Nonlinear force-free magnetic field extrapolations: comparison of the Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithm

We compare the performance of two alternative algorithms which aim to construct a force-free magnetic field given suitable boundary conditions. For this comparison, we have implemented both algorithms on the same finite element grid which uses Whitney forms to describe the fields within the grid cells. The additional use of conjugate gradient and multigrid iterations result in quite effective codes. The Grad-Rubin and Wheatland-Sturrock-Roumeliotis algorithms both perform well for the reconstruction of a known analytic force-free field. For more arbitrary boundary conditions the Wheatland-Sturrock-Roumeliotis approach has some difficulties because it requires overdetermined boundary information which may include inconsistencies. The Grad-Rubin code on the other hand loses convergence for strong current densities. For the example we have investigated, however, the maximum possible current density seems to be not far from the limit beyond which a force free field cannot exist anymore for a given normal magnetic field intensity on the boundary.Comment: 21 pages, 13 figure

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

Can We Improve the Preprocessing of Photospheric Vector Magnetograms by the Inclusion of Chromospheric Observations?

The solar magnetic field is key to understanding the physical processes in the solar atmosphere. Nonlinear force-free codes have been shown to be useful in extrapolating the coronal field upward from underlying vector boundary data. However, we can only measure the magnetic field vector routinely with high accuracy in the photosphere, and unfortunately these data do not fulfill the force-free condition. We must therefore apply some transformations to these data before nonlinear force-free extrapolation codes can be self-consistently applied. To this end, we have developed a minimization procedure that yields a more chromosphere-like field, using the measured photospheric field vectors as input. The procedure includes force-free consistency integrals, spatial smoothing, and -- newly included in the version presented here -- an improved match to the field direction as inferred from fibrils as can be observed in, e.g., chromospheric H$\alpha$ images. We test the procedure using a model active-region field that included buoyancy forces at the photospheric level. The proposed preprocessing method allows us to approximate the chromospheric vector field to within a few degrees and the free energy in the coronal field to within one percent.Comment: 22 pages, 6 Figur

Magnetic Connectivity between Active Regions 10987, 10988, and 10989 by Means of Nonlinear Force-Free Field Extrapolation

Extrapolation codes for modelling the magnetic field in the corona in cartesian geometry do not take the curvature of the Sun's surface into account and can only be applied to relatively small areas, \textit{e.g.}, a single active region. We apply a method for nonlinear force-free coronal magnetic field modelling of photospheric vector magnetograms in spherical geometry which allows us to study the connectivity between multi-active regions. We use vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS)/Vector Spectromagnetograph(VSM) to model the coronal magnetic field, where we study three neighbouring magnetically connected active regions (ARs: 10987, 10988, 10989) observed on 28, 29, and 30 March 2008, respectively. We compare the magnetic field topologies and the magnetic energy densities and study the connectivities between the active regions(ARs). We have studied the time evolution of magnetic field over the period of three days and found no major changes in topologies as there was no major eruption event. From this study we have concluded that active regions are much more connected magnetically than the electric current.Comment: Solar Physic

Coronal Magnetic Field Structure and Evolution for Flaring AR 11117 and its Surroundings

In this study, photospheric vector magnetograms obtained with the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS), are used as boundary conditions to model the three-dimensional nonlinear force-free (NLFF) coronal magnetic fields as a sequence of nonlinear force-free equilibria in spherical geometry. We study the coronal magnetic field structure inside active regions and its temporal evolution. We compare the magnetic field configuration obtained from NLFF extrapolation before and after flaring event in active region (AR) 11117 and its surroundings observed on 27 October 2010. We compare the magnetic field topologies and the magnetic energy densities and study the connectivities between AR 11117 and its surroundings. During the investigated time period, we estimate the change in free magnetic energy from before to after the flare to be 1.74x10^{32}erg which represents about 13.5% of nonlinear force-free magnetic energy before the flare. In this study, we find that electric currents from AR 11117 to its surroundings were disrupted after the flare.Comment: 14 pages, 14 figures, Accepted by Solar Physics Journa

PROFIL WISATAWAN MUSEUM RADYA PUSTAKA SURAKARTA

Anggit Margaret, C9407031 2011. Profil Wisatawan Museum Radya Pustaka Surakarta. Program Studi Diploma III Usaha Perjalanan Wisata Fakultas Sastra Dan Seni Rupa Universitas Sebelas Maret Surakarta. Penelitian tugas akhir ini mengkaji tentang Profil Wisatawan di Museum Radya Pustaka Surakarta. Tujuan dari penelitian ini adalah untuk mengetahui dari daerah mana saja wisatawan yang berkunjung ke Museum Radya Pustaka, bagaimana ciri-ciri wisatawan yang berkunjung ke Museum Radya Pustaka serta harapan-harapan yang diinginkan wisatawan terhadap Museum Radya Pustaka. Penelitian dilakukan dengan metode kualitatif. Pengumpulan data dilakukan melalui wawancara dengan narasumber wisatawan yang berkujung di Museum Radya Pustaka Surakarta tempat penulis melakukan penelitian, serta studi pustaka dan studi dokumen guna menambah sumber data. Hasil penelitian menunjukkan bahwa (1) Sebagian besar wisatawan yang datang berasal dari Semarang sebesar 32%. (2) Mayoritas wisatawan yang berkunjung ke Museum Radya Pustaka berusia antara 17-25 tahun dan kebanyakan dari mereka adalah pelajar atau mahasiswa dengan prosentase 52%. (3) Sebagian besar wisatawan yang datang ke Museum Radya Pustaka adalah bertujuan untuk melakukan penelitian yaitu sebesar 34%. (4) Harapan wisatawan yang berkunjung terhadap kelangsungan Museum Radya Pustaka sebagian besar adalah agar ditingkatkan lagi pengelolaan dan keamanan museum, agar kejadian hilangnya benda-benda koleksi museum tidak terulang lagi dikemudian hari. Kesimpulan dari hasil penelitian ini bahwa wisatawan yang berkujung ke Museum Radya Pustaka Surakarta mayoritas berasal dari Semarang, mayoritas berusia 17-25 tahun dan kebanyakan dari mereka adalah berprofesi sebagai pelajar dan mahasiswa. Kebanyakan wisatawan yang datang bertujuan untuk melakukan penelitian, serta harapan wisatawan terhadap Museum Radya Pustaka adalah supaya lebih ditingkatkan lagi pengelolaan dan keamanan museum