On the Absence of Photospheric Net Currents in Vector Magnetograms of Sunspots Obtained From Hinode (SOT/SP)

Various theoretical and observational results have been reported regarding the presence/absence of net electric currents in the sunspots. The limited spatial resolution of the earlier observations perhaps obscured the conclusions. We have analyzed 12 sunspots observed from Hinode (SOT/SP) to clarify the issue. The azimuthal and radial components of magnetic fields and currents have been derived. The azimuthal component of the magnetic field of sunspots is found to vary in sign with azimuth. The radial component of the field also varies in magnitude with azimuth. While the latter pattern is a confirmation of the interlocking combed structure of penumbral filaments, the former pattern shows that the penumbra is made up of a "curly interlocking combed" magnetic field. The azimuthally averaged azimuthal component is seen to decline much faster than 1/$\varpi$ in the penumbra, after an initial increase in the umbra, for all the spots studied. This confirms the confinement of magnetic fields and absence of a net current for sunspots as postulated by \cite{parker96}. The existence of a global twist for a sunspot even in the absence of a net current is consistent with a fibril-bundle structure of the sunspot magnetic fields.Comment: 15 pages, 4 figures, 1 table; accepted for publication in the ApJ Letter

Magnetic Non-Potentiality of Solar Active Regions and Peak X-Ray Flux of the Associated Flares

Predicting the severity of the solar eruptive phenomena like flares and Coronal Mass Ejections (CMEs) remains a great challenge despite concerted efforts for several decades. The advent of high quality vector magnetograms obtained from Hinode (SOT/SP) has increased the possibility of meeting this challenge. In particular, the Spatially Averaged Signed Shear Angle (SASSA) seems to be an unique parameter to quantify the non-potentiality of the active regions. We demonstrate the usefulness of SASSA for predicting the flare severity. For this purpose we present case studies of the evolution of magnetic non-potentiality using 115 vector magnetograms of four active regions namely ARs NOAA 10930, 10960, 10961 and 10963 during December 08-15, 2006, June 03-10, 2007, June 28-July 5, 2007 and July 10-17, 2007 respectively. The NOAA ARs 10930 and 10960 were very active and produced X and M class flares respectively, along with many smaller X-ray flares. On the other hand, the NOAA ARs 10961 and 10963 were relatively less active and produced only very small (mostly A and B-class) flares. For this study we have used a large number of high resolution vector magnetograms obtained from Hinode (SOT/SP). The analysis shows that the peak X-ray flux of the most intense solar flare emanating from the active regions depends on the magnitude of the SASSA at the time of the flare. This finding of the existence of a lower limit of SASSA for a given class of X-ray flare will be very useful for space weather forecasting. We have also studied another non-potentiality parameter called mean weighted shear angle (MWSA) of the vector magnetograms along with SASSA. We find that the MWSA does not show such distinction as the SASSA for upper limits of GOES X-Ray flux of solar flares, however both the quantities show similar trends during the evolution of all active regions studied.Comment: 25 pages, 5 figures, accepted for publication in the Astrophysical Journa

Global Twist of Sunspot Magnetic Fields Obtained from High Resolution Vector Magnetograms

The presence of fine structures in the sunspot vector magnetic fields has been confirmed from Hinode as well as other earlier observations. We studied 43 sunspots based on the data sets taken from ASP/DLSP, Hinode (SOT/SP) and SVM (USO). In this \emph{Letter}, (i) We introduce the concept of signed shear angle (SSA) for sunspots and establish its importance for non force-free fields. (ii) We find that the sign of global $\alpha$ (force-free parameter) is well correlated with the global SSA and the photospheric chirality of sunspots. (iii) Local $\alpha$ patches of opposite signs are present in the umbra of each sunspot. The amplitude of the spatial variation of local $\alpha$ in the umbra is typically of the order of the global $\alpha$ of the sunspot. (iv) We find that the local $\alpha$ is distributed as alternately positive and negative filaments in the penumbra. The amplitude of azimuthal variation of the local $\alpha$ in the penumbra is approximately an order of magnitude larger than that in the umbra. The contributions of the local positive and negative currents and $\alpha$ in the penumbra cancel each other giving almost no contribution for their global values for whole sunspot. (v) Arc-like structures (partial rings) with a sign opposite to that of the dominant sign of $\alpha$ of the umbral region are seen at the umbral-penumbral boundaries of some sunspots. (vi) Most of the sunspots studied, belong to the minimum epoch of the 23$^{rd}$ solar cycle and do not follow the so-called hemispheric helicity rule.Comment: 15 pages, 3 figures, 1 table; Accepted for publication in the ApJ Letter

Effect of Polarimetric Noise on the Estimation of Twist and Magnetic Energy of Force-Free Fields

The force-free parameter $\alpha$, also known as helicity parameter or twist parameter, bears the same sign as the magnetic helicity under some restrictive conditions. The single global value of $\alpha$ for a whole active region gives the degree of twist per unit axial length. We investigate the effect of polarimetric noise on the calculation of global $\alpha$ value and magnetic energy of an analytical bipole. The analytical bipole has been generated using the force-free field approximation with a known value of constant $\alpha$ and magnetic energy. The magnetic parameters obtained from the analytical bipole are used to generate Stokes profiles from the Unno-Rachkovsky solutions for polarized radiative transfer equations. Then we add random noise of the order of 10$^{-3}$ of the continuum intensity (I$_{c}$) in these profiles to simulate the real profiles obtained by modern spectropolarimeters like Hinode (SOT/SP), SVM (USO), ASP, DLSP, POLIS, SOLIS etc. These noisy profiles are then inverted using a Milne-Eddington inversion code to retrieve the magnetic parameters. Hundred realizations of this process of adding random noise and polarimetric inversion is repeated to study the distribution of error in global $\alpha$ and magnetic energy values. The results show that : (1). the sign of $\alpha$ is not influenced by polarimetric noise and very accurate values of global twist can be calculated, and (2). accurate estimation of magnetic energy with uncertainty as low as 0.5% is possible under the force-free condition.Comment: 33 pages, 6 figures, 1 table; Accepted for publication in the Ap

Nonlinear force-free modelling: influence of inaccuracies in the measured magnetic vector

Context: Solar magnetic fields are regularly extrapolated into the corona starting from photospheric magnetic measurements that can suffer from significant uncertainties. Aims: Here we study how inaccuracies introduced into the maps of the photospheric magnetic vector from the inversion of ideal and noisy Stokes parameters influence the extrapolation of nonlinear force-free magnetic fields. Methods: We compute nonlinear force-free magnetic fields based on simulated vector magnetograms, which have been produced by the inversion of Stokes profiles, computed froma 3-D radiation MHD simulation snapshot. These extrapolations are compared with extrapolations starting directly from the field in the MHD simulations, which is our reference. We investigate how line formation and instrumental effects such as noise, limited spatial resolution and the effect of employing a filter instrument influence the resulting magnetic field structure. The comparison is done qualitatively by visual inspection of the magnetic field distribution and quantitatively by different metrics. Results: The reconstructed field is most accurate if ideal Stokes data are inverted and becomes less accurate if instrumental effects and noise are included. The results demonstrate that the non-linear force-free field extrapolation method tested here is relatively insensitive to the effects of noise in measured polarization spectra at levels consistent with present-day instruments. Conclusions heading: Our results show that we can reconstruct the coronal magnetic field as a nonlinear force-free field from realistic photospheric measurements with an accuracy of a few percent, at least in the absence of sunspots.Comment: A&A, accepted, 9 Pages, 4 Figure

Magnetic Tension of Sunspot Fine Structures

The equilibrium structure of sunspots depends critically on its magnetic topology and is dominated by magnetic forces. Tension force is one component of the Lorentz force which balances the gradient of magnetic pressure in force-free configurations. We employ the tension term of the Lorentz force to clarify the structure of sunspot features like penumbral filaments, umbral light bridges and outer penumbral fine structures. We compute vertical component of tension term of Lorentz force over two active regions namely NOAA AR 10933 and NOAA AR 10930 observed on 05 January 2007 and 12 December 2006 respectively. The former is a simple while latter is a complex active region with highly sheared polarity inversion line (PIL). The vector magnetograms used are obtained from Hinode(SOT/SP). We find an inhomogeneous distribution of tension with both positive and negative signs in various features of the sunspots. The existence of positive tension at locations of lower field strength and higher inclination is compatible with the uncombed model of the penumbral structure. Positive tension is also seen in umbral light bridges which could be indication of uncombed structure of the light bridge. Likewise, the upward directed tension associated with bipolar regions in the penumbra could be a direct confirmation of the sea serpent model of penumbral structures. Upward directed tension at the PIL of AR 10930 seems to be related to flux emergence. The magnitude of the tension force is greater than the force of gravity in some places, implying a nearly force-free configuration for these sunspot features. From our study, magnetic tension emerges as a useful diagnostic of the local equilibrium of the sunspot fine structures.Comment: 06 pages, 6 figures; Accepted for publication in the Astronomy & Astrophysics as a "Letter to the Editor

On the Force-Freeness of the Photospheric Sunspot Magnetic Fields as Observed from Hinode (SOT/SP)

A magnetic field is force-free if there is no interaction between the magnetic field and plasma in surrounding atmosphere i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. Computation of various magnetic parameters such as magnetic energy, gradient of twist of sunspot fields and any kind of extrapolations, heavily hinge on the force-free approximation of the photospheric sunspot magnetic fields. Thus it is important to inspect the force-freeness of sunspot fields. The force-freeness of sunspot magnetic fields has been examined earlier by some researchers ending with incoherent results. Accurate photospheric vector field measurements with high spatial resolution are required to inspect the force-free nature of sunspots. We use several such vector magnetograms obtained from the Solar Optical Telescope/Spectro-Polarimeter aboard the Hinode. Both necessary and sufficient conditions for force-freeness are examined by checking global and local nature of magnetic forces over sunspots. We find that the sunspot magnetic fields are not much away from force-free configuration, although they are not completely force-free on the photosphere. The umbral and inner penumbral fields are more force-free than the middle and the outer penumbral fields. During their evolution, sunspot magnetic fields are found to maintain their proximity to force-free behaviour. Although a dependence of net Lorentz force components is seen on the evolutionary stages of the sunspots, we don't find a systematic relationship between the nature of sunspot fields and associated flare activity. Further, we examine whether the fields at photosphere follow linear or non-linear force free conditions. After examining this in various complex and simple sunspots we conclude that,in either case,the photospheric sunspot fields are closer to satisfy non linear force-free field approximation.Comment: 34 pages, 4 figures, 2 tables; accepted for publication in the Astrophysical Journa