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Register a new userModels of force-free spheres and applications to solar active regions
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Authors
A. Prasad
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Here we present a systematic study of force-free field equation for simple axisymmetric configurations in spherical geometry. The condition of separability of solutions in radial and angular variables leads to two classes of solutions: linear and non-linear force-free fields. We have studied these linear solutions Chandrasekhar (1956) and extended the non-linear solutions given in Low & Lou (1990) to the irreducible rational form $n= p/q$, which is allowed for all cases of odd $p$ and to cases of $q>p$ for even $p$. We have further calculated their energies and relative helicities for magnetic field configurations in finite and infinite shell geometries. We demonstrate here a method here to be used to fit observed magnetograms as well as to provide good exact input fields for testing other numerical codes used in reconstruction on the non-linear force-free fields.
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The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces like plasma pressure gradient and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relation between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently of large interests, as accurate measurements of the photospheric field become available from ground-based (for example SOLIS) and space-born (for example Hinode and SDO) instruments. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV-images of the radiating coronal plasma.
Adopting the thermal free-free emission mechanism, the coronal and chromospheric magnetic fields are derived from the polarization and spectral observations with the Nobeyama Radioheliograph at 1.76 cm. The solar active regions (AR) located near the disk center observed on January 8, 2015 (AR 12257) and December 4, 2016 (AR 12615) are used for the estimate of the chromospheric and coronal magnetic fields with the microwave radio observations. We compare solar radio maps of active regions for both intensity and circularly polarized component with the optical maps from observations with the Helioseismic and Magnetic Imager and the chromosphere and corona transition region images obtained with the Atmospheric Imaging Assembly instrument, on board the Solar Dynamic Observatory. We notice from the comparison between radio maps of both AR that the circular polarization degree in the AR 12257 is about 2 percent, but the AR 12615 has a higher existent value by 3 percent. Radio observations provide us for direct measurements of magnetic fields in the chromospheric and coronal layers. We estimate the coronal magnetic fields using the Atmospheric Imaging Assembly observations by adopting magnetic loops in the corona over some patches with weak photospheric magnetic fields. The coronal magnetic field derived from the Atmospheric Imaging Assembly data was from 90 to 240 Gauss. We also study the coronal magnetic fields based on the structure of the extrapolated field, where the result of the magnetic fields was in the range from 35 to 145 Gauss, showing that the difference in the coronal magnetic fields between both results is attributed to the assumption of the force-free approximation.
We use SDO/HMI and SOLIS/VSM photospheric magnetic field measurements to model the force-free coronal field above a solar active region, assuming magnetic forces to dominate. We take measurement uncertainties caused by, e.g., noise and the particular inversion technique into account. After searching for the optimum modeling parameters for the particular data sets, we compare the resulting nonlinear force-free model fields. We show the degree of agreement of the coronal field reconstructions from the different data sources by comparing the relative free energy content, the vertical distribution of the magnetic pressure and the vertically integrated current density. Though the longitudinal and transverse magnetic flux measured by the VSM and HMI is clearly different, we find considerable similarities in the modeled fields. This indicates the robustness of the algorithm we use to calculate the nonlinear force-free fields against differences and deficiencies of the photospheric vector maps used as an input. We also depict how much the absolute values of the total force-free, virial and the free magnetic energy differ and how the orientation of the longitudinal and transverse components of the HMI- and VSM-based model volumes compares to each other.
We use observations of line-of-sight magnetograms from Helioseismic and Magnetic Imager (HMI) on board of Solar Dynamics Observatory (SDO) to investigate polarity separation, magnetic flux, flux emergence rate, twist and tilt of solar emerging active regions. Functional dependence of polarity separation and maximum magnetic flux of an active region is in agreement with a simple model of flux emergence as the result of buoyancy forces. Our investigation did not reveal any strong dependence of emergence rate on twist properties of active regions.
Dynamical changes in the solar corona have proven to be very important in inducing seismic waves into the photosphere. Different mechanisms for their generation have been proposed. In this work, we explore the magnetic field forces as plausible mechanisms to generate sunquakes as proposed by Hudson, Fisher and Welsch. We present a spatial and temporal analysis of the line-of-sight magnetic field variations induced by the seismically active 2003 October 29 and 2005 January 15 solar flares and compare these results with other supporting observations.
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