eSDO 1121: Helicity Computation
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Deliverable eSDO-1121: Helicity Computation
M. Smith, E.Auden, L. van Driel-Gesztelyi
28 June 2005
Description
Magnetic helicity is a measurement of the magnetic chirality or "handedness" of the shear and twist that has occured to the solar magnetic field. Over the last decade, researchers have investigated observations that solar features such as coronal loops and active regions tend to exhibit clockwise patterns if they are located in the Sun's southern hemisphere, while those in the Sun's northern hemisphere exhibit counter-clockwise patterns. Solar physicists continue to search for a mechanism that causes this hemispheric tendency to clockwise or counter-clockwise patterns. Measuring the helicity of emerging solar features will elucidate the relationship between the Sun's magnetic field and solar behaviour. [1].
Relative magnetic helicity can be defined by solving the volume integral of the cross product of the magnetic vector potential A with the magnetic field B [2]:
∆H_{m} ∫_{Ω} (A-A_{0}) · (B-B_{0}) dV
Most studies of magnetic helicity have used a simple linear force-free model of the solar magnetic field; because this approach requires only the observed horizontal magnetic component, line-of-sight magnetograms from space and ground based telescopes can be used. However, use of increasingly complex nonlinear magnetic models for helicity computation now look promising as high resolution vector magnetograms become available. Regnier and Amari [3] have demonstrated a technique for extrapolating a non-linear force free magnetic field model using the Grad-Rubin technique, and they use thhis 3-D magnetic field and associated solar volume to calculate helicity. The eSDO helicity computation will use a similar helicity computation method, but the non-linear force free magnetic field will be calculated using the optimization method in the MagneticFieldExtrapolation algorithm.
Inputs
Outputs
- Variable (double) returned in G^{2}cm^{4}
Tool Interface
- commandline:
- AstroGrid CEA web service: this algorithm depends on the magnetic field extrapolation algorithm. Once that algorithm has been deployed as a CEA service hosted in the UK, the helicity algorithm can be accessed at the same time.
- SolarSoft routine: the C module will be wrapped in IDL and distributed through the MSSL SolarSoft gateway. Users will access to a SolarSoft installation can call the routine from the commandline or GUI to process locally held data. However, due to the computational intensity of the magnetic field extrapolation algorithm, the helicity computation method may need to be accessed with the assumption that the user can input a datacube containing the extrapolated magnetic field.
- JSOC module: the C module will be installed in the JSOC pipeline. Users can access the routine through pipeline execution to operate on data local to the JSOC data centre.
Science Use Case
- A user wishes to calculate the helcity of a region in addition to its nonlinear magnetic field.
- The user inputs an HMI vector magnetogram into the MagneticFieldExtrapolation algorithm and specifies that helicity shall be calculated as well.
- The MagneticFieldExtrapolation algorithm defines a volume over a solar region, calculates the nonlinear magnetic field over the volume, and then uses the resulting 3-D magnetic field to calculate a helicity value for the given volume.
- The value for helicity in G^{2}cm^{4} is returned to the user along with the magnetic field.
- The user can now compare the chirality or "handedness" of the solar region with the helicity of similar solar structures.
Technical Use Case
- MagneticFieldExtrapolation algorithm begins with an HMI vector magnetogram as input.
- The algorithm defines a volume over which the magnetic field field will be calcuated.
- Using the optimization method, the algorithm calculated the 3-D non-linear magnetic field over the volume.
- The helicity algorithm is now started with the 3-D nonlinear magnetic field and volume as inputs.
- The relative magnetic helicity integral defined by Berger and Field is solved over the volume:
∆H_{m} ∫_{Ω} (A-A_{0}) · (B-B_{0}) dV
- A value for helicity is returned in units G^{2}cm^{4}
Test Data
- Test magnetic field calculated by the MagneticFieldExtrapolation algorithm using SOHO-MDI vector magnetograms (and later Solar-B vector magnetograms)
Quicklook Products
Support Information
- van Driel-Gesztelyi, L.; Démoulin, P.; Mandrini, C. H. 2003, Advances in Space Research, 32, 10, 1855
- Régnier, S. & Amari, T. 2004, Astronomy and Astrophysics, 425, 345
- Berger, M. A. & Field, G. B. 1984, Journal of Fluid Mechanics, 147, 133
- De Moortel, I., 2005, Phil Trans R. Soc A, Vol 363, 2743 - 2760 (full paper)
- DeVore, C, 2000, ApJ, 539, 944 - 953
-- ElizabethAuden - 25 Aug 2005