K. D. Leka

A Critical Assessment of Nonlinear Force-Free Field Modeling of the Solar Corona for Active Region 10953

Nonlinear force-free field (NLFFF) models are thought to be viable tools for investigating the structure, dynamics, and evolution of the coronae of solar active regions. In a series of NLFFF modeling studies, we have found that NLFFF models are successful in application to analytic test cases, and relatively successful when applied to numerically constructed Sun-like test cases, but they are less successful in application to real solar data. Different NLFFF models have been found to have markedly different field line configurations and to provide widely varying estimates of the magnetic free energy in the coronal volume, when applied to solar data. NLFFF models require consistent, force-free vector magnetic boundary data. However, vector magnetogram observations sampling the photosphere, which is dynamic and contains significant Lorentz and buoyancy forces, do not satisfy this requirement, thus creating several major problems for force-free coronal modeling efforts. In this paper, we discuss NLFFF modeling of NOAA Active Region 10953 using Hinode/SOT-SP, Hinode/XRT, STEREO/SECCHI-EUVI, and SOHO/MDI observations, and in the process illustrate three such issues we judge to be critical to the success of NLFFF modeling: (1) vector magnetic field data covering larger areas are needed so that more electric currents associated with the full active regions of interest are measured, (2) the modeling algorithms need a way to accommodate the various uncertainties in the boundary data, and (3) a more realistic physical model is needed to approximate the photosphere-to-corona interface in order to better transform the forced photospheric magnetograms into adequate approximations of nearly force-free fields at the base of the corona. We make recommendations for future modeling efforts to overcome these as yet unsolved problems.

The Helioseismic and Magnetic Imager (HMI) vector magnetic field pipeline: overview and performance

The Helioseismic and Magnetic Imager (HMI) began near-continuous full-disk solar measurements on 1 May 2010 from the Solar Dynamics Observatory (SDO). An automated processing pipeline keeps pace with observations to produce observable quantities, including the photospheric vector magnetic field, from sequences of filtergrams. The basic vector-field frame list cadence is 135 seconds, but to reduce noise the filtergrams are combined to derive data products every 720 seconds. The primary 720xa0s observables were released in mid-2010, including Stokes polarization parameters measured at six wavelengths, as well as intensity, Doppler velocity, and the line-of-sight magnetic field. More advanced products, including the full vector magnetic field, are now available. Automatically identified HMI Active Region Patches (HARPs) track the location and shape of magnetic regions throughout their lifetime.The vector field is computed using the Very Fast Inversion of the Stokes Vector (VFISV) code optimized for the HMI pipeline; the remaining 180∘ azimuth ambiguity is resolved with the Minimum Energy (ME0) code. The Milne–Eddington inversion is performed on all full-disk HMI observations. The disambiguation, until recently run only on HARP regions, is now implemented for the full disk. Vector and scalar quantities in the patches are used to derive active region indices potentially useful for forecasting; the data maps and indices are collected in the SHARP data series, hmi.sharp_720s. Definitive SHARP processing is completed only after the region rotates off the visible disk; quick-look products are produced in near real time. Patches are provided in both CCD and heliographic coordinates.HMI provides continuous coverage of the vector field, but has modest spatial, spectral, and temporal resolution. Coupled with limitations of the analysis and interpretation techniques, effects of the orbital velocity, and instrument performance, the resulting measurements have a certain dynamic range and sensitivity and are subject to systematic errors and uncertainties that are characterized in this report.

The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: SHARPs – Space-Weather HMI Active Region Patches

A new data product from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) called Space-weather HMI Active Region Patches (SHARPs) is now available. SDO/HMI is the first space-based instrument to map the full-disk photospheric vector magnetic field with high cadence and continuity. The SHARP data series provide maps in patches that encompass automatically tracked magnetic concentrations for their entire lifetime; map quantities include the photospheric vector magnetic field and its uncertainty, along with Doppler velocity, continuum intensity, and line-of-sight magnetic field. Furthermore, keywords in the SHARP data series provide several parameters that concisely characterize the magnetic-field distribution and its deviation from a potential-field configuration. These indices may be useful for active-region event forecasting and for identifying regions of interest. The indices are calculated per patch and are available on a twelve-minute cadence. Quick-look data are available within approximately three hours of observation; definitive science products are produced approximately five weeks later. SHARP data are available at jsoc.stanford.edu and maps are available in either of two different coordinate systems. This article describes the SHARP data products and presents examples of SHARP data and parameters.

The influence of spatial resolution on nonlinear force-free modeling

The nonlinear force-free field (NLFFF) model is often used to describe the solar coronal magnetic field, however a series of earlier studies revealed difficulties in the numerical solution of the model in application to photospheric boundary data. We investigate the sensitivity of the modeling to the spatial resolution of the boundary data, by applying multiple codes that numerically solve the NLFFF model to a sequence of vector magnetogram data at different resolutions, prepared from a single Hinode/SOT-SP scan of NOAA Active Region 10978 on 2007 December 13. We analyze the resulting energies and relative magnetic helicities, employ a Helmholtz decomposition to characterize divergence errors, and quantify changes made by the codes to the vector magnetogram boundary data in order to be compatible with the force-free model. This study shows that NLFFF modeling results depend quantitatively on the spatial resolution of the input boundary data, and that using more highly resolved boundary data yields more self-consistent results. The free energies of the resulting solutions generally trend higher with increasing resolution, while relative magnetic helicity values vary significantly between resolutions for all methods. All methods require changing the horizontal components, and for some methods also the vertical components, of the vector magnetogram boundary field in excess of nominal uncertainties in the data. The solutions produced by the various methods are significantly different at each resolution level. We continue to recommend verifying agreement between the modeled field lines and corresponding coronal loop images before any NLFFF model is used in a scientific setting.

Achieving Self-Consistent Nonlinear Force-free Modeling of Solar Active Regions

A nonlinear force-free solution is constructed for the coronal magnetic field in NOAA solar active region AR 10953 based on a photospheric vector magnetogram derived from Hinode satellite observations on 30 April 2007, taking into account uncertainties in the boundary data and using improved methods for merging multiple-instrument data. The solution demonstrates the self-consistency pro- cedure of Wheatland & Regnier (2009), for the first time including uncertainties. The self-consistency procedure addresses the problem that photospheric vector magnetogram data are inconsistent with the force-free model, and in particular that the boundary conditions on vertical electric current density are over-specified and permit the construction of two different nonlinear force-free solutions. The procedure modifies the boundary conditions on current density during a sequence of cycles until the two nonlinear force-free solutions agree. It hence constructs an accurate single solution to the force-free model, with boundary values close, but not matched exactly, to the vector magnetogram data. The inclusion of un- certainties preserves the boundary conditions more closely at points with smaller uncertainties. The self-consistent solution obtained for active region AR 10953 is

Forward Modeling of Active Region Coronal Emissions. II. Implications for Coronal Heating

In Paper I, we introduced and tested a method for predicting solar active region coronal emissions using magnetic field measurements and a chosen heating relationship. Here, we apply this forward-modeling technique to 10 active regions observed with the Mees Solar Observatory Imaging Vector Magnetograph and the Yohkoh Soft X-ray Telescope. We produce synthetic images of each region using four parameterized heating relationships depending on magnetic field strength and geometry. We find a volumetric coronal heating rate (dEH/dV, not to be confused with dEH/dA quoted by some authors) proportional to magnetic field and inversely proportional to field-line loop length (BL−1) best matches observed coronal emission morphologies. This parameterization is most similar to the steady-state scaling of two proposed heating mechanisms: van Ballegooijens current layers theory, taken in the AC limit, and Parkers critical angle mechanism, in the case where the angle of misalignment is a twist angle. Although this parameterization best matches the observations, it does not match well enough to make a definitive statement as to the nature of coronal heating. Instead, we conclude that (1) the technique requires better magnetic field measurement and extrapolation techniques than currently available, and (2) forward-modeling methods that incorporate properties of transiently heated loops are necessary to make a more conclusive statement about coronal heating mechanisms.

Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: Application to Discrete Data

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.

Achieving Consistent Doppler Measurements from SDO/HMI Vector Field Inversions

NASAs Solar Dynamics Observatory is delivering vector field observations of the full solar disk with unprecedented temporal and spatial resolution; however, the satellite is in a highly inclined geostationary orbit. The relative spacecraft-Sun velocity varies by

The Free Energy of NOAA Solar Active Region AR 11029

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THE ROLE OF MAGNETIC TOPOLOGY IN THE HEATING OF ACTIVE REGION CORONAL LOOPS

~km/s over a day which introduces major orbital artifacts in the Helioseismic Magnetic Imager data. We demonstrate that the orbital artifacts contaminate all spatial and temporal scales in the data. We describe a newly-developed three stage procedure for mitigating these artifacts in the Doppler data derived from the Milne-Eddington inversions in the HMI Pipeline. This procedure was applied to full disk images of AR11084 to produce consistent Dopplergrams. The data adjustments reduce the power in the orbital artifacts by 31dB. Furthermore, we analyze in detail the corrected images and show that our procedure greatly improve the temporal and spectral properties of the data without adding any new artifacts. We conclude that this new and easily implemented procedure makes a dramatic improvement in the consistency of the HMI data and in its usefulness for precision scientific studies.