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Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: the Effects of Noise and Limited Spatial Resolution  

Ashley Crouch   Submitted: 2012-10-15 17:56

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 are 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.

Authors: Ashley D. Crouch
Projects: None

Publication Status: Accepted for publication in Solar Physics
Last Modified: 2012-10-19 09:58
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Least-Squares Fitting Methods for Estimating the Winding Rate in Twisted Magnetic-Flux Tubes  

Ashley Crouch   Submitted: 2012-10-15 17:54

We investigate least-squares fitting methods for estimating the winding rate of field lines about the axis of twisted magnetic-flux tubes. These methods estimate the winding rate by finding the values for a set of parameters that correspond to the minimum of the discrepancy between magnetic-field measurements and predictions from a twisted flux-tube model. For the flux-tube model used in the fitting, we assume that the magnetic field is static, axisymmetric, and does not vary in the vertical direction. Using error-free, synthetic vector magnetic-field data constructed with models for twisted magnetic-flux tubes, we test the efficacy of fitting methods at recovering the true winding rate. Furthermore, we demonstrate how assumptions built into the flux-tube models used for the fitting influence the accuracy of the winding-rate estimates. We identify the radial variation of the winding rate within the flux tube as one assumption that can have a significant impact on the winding-rate estimates. We show that the errors caused by making a fixed, incorrect assumption about the radial variation of the winding rate can be largely avoided by fitting directly for the radial variation of the winding rate. Other assumptions that we investigate include the lack of variation of the field in the azimuthal and vertical directions in the flux tube model used for the fitting, and the inclination, curvature, and location of the flux-tube axis. When the observed field deviates substantially from the flux-tube model used for the fitting, we find that the winding-rate estimates can be unreliable. We conclude that the magnetic-flux tube models used in this investigation are probably too simple to yield reliable estimates for the winding rate of the field lines in solar magnetic structures in general, unless additional information is available to justify the choice of flux-tube model used for the fitting.

Authors: Ashley D. Crouch
Projects: None

Publication Status: Accepted for publication in Solar Physics
Last Modified: 2012-10-19 09:58
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Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: Application to Discrete Data  

Ashley Crouch   Submitted: 2009-11-04 20:57

We investigate how the divergence-free property of magnetic fields can be exploited to resolve the azimuthal ambiguity present in solar vector magnetogram data, by using line-of-sight and horizontal heliographic derivative information as approximated from discrete measurements. Using synthetic data we test several methods that each make different assumptions about how the divergence-free property can be used to resolve the ambiguity. We find that the most robust algorithm involves the minimisation of the absolute value of the divergence summed over the entire field of view. Away from disk centre this method requires the sign and magnitude of the line-of-sight derivatives of all three components of the magnetic field vector.

Authors: Ashley D. Crouch, Graham Barnes, K.D. Leka
Projects: None

Publication Status: Solar Physics, in press
Last Modified: 2009-11-05 08:15
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Subject will be restored when possible  

Ashley Crouch   Submitted: 2008-02-26 16:48

We present a model for the total solar irradiance. The model takes the observed location, timing, and area of emerging active regions as input and produces a time-evolving size distribution of magnetic structures over the solar surface. We assume that the bright magnetic structures (faculae), which counteract the irradiance deficit caused by sunspots, consist of the products of active region decay. We simulate the decay process as a combination of fragmentation and boundary erosion of large-scale magnetic structures. The model has several adjustable parameters that control the decay processes and the irradiance contribution from the quiet Sun and the small-scale magnetic elements that are produced during the decay process. We use a genetic algorithm to estimate these parameters by fitting to the observed irradiance and daily sunspot area time series over the 1978-2007 time interval. Given the simplifications associated with the model, the resultant parameter values are well constrained within the imposed ranges. In addition, the irradiance and daily sunspot area time series produced by the best-fit models agree very well with the observations, although the sunspot area fits tend to perform better than the irradiance fits. However, it is evident that the model is neglecting a significant source of excess brightness, which manifests itself in two ways. First, the optimal values for the lifetime and intensity contrast of the bright, small-scale flux elements are both larger than expected. Second, the synthetic irradiance consistently underestimates the observations during the ascending phase of a cycle, despite the daily sunspot area fitting the observations quite well during these times. We also show that this genetic forward modelling approach can be used to detect a long term trend of decadal timescale in the quiet-Sun irradiance. Assuming a constant quiet-Sun irradiance, we reconstruct the total solar irradiance over the 1874-1978 time interval, for which observational data of emerging active regions are available.

Authors: A. D. Crouch, P. Charbonneau, G. Beaubien, D. Paquin-Ricard
Projects: None

Publication Status: ApJ, in press
Last Modified: 2008-09-23 21:22
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Subject will be restored when possible  

Ashley Crouch   Submitted: 2007-12-03 13:32

We demonstrate that the azimuthal ambiguity that is present in solar vector magnetogram data can be resolved with line-of-sight and horizontal heliographic derivative information by using the divergence-free property of magnetic fields without additional assumptions. We discuss the specific derivative information that is sufficient to resolve the ambiguity away from disk centre, with particular emphasis on the line-of-sight derivatives of the various components of the magnetic field. Conversely, we also show cases where ambiguity resolution fails because sufficient line-of-sight derivative information is not available. For example, knowledge of only the line-of-sight derivative of the line-of-sight component of the field is not sufficient to resolve the ambiguity away from disk centre. The original publication is available at www.springerlink.com.

Authors: A. D. Crouch and G. Barnes
Projects: None

Publication Status: Solar Physics, in press
Last Modified: 2007-12-03 14:51
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Subject will be restored when possible  

Ashley Crouch   Submitted: 2007-12-03 13:32

We demonstrate that the azimuthal ambiguity that is present in solar vector magnetogram data can be resolved with line-of-sight and horizontal heliographic derivative information by using the divergence-free property of magnetic fields without additional assumptions. We discuss the specific derivative information that is sufficient to resolve the ambiguity away from disk centre, with particular emphasis on the line-of-sight derivatives of the various components of the magnetic field. Conversely, we also show cases where ambiguity resolution fails because sufficient line-of-sight derivative information is not available. For example, knowledge of only the line-of-sight derivative of the line-of-sight component of the field is not sufficient to resolve the ambiguity away from disk centre. The original publication is available at www.springerlink.com.

Authors: A. D. Crouch and G. Barnes
Projects:

Publication Status: Solar Physics (in press)
Last Modified: 2007-12-03 16:08
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Abstracts by Author
Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: the Effects of Noise and Limited Spatial Resolution
Least-Squares Fitting Methods for Estimating the Winding Rate in Twisted Magnetic-Flux Tubes
Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: Application to Discrete Data
Subject will be restored when possible
Subject will be restored when possible
Subject will be restored when possible

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