Least-Squares Fitting Methods for Estimating the Winding Rate in Twisted Magnetic-Flux Tubes
arXiv:1210.3369 · doi:10.1007/s11207-012-0095-5
Abstract
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.
arXiv commentAccepted for publication in Solar Physics
References in corpus (13)
- The Solar Optical Telescope for the Hinode Mission: An Overview
- Ideal kink instability of a magnetic loop equilibrium
- Simulation of the Formation of a Solar Active Region
- The physics of twisted magnetic tubes rising in a stratified medium: two dimensional results
- Modelling the Global Solar Corona II: Coronal Evolution and Filament Chirality Comparison
- The Three-dimensional Evolution of Rising, Twisted Magnetic Flux Tubes in a Gravitationally Stratified Model Convection Zone
- Initiation of Coronal Mass Ejections in a Global Evolution Model
- Global Twist of Sunspot Magnetic Fields Obtained from High Resolution Vector Magnetograms
- On the emergence of toroidal flux tubes: general dynamics and comparisons with the cylinder model
- Effect of Polarimetric Noise on the Estimation of Twist and Magnetic Energy of Force-Free Fields
- Numerical Experiments on the Two-step Emergence of Twisted Magnetic Flux Tubes in the Sun
- Comparison of a Global Magnetic Evolution Model with Observations of Coronal Mass Ejections
- Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: Application to Discrete Data