calculation performs a potential extrapolation in each iteration. Therefore, it generally requires flux-balanced magnetic structures on the boundary The technique relies on Bz. Therefore, it may be compromised where magnetic fields are strongly horizontal and / or show only a weak vertical component
Simulation fan_simu_ts56
h
z
B
B
0.01B
B ,G 500 B
h
zh
Boulder, 09/26/05
Other examples of nonpotential field disambiguation
Simulation cl1
ASP, 03/11/03
Boulder, 09/26/05
Synopsis of the nonpotential field calculation technique
Boulder, 09/26/05
Strengths:
Very Fast (average running time ~ 1 – 5 min) and fully automatic
Effective to ARs both close and far from disk center
Physically sound and eliminates the need of smoothing
Weaknesses:
Biased toward Bz – it may be compromised in case of strong horizontal fields and very weak vertical fields
Can the technique be improved further?
Yes, if one uses a more reliable estimate of the proxy vertical current density The “off – center” case of the minimum vertical current (Semel &
Skumanich 1998)
Modeling of the vertical current density (Gary & Demoulin 1995) However, any refinement should not
compromise the computational speed of the technique !
Conclusions
Two reliable techniques for a routine azimuth disambiguation of solar vector magnetograms
Both are fast and automatic
Near real-time disambiguation of SOLIS, Solar-B, SDO/HMI data
Structure minimizatio
n
Non-potential field
calculation
Boulder, 09/26/05
http://sd-www.jhuapl.edu/FlareGenesis/Team/Manolis/codes/ambiguity_resolution/
Want to try yourself ? Check out the nonpotential field method @