Abstract
We investigate how the azimuthal ambiguity in solar vector magnetogram data can be resolved by using the divergence-free property of magnetic fields. In a previous article, by Crouch, Barnes, and Leka (Solar Phys. 260, 271, 2009), error-free synthetic data were used to test several methods that each make a different assumption about how the divergence-free property can be used to resolve the ambiguity. In this paper this testing is continued with an examination of the effects of Poisson photon noise and limited instrumental spatial resolution. We find that all currently available methods based on the divergence-free property can produce undesirable results when photon noise or unresolved structure is present in the data. We perform a series of experiments aimed at improving the performance of the global minimisation method, which is the most promising of the methods. We present a two-step approach that produces reasonable results in tests using synthetic data. The first step of this approach involves the global minimisation of a combination of the absolute value of the approximation for the divergence and a smoothness constraint, which is designed to minimise the difference between the magnetic field in neighbouring pixels. In the second step, pixels with measurements known to be strongly affected by photon noise are revisited with a smoothing algorithm that also seeks to minimise the difference between the magnetic field in neighbouring pixels.
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Ahnert, K., Abel, M.: 2007, Comput. Phys. Commun. 177, 764. doi: 10.1016/j.cpc.2007.03.009 .
Boulmezaoud, T.Z., Amari, T.: 1999, Astron. Astrophys. 347, 1005.
Chiu, Y.T., Hilton, H.H.: 1977, Astrophys. J. 212, 873. doi: 10.1086/155111 .
Collados, M., Martinez Pillet, V., Ruiz Cobo, B., del Toro Iniesta, J.C., Vazquez, M.: 1994, Astron. Astrophys. 291, 622.
Crouch, A.D., Barnes, G.: 2008, Solar Phys. 247, 25. doi: 10.1007/s11207-007-9096-1 .
Crouch, A.D., Barnes, G., Leka, K.D.: 2009, Solar Phys. 260, 271 (Paper I). doi: 10.1007/s11207-009-9454-2 .
Cullum, J.: 1971, SIAM J. Numer. Anal. 8, 254. doi: 10.1137/0708026 .
Cuperman, S., Li, J., Semel, M.: 1993, Astron. Astrophys. 278, 279.
del Toro Iniesta, J.C., Ruiz Cobo, B.: 1996, Solar Phys. 164, 169. doi: 10.1007/BF00146631 .
Eibe, M.T., Aulanier, G., Faurobert, M., Mein, P., Malherbe, J.M.: 2002, Astron. Astrophys. 381, 290. doi: 10.1051/0004-6361:20011495 .
Gary, G.A., Hagyard, M.J.: 1990, Solar Phys. 126, 21. doi: 10.1007/BF00158295 .
Georgoulis, M.K.: 2012, Solar Phys. 276, 423. doi: 10.1007/s11207-011-9819-1 .
Harvey, J.W.: 1969, Magnetic Fields Associated with Solar Active-Region Prominences. Ph.D. thesis, University of Colorado, Boulder.
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: 1983, Science 220, 671. doi: 10.1126/science.220.4598.671 .
Leka, K.D., Barnes, G.: 2012, Solar Phys. 277, 89. doi: 10.1007/s11207-011-9821-7 .
Leka, K.D., Metcalf, T.R.: 2003, Solar Phys. 212, 361. doi: 10.1023/A:1022996404064 .
Leka, K.D., Barnes, G., Crouch, A.: 2009, In: Lites, B., Cheung, M., Magara, T., Mariska, J., Reeves, K. (eds.) The Second Hinode Science Meeting: Beyond Discovery-Toward Understanding, ASP Conf. Ser. 415, 365.
Leka, K.D., Barnes, G., Crouch, A.D., Metcalf, T.R., Gary, G.A., Jing, J., Liu, Y.: 2009, Solar Phys. 260, 83. doi: 10.1007/s11207-009-9440-8 .
Leka, K.D., Barnes, G., Gary, G.A., Crouch, A.D., Liu, Y.: 2012, Solar Phys. 276, 441. doi: 10.1007/s11207-011-9879-2 .
Li, J., Amari, T., Fan, Y.: 2007, Astrophys. J. 654, 675. doi: 10.1086/509062 .
Li, J., Cuperman, S., Semel, M.: 1993, Astron. Astrophys. 279, 214.
Liu, Y., Wang, J., Yan, Y., Ai, G.: 1996, Solar Phys. 169, 79. doi: 10.1007/BF00153835 .
Maltby, P., Avrett, E.H., Carlsson, M., Kjeldseth-Moe, O., Kurucz, R.L., Loeser, R.: 1986, Astrophys. J. 306, 284. doi: 10.1086/164342 .
Metcalf, T.R.: 1994, Solar Phys. 155, 235. doi: 10.1007/BF00680593 .
Metcalf, T.R., Jiao, L., McClymont, A.N., Canfield, R.C., Uitenbroek, H.: 1995, Astrophys. J. 439, 474. doi: 10.1086/175188 .
Metcalf, T.R., Leka, K.D., Barnes, G., Lites, B.W., Georgoulis, M.K., Pevtsov, A.A., Balasubramaniam, K.S., Gary, G.A., Jing, J., Li, J., Liu, Y., Wang, H.N., Abramenko, V., Yurchyshyn, V., Moon, Y.J.: 2006, Solar Phys. 237, 267. doi: 10.1007/s11207-006-0170-x .
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E.: 1953, J. Chem. Phys. 21, 1087. doi: 10.1063/1.1699114 .
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: 1992, Numerical Recipes in FORTRAN. The Art of Scientific Computing, Cambridge University Press, Cambridge, 436.
Ruiz Cobo, B., del Toro Iniesta, J.C.: 1992, Astrophys. J. 398, 375. doi: 10.1086/171862 .
Socas-Navarro, H.: 2005, Astrophys. J. Lett. 631, L167. doi: 10.1086/497334 .
Socas-Navarro, H.: 2007, Astrophys. J. Suppl. 169, 439. doi: 10.1086/510336 .
Socas-Navarro, H., Trujillo Bueno, J., Ruiz Cobo, B.: 2000, Astrophys. J. 530, 977. doi: 10.1086/308414 .
Vernazza, J.E., Avrett, E.H., Loeser, R.: 1981, Astrophys. J. Suppl. 45, 635. doi: 10.1086/190731 .
Westendorp Plaza, C., del Toro Iniesta, J.C., Ruiz Cobo, B., Martinez Pillet, V., Lites, B.W., Skumanich, A.: 1998, Astrophys. J. 494, 453. doi: 10.1086/305192 .
Westendorp Plaza, C., del Toro Iniesta, J.C., Ruiz Cobo, B., Martínez Pillet, V., Lites, B.W., Skumanich, A.: 2001, Astrophys. J. 547, 1130. doi: 10.1086/318376 .
Wu, L.X., Ai, G.X.: 1990, Acta Astrophys. Sin. 10, 371.
Acknowledgements
The author thanks K.D. Leka and Graham Barnes for providing the synthetic datasets used in this investigation. The author thanks the referee for helpful suggestions. This work was supported by funding from NASA under contracts NNH05CC49C/NNH05CC75C and NNH09CE60C. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575.
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Crouch, A.D. Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: The Effects of Noise and Limited Spatial Resolution. Sol Phys 282, 107–131 (2013). https://doi.org/10.1007/s11207-012-0149-8
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DOI: https://doi.org/10.1007/s11207-012-0149-8