Azimuth disambiguation of solar vector magnetograms M. K. Georgoulis JHU/APL 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 B long B trans Sun Therefore: is unambiguously measured The orientation of is ambiguous with two equally likely  -differing solutions Vector magnetic field measurements are performed across and perpendicular to the observer’s line of sight The deduced quantities are, and the azimuth  of The properties of the transverse Zeeman effect remain invariant under the transformation 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 If the target AR is close to disk centerIf the target AR is far from disk center 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 : Notice that Both can be readily calculated The current density becomes fully known if is found The current density maximizes on the interface between flux tubes 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 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 To perform azimuth disambiguation, we assume that in sunspots (physical argument) has to be minimum in plages, because there and (geometrical argument) Boulder, 09/26/05

Implementation - Analysis Vertical magnetic fieldNormalized wl continuum We construct the following quantity: Typical - profile 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 F This 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 field Close to disk center The two solutions for Bz are very similar; the two azimuth solutions are very different Far from disk center Azimuth 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: Gauge conditions: All three components above are divergence-free: The total and potential component share the same boundary condition on B z, so the nonpotential component is purely horizontal: The nonpotential component is responsible for any electric currents Boulder, 09/26/05

Nonpotential magnetic field calculation (cont’d) Assumption: Assume that the vertical electric current density is known Then the definition of the nonpotential field is From this definition, is fully-determined (Chae 2001):Therefore, if we know we can find the distribution of B z whose potential extrapolation + best match the observed horizontal magnetic field This can be done iteratively, starting from any random, but relatively smooth, initial configuration of B z The problem is how to find J z, 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 J z as possible from the ambiguity- free longitudinal magnetic field Relation between the heliographic and the line-of-sight magnetic field components: Because of the azimuthal ambiguity we have Therefore, the average of the two ambiguity solutions is fully known and ambiguity-free : From this we can find a proxy vertical current density Boulder, 09/26/05

Examples of the proxy vertical current Longitudinal magnetic fieldProxy vertical current density The used proxy generally underestimates the actual vertical current density with the bias depending on the target’s position on the solar disk Close to disk centerFar from disk center Therefore, 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 on Proxy vertical electric current density 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 B z. Therefore, it may be compromised where magnetic fields are strongly horizontal and / or show only a weak vertical component Simulation fan_simu_ts56 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 B z – 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 minimization Non-potential field calculation Boulder, 09/26/05 Want to try yourself ? Check out the nonpotential field