Are the photospheric sunspots magnetically force-free in nature?

In a force-free magnetic field, there is no interaction of field and the plasma in the surrounding atmosphere i.e., electric currents are aligned with the magnetic field, giving rise to zero Lorentz force. The computation of many magnetic parameters like magnetic energy, gradient of twist of sunspot magnetic fields (computed from the force-free parameter $\alpha$), including any kind of extrapolations heavily hinge on the force-free approximation of the photospheric magnetic fields. The force-free magnetic behaviour of the photospheric sunspot fields has been examined by \cite{metc95} and \cite{moon02} ending with inconsistent results. \cite{metc95} concluded that the photospheric magnetic fields are far from the force-free nature whereas \cite{moon02} found the that the photospheric magnetic fields are not so far from the force-free nature as conventionally regarded. The accurate photospheric vector field measurements with high resolution are needed to examine the force-free nature of sunspots. We use high resolution vector magnetograms obtained from the Solar Optical Telescope/Spectro-Polarimeter (SOT/SP) aboard Hinode to inspect the force-free behaviour of the photospheric sunspot magnetic fields. Both the necessary and sufficient conditions for force-freeness are examined by checking global as well as as local nature of sunspot magnetic fields. We find that the sunspot magnetic fields are very close to the force-free approximation, although they are not completely force-free on the photosphere.Comment: 04 pages; To appear in the "Physics of Sun and star spots", Proceedings of IAU Symposium 273, eds. D.P. Choudhary and K.G. Strassmeie

Structure of sunspot penumbral filaments: a remarkable uniformity of properties

The sunspot penumbra comprises numerous thin, radially elongated filaments that are central for heat transport within the penumbra, but whose structure is still not clear. To investigate the fine-scale structure of these filaments, we perform a depth-dependent inversion of spectropolarimetric data of a sunspot very close to solar disk center obtained by Hinode (SOT/SP). We have used a recently developed spatially coupled 2D inversion scheme which allows us to analyze the fine structure of individual penumbral filaments up to the diffraction limit of the telescope. Filaments of different sizes in all parts of penumbra display very similar magnetic field strengths, inclinations and velocity patterns. The similarities allowed us to average all these filaments and to extract the physical properties common to all of them. This average filament shows upflows associated with an upward pointing field at its inner, umbral end and along its axis, downflows along the lateral edge and strong downflows in the outer end associated with a nearly vertical, strong and downward pointing field. The upflowing plasma is significantly hotter than the downflowing plasma. The hot, tear-shaped head of the averaged filament can be associated with a penumbral grain. The central part of the filament shows nearly horizontal fields with strengths of ~1kG. The field above the filament converges, whereas a diverging trend is seen in the deepest layers near the head of the filament. We put forward a unified observational picture of a sunspot penumbral filament. It is consistent with such a filament being a magneto-convective cell, in line with recent MHD simulations. The uniformity of its properties over the penumbra sets constraints on penumbral models and simulations. The complex and inhomogeneous structure of the filament provides a natural explanation for a number of long-running controversies in the literature.Comment: 19 pages; 12 figures; accepted for publication in A&

Hybrid Taguchi-GRA-CRITIC Optimization Method for Multi-Response Optimization of Micro-EDM Drilling Process Parameters

In this study, an attempt is made to investigate how the operational parameters such as capacitance, voltage, feed rate, and rotating speed affect the material removal rate, tool wear, overcut, and taper angle for micro-EDM drilling of aluminium 6061 utilizing brass C360 electrode. A novel Taguchi-GRA-CRITIC hybrid optimization methodology is used to obtain the optimal combination of micro-EDM drilling process parameters. The experiment was designed using the Taguchi L18 orthogonal array, and responses were recorded for each experiment. Grey Relational Analysis (GRA) is applied to improve the multi-response of the planned experiment. The weighting values corresponding to various responses are determined using CRITIC (criterion importance through intercriteria correlation) analysis. The hybrid methodology determines the best combination of process parameters for different responses. ANOVA was used to discover the most critical parameters. Finally, confirmation experiments were conducted with optimal parameters to identify improvement in grey relational grade over the initial parameters. The study\u27s findings indicate that, compared to the initial process parameter setting, the grey relational grade (GRG) increased by 92.36% with the optimal parameter setting

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

On the estimate of magnetic non-potentiality of sunspots derived using Hinode SOT/SP observations: Effect of polarimetric noise

The accuracy of Milne-Eddington (ME) inversions, used to retrieve the magnetic field vector, depends upon the signal-to-noise ratio (SNR) of the spectro-polarimetric observations. The SNR in real observations varies from pixel to pixel, therefore the accuracy of the field vector also varies over the map. The aim of this work is to study the effect of polarimetric noise on the inference of magnetic field vector and the magnetic non-potentiality of a real sunspot. To this end, we use Hinode SOT/SP vector magnetogram of a real sunspot NOAA 10933 as an input to generate synthetic Stokes profiles under ME model assumptions. We then add normally-distributed polarimetric noise of the level 0.5\% of continuum intensity to these synthetic profiles and invert them again using ME code. This process is repeated 100 times with different realizations of noise. It is found that within most of the sunspot area (> 90% area) the spread in the (i) field strength is less than 8 Gauss, (ii) field inclination is less than 1 degree, and (iii) field azimuth is less than 5 degrees. Further, we determine the uncertainty in the magnetic non-potentiality of a sunspot as determined by the force-free parameter alpha_g and Spatially Averaged Signed Shear Angle (SASSA). It is found that for the sunspot studied here these parameters are alpha_g = -3.5 +/- 0.37 (x 10^{-9} m^{-1}) and SASSA = -1.68 +/- 0.014 degrees. This suggests that the SASSA is a less dispersion non-potentiality parameter as compared to alpha_g. Further, we examine the effect of increasing noise levels viz. 0.01, 0.1, 0.5 and 1% of continuum intensity and find that SASSA is less vulnerable to noise as compared to alpha_g parameter.Comment: Astrophysical Journal (In Press) 29 pages, 5 figures (scatterplots do not appear in soft-copy but appear on laser-printer