How to optimize nonlinear force-free coronal magnetic field extrapolations from SDO/HMI vector magnetograms?

The SDO/HMI instruments provide photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semi-analytic and numeric equilibria and been applied before to vector magnetograms from Hinode and ground based observations. Recently we implemented a new version which takes measurement errors in photospheric vector magnetograms into account. Photospheric field measurements are often due to measurement errors and finite nonmagnetic forces inconsistent as a boundary for a force-free field in the corona. In order to deal with these uncertainties, we developed two improvements: 1.) Preprocessing of the surface measurements in order to make them compatible with a force-free field 2.) The new code keeps a balance between the force-free constraint and deviation from the photospheric field measurements. Both methods contain free parameters, which have to be optimized for use with data from SDO/HMI. Within this work we describe the corresponding analysis method and evaluate the force-free equilibria by means of how well force-freeness and solenoidal conditions are fulfilled, the angle between magnetic field and electric current and by comparing projections of magnetic field lines with coronal images from SDO/AIA. We also compute the available free magnetic energy and discuss the potential influence of control parameters.Comment: 17 Pages, 6 Figures, Sol. Phys., accepte

A spatio-temporal description of the abrupt changes in the photospheric magnetic and Lorentz-force vectors during the 2011 February 15 X2.2 flare

The active region NOAA 11158 produced the first X-class flare of Solar Cycle 24, an X2.2 flare at 01:44 UT on 2011 February 15. Here we analyze SDO/HMI magnetograms covering a 12-hour interval centered at the time of this flare. We describe the spatial distributions of the photospheric magnetic changes associated with this flare, including the abrupt changes in the field vector, vertical electric current and Lorentz force vector. We also trace these parameters' temporal evolution. The abrupt magnetic changes were concentrated near the neutral line and in two neighboring sunspots. Near the neutral line, the field vectors became stronger and more horizontal during the flare and the shear increased. This was due to an increase in strength of the horizontal field components near the neutral line, most significant in the horizontal component parallel to the neutral line but the perpendicular component also increased in strength. The vertical component did not show a significant, permanent overall change at the neutral line. The increase in total flux at the neutral line was accompanied by a compensating flux decrease in the surrounding volume. In the two sunspots near the neutral line the azimuthal flux abruptly decreased during the flare but this change was permanent in only one of the spots. There was a large, abrupt, downward vertical Lorentz force change during the flare, consistent with results of past analyses and recent theoretical work. The horizontal Lorentz force acted in opposite directions along each side of neutral line, with the two sunspots at each end subject to abrupt torsional forces. The shearing forces were consistent with field contraction and decrease of shear near the neutral line, whereas the field itself became more sheared as a result of the flux collapsing towards the neutral line from the surrounding volume.Comment: DOI 10.1007/s11207-012-0071-0. Accepted for publication in Solar Physics SDO3 Topical Issue. Some graphics missing due to 15MB limi

Modeling the Subsurface Structure of Sunspots

While sunspots are easily observed at the solar surface, determining their subsurface structure is not trivial. There are two main hypotheses for the subsurface structure of sunspots: the monolithic model and the cluster model. Local helioseismology is the only means by which we can investigate subphotospheric structure. However, as current linear inversion techniques do not yet allow helioseismology to probe the internal structure with sufficient confidence to distinguish between the monolith and cluster models, the development of physically realistic sunspot models are a priority for helioseismologists. This is because they are not only important indicators of the variety of physical effects that may influence helioseismic inferences in active regions, but they also enable detailed assessments of the validity of helioseismic interpretations through numerical forward modeling. In this paper, we provide a critical review of the existing sunspot models and an overview of numerical methods employed to model wave propagation through model sunspots. We then carry out an helioseismic analysis of the sunspot in Active Region 9787 and address the serious inconsistencies uncovered by \citeauthor{gizonetal2009}~(\citeyear{gizonetal2009,gizonetal2009a}). We find that this sunspot is most probably associated with a shallow, positive wave-speed perturbation (unlike the traditional two-layer model) and that travel-time measurements are consistent with a horizontal outflow in the surrounding moat.Comment: 73 pages, 19 figures, accepted by Solar Physic

Evolution of the Fine Structure of Magnetic Fields in the Quiet Sun: Observations from Sunrise/IMaX and Extrapolations

Observations with the balloon-borne Sunrise/Imaging Magnetograph eXperiment (IMaX) provide high spatial resolution (roughly 100 km at disk center) measurements of the magnetic field in the photosphere of the quiet Sun. To investigate the magnetic structure of the chromosphere and corona, we extrapolate these photospheric measurements into the upper solar atmosphere and analyze a 22-minute long time series with a cadence of 33 seconds. Using the extrapolated magnetic-field lines as tracer, we investigate temporal evolution of the magnetic connectivity in the quiet Sun’s atmosphere. The majority of magnetic loops are asymmetric in the sense that the photospheric field strength at the loop foot points is very different. We find that the magnetic connectivity of the loops changes rapidly with a typical connection recycling time of about 3±1 minutes in the upper solar atmosphere and 12±4 minutes in the photosphere. This is considerably shorter than previously found. Nonetheless, our estimate of the energy released by the associated magnetic-reconnection processes is not likely to be the sole source for heating the chromosphere and corona in the quiet Sun

Influência da nutrição mineral na intensidade da mancha-de-olho-pardo em mudas de cafeeiro Influence of the mineral nutrition on intensity of brown-eye spot in young coffee plants

Objetivando avaliar a intensidade da mancha-de-olho-pardo do cafeeiro, variedade Catuaí Vermelho, com relação ao estado nutricional das plantas quanto a N e K, realizou-se um experimento no viveiro da Universidade Federal de Viçosa, em Viçosa, MG, utilizando solução nutritiva circulante. Empregaram-se 16 tratamentos, em delineamento inteiramente casualizado, com três repetições e duas plantas por parcela, em esquema fatorial com quatro doses de K (3, 5, 7 e 9mmol/L) e quatro doses de N (3, 7, 11 e 15mmol/L). Após sete inoculações de conídios, e avaliações, colheram-se as plantas. A produção de matéria seca total, a área foliar total, e a área abaixo da curva de progresso (AACP) do número total de folhas não foram influenciadas pelas doses de K, mas aumentaram com o incremento das doses de N. Observou-se elevação, na AACP, do número de lesões por folha, e na desfolha com o aumento das doses de K e a redução das doses de N. A elevação nas doses de K promoveu redução nos teores foliares de Ca e Cu. Osteores foliares de P, Mg, Mn e Fe não foram influenciados pelas doses de K e tiveram pequena redução com o aumento de N na solução, elevando-se a seguir.<br>The experiment was carried out at the coffee nursery of the Universide Federal de Viçosa, in Viçosa, MG, Brazil, using nutrient circulating solution to evaluate the intensity of brown-eye spot (Cercospora coffeicola), variety Catuaí Vermelho, as a function of N and K. Acompletely randomized design with 16 treatments, three replicates, and two plants per plot was used in a factorial with four levels of K (3, 5, 7 and 9mmol/L) combined with four levels of N (3, 7, 11 and 15mmol/L). After seven inoculations and evaluations, the plants were picked. Total dry matter production, total leaf area, and the area below the curve of progress (AACP) for the total number of leaves were not influenced by the levels of K, but increased with increasing levels of N. There was increase in AACP areas for the number of lesions per leaf and defoliation, with the increase of K levels, and a reduction of N levels. The increase in K levels reduced the Ca and Cu leaf contents, indicating possible relation between its contents and the increase of the disease. The P, Mg, Mn, and Fe leaf contents were not influenced by the K levels, and had a small reduction with increased N contents in the nutrient solution, increasing thereafter