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We performed two data-based magnetohydrodynamic (MHD) simulations for solar active region 12371 which produced an M6.5 flare. The first simulation is a full data-driven simulation where the initial condition is given by a nonlinear force-free field (NLFFF). This NLFFF was extrapolated from photospheric magnetograms approximately 1 hour prior to the flare, and then a time-varying photospheric magnetic field is imposed at the bottom surface. The second simulation is also a data-driven simulation, but it stops driving at the bottom before the time of flare onset and then switches to the data-constrained simulation, where the horizontal component of the magnetic field varies according to an induction equation while the normal component is fixed with time. Both simulations lead to an eruption, with both simulations producing highly twisted field lines before the eruption which were not found in the NLFFF alone. After the eruption, the first simulation based on the time-varying photospheric magneitic field, continues to produce sheared field lines after the flare without reproducing phenomena such as post-flare loops. The second simulation reproduces the phenomena associated with flares well. However in this case the evolution of the bottom magnetic field is inconsistent with the evolution of the observed magnetic field. In this letter, we report potential advantages and disadvantages in data-constrained and data-driven MHD simulations that need to be taken into consideration by future studies., Comment: Accepted for Publication in The Astrophysical Journal Letters

We present a newly developed data-driven magnetohydrodynamics (MHD) simulation code under a zero-beta approximation based on a method proposed by Hayashi et al. 2018 and 2019. Although many data-driven MHD simulations have been developed and conducted, there are not many studies on how accurately those simulations can reproduce the phenomena observed in the solar corona. In this study, we investigated the performance of our data-driven simulation quantitatively using ground-truth data. The ground-truth data was produced by an MHD simulation in which the magnetic field is twisted by the sunspot motions. A magnetic flux rope (MFR) is created by the cancellation of the magnetic flux at the polarity inversion line due to the converging flow on the sunspot, which eventually leads the eruption of the MFR. We attempted to reproduce these dynamics using the data-driven MHD simulation. The coronal magnetic fields are driven by the electric fields, which are obtained from a time-series of the photospheric magnetic field that is extracted from the ground-truth data, on the surface. As a result, the data-driven simulation could capture the subsequent MHD processes, the twisted coronal magnetic field and formation of the MFR, and also its eruption. We report these results and compare with the ground-truth data, and discuss how to improve the accuracy and optimize numerical method., Comment: Accepted for publication in ApJ

The Coronal Global Evolutionary Model (CGEM) provides data-driven simulations of the magnetic field in the solar corona to better understand the build-up of magnetic energy that leads to eruptive events. The CGEM project has developed six capabilities. CGEM modules (1) prepare time series of full-disk vector magnetic field observations to (2) derive the changing electric field in the solar photosphere over active-region scales. This local electric field is (3) incorporated into a surface flux transport model that reconstructs a global electric field that evolves magnetic flux in a consistent way. These electric fields drive a (4) 3D spherical magneto-frictional (SMF) model, either at high-resolution over a restricted range of solid angle or at lower resolution over a global domain, to determine the magnetic field and current density in the low corona. An SMF-generated initial field above an active region and the evolving electric field at the photosphere are used to drive (5) detailed magneto-hydrodynamic (MHD) simulations of active regions in the low corona. SMF or MHD solutions are then used to compute emissivity proxies that can be compared with coronal observations. Finally, a lower-resolution SMF magnetic field is used to initialize (6) a global MHD model that is driven by an SMF electric-field time series to simulate the outer corona and heliosphere, ultimately connecting Sun to Earth. As a demonstration, this report features results of CGEM applied to observations of the evolution of NOAA Active Region 11158 in February 2011., Comment: 19 pages, 8 figures

For a better understanding of magnetic field in the solar corona and dynamic activities such as flares and coronal mass ejections, it is crucial to measure the time-evolving coronal field and accurately estimate the magnetic energy. Recently, a new modeling technique called the data-driven coronal field model, in which the time evolution of magnetic field is driven by a sequence of photospheric magnetic and velocity field maps, has been developed and revealed the dynamics of flare-productive active regions. Here we report on the first qualitative and quantitative assessment of different data-driven models using a magnetic flux emergence simulation as a ground-truth (GT) data set. We compare the GT field with those reconstructed from the GT photospheric field by four data-driven algorithms. It is found that, at least, the flux rope structure is reproduced in all coronal field models. Quantitatively, however, the results show a certain degree of model dependence. In most cases, the magnetic energies and relative magnetic helicity are comparable to or at most twice of the GT values. The reproduced flux ropes have a sigmoidal shape (consistent with GT) of various sizes, a vertically-standing magnetic torus, or a packed structure. The observed discrepancies can be attributed to the highly non-force-free input photospheric field, from which the coronal field is reconstructed, and to the modeling constraints such as the treatment of background atmosphere, the bottom boundary setting, and the spatial resolution., Comment: 17 pages, 11 figures, 1 table, accepted for publication in ApJ. The ground-truth dataset (photospheric slices of the flux emergence simulation) is available online at https://doi.org/10.5281/zenodo.3591984

The Coronal Global Evolutionary Model (CGEM) provides data-driven simulations of the magnetic field in the solar corona to better understand the build-up of magnetic energy that leads to eruptive events. The CGEM project has developed six capabilities. CGEM modules (1) prepare time series of full-disk vector magnetic field observations to (2) derive the changing electric field in the solar photosphere over active-region scales. This local electric field is (3) incorporated into a surface flux transport model that reconstructs a global electric field that evolves magnetic flux in a consistent way. These electric fields drive a (4) 3D spherical magneto-frictional (SMF) model, either at high-resolution over a restricted range of solid angle or at lower resolution over a global domain, to determine the magnetic field and current density in the low corona. An SMF-generated initial field above an active region and the evolving electric field at the photosphere are used to drive (5) detailed magneto-hydrodynamic (MHD) simulations of active regions in the low corona. SMF or MHD solutions are then used to compute emissivity proxies that can be compared with coronal observations. Finally, a lower-resolution SMF magnetic field is used to initialize (6) a global MHD model that is driven by an SMF electric-field time series to simulate the outer corona and heliosphere, ultimately connecting Sun to Earth. As a demonstration, this report features results of CGEM applied to observations of the evolution of NOAA Active Region 11158 in February 2011., Comment: 19 pages, 8 figures

For a better understanding of magnetic field in the solar corona and dynamic activities such as flares and coronal mass ejections, it is crucial to measure the time-evolving coronal field and accurately estimate the magnetic energy. Recently, a new modeling technique called the data-driven coronal field model, in which the time evolution of magnetic field is driven by a sequence of photospheric magnetic and velocity field maps, has been developed and revealed the dynamics of flare-productive active regions. Here we report on the first qualitative and quantitative assessment of different data-driven models using a magnetic flux emergence simulation as a ground-truth (GT) data set. We compare the GT field with those reconstructed from the GT photospheric field by four data-driven algorithms. It is found that, at least, the flux rope structure is reproduced in all coronal field models. Quantitatively, however, the results show a certain degree of model dependence. In most cases, the magnetic energies and relative magnetic helicity are comparable to or at most twice of the GT values. The reproduced flux ropes have a sigmoidal shape (consistent with GT) of various sizes, a vertically-standing magnetic torus, or a packed structure. The observed discrepancies can be attributed to the highly non-force-free input photospheric field, from which the coronal field is reconstructed, and to the modeling constraints such as the treatment of background atmosphere, the bottom boundary setting, and the spatial resolution., Comment: 17 pages, 11 figures, 1 table, accepted for publication in ApJ. The ground-truth dataset (photospheric slices of the flux emergence simulation) is available online at https://doi.org/10.5281/zenodo.3591984

The largest magnetic storm in solar cycle 24 was caused by a fast coronal mass ejection (CME) that was related to a small C9.1 flare that occurred on 15 March 2015 in solar active region (AR) NOAA 12297. The purpose of this study is to understand the onset mechanism of the geo-effective huge solar eruption. We focused on the C2.4 flare that occurred prior to the C9.1 flare of the filament eruption. The magnetic field structure in the AR was complicated: there were several filaments including the one that erupted and caused the CME. We hence carefully investigated the photospheric magnetic field, brightenings observed in the solar atmosphere, and the three-dimensional coronal magnetic field extrapolated from nonlinear force-free field modeling, using data from Hinode and Solar Dynamics Observatory. We found three intriguing points : (1) There was a compact but noticeably highly twisted magnetic field structure that is represented by a small filament in the C2.4 flaring region, where a tiny precursor brightening was observed before the C2.4 flare. (2) The C2.4 flaring region is located in the vicinity of a foot point of the closed field that prohibits the filament from erupting. (3) The filament shows a sudden eruption after the C2.4 flare and accompanying small filament eruption. From our analysis, we suggest that a small magnetic disturbance that was represented by the tiny precursor brightening at the time of the C2.4 flare is related to the trigger of the huge filament eruption., Comment: 18 pages, 7 figures, accepted by the Astrophysical Journal. There is an animation file that is corresponding to Figure 3 exist but it is not available here. Please see the ApJ publication

The largest magnetic storm in solar cycle 24 was caused by a fast coronal mass ejection (CME) that was related to a small C9.1 flare that occurred on 15 March 2015 in solar active region (AR) NOAA 12297. The purpose of this study is to understand the onset mechanism of the geo-effective huge solar eruption. We focused on the C2.4 flare that occurred prior to the C9.1 flare of the filament eruption. The magnetic field structure in the AR was complicated: there were several filaments including the one that erupted and caused the CME. We hence carefully investigated the photospheric magnetic field, brightenings observed in the solar atmosphere, and the three-dimensional coronal magnetic field extrapolated from nonlinear force-free field modeling, using data from Hinode and Solar Dynamics Observatory. We found three intriguing points : (1) There was a compact but noticeably highly twisted magnetic field structure that is represented by a small filament in the C2.4 flaring region, where a tiny precursor brightening was observed before the C2.4 flare. (2) The C2.4 flaring region is located in the vicinity of a foot point of the closed field that prohibits the filament from erupting. (3) The filament shows a sudden eruption after the C2.4 flare and accompanying small filament eruption. From our analysis, we suggest that a small magnetic disturbance that was represented by the tiny precursor brightening at the time of the C2.4 flare is related to the trigger of the huge filament eruption., Comment: 18 pages, 7 figures, accepted by the Astrophysical Journal. There is an animation file that is corresponding to Figure 3 exist but it is not available here. Please see the ApJ publication

Time-dependent three-dimensional magnetohydrodynamics (MHD) simulation modules are implemented at the Joint Science Operation Center (JSOC) of Solar Dynamics Observatory (SDO). The modules regularly produce three-dimensional data of the time-relaxed minimum-energy state of the solar corona using global solar-surface magnetic-field maps created from Helioseismic Magnetic Imager (HMI) full-disk magnetogram data. With the assumption of polytropic gas with specific heat ratio of 1.05, three types of simulation products are currently generated: i) simulation data with medium spatial resolution using the definitive calibrated synoptic map of the magnetic field with a cadence of one Carrington rotation, ii) data with low spatial resolution using the definitive version of the synchronic frame format of the magnetic field, with a cadence of one day, and iii) low-resolution data using near-real-time (NRT) synchronic format of the magnetic field on daily basis. The MHD data available in the JSOC database are three-dimensional, covering heliocentric distances from 1.025 to 4.975 solar radii, and contain all eight MHD variables: the plasma density, temperature and three components of motion velocity, and three components of the magnetic field. This article describes details of the MHD simulations as well as the production of the input magnetic-field maps, and details of the products available at the JSOC database interface. In order to assess the merits and limits of the model, we show the simulated data in early 2011 and compare with the actual coronal features observed by the Atmospheric Imaging Assembly (AIA) and the near-Earth in-situ data., Comment: Accepted for publication in Solar Physics

The most violent space weather events (eruptive solar flares and coronal mass ejections) are driven by the release of free magnetic energy stored in the solar corona. Energy can build up on timescales of hours to days, and then may be suddenly released in the form of a magnetic eruption, which then propagates through interplanetary space, possibly impacting the Earth's space environment. Can we use the observed evolution of the magnetic and velocity fields in the solar photosphere to model the evolution of the overlying solar coronal field, including the storage and release of magnetic energy in such eruptions? The objective of CGEM, the Coronal Global Evolutionary Model, funded by the NASA/NSF Space Weather Modeling program, is to develop and evaluate such a model for the evolution of the coronal magnetic field. The evolving coronal magnetic field can then be used as a starting point for magnetohydrodynamic (MHD) models of the corona, which can then be used to drive models of heliospheric evolution and predictions of magnetic field and plasma density conditions at 1AU., Comment: 7 pages, 2 figures. Feature article in Space Weather 13

We have compared time history of integrated flux of Jupiter's H3(+) aurora, acquired in 1998-2000, with the sola-wind database. The solar wind at Jupiter is simulated based on the MHD (MagnetoHydroDynamic) tomography analysis of InterPlanetary Scintillation (IPS). The auroral flux is found to be affected by the solar-wind dynamic pressure and by the polarity of Interplanetary Magnetic Field (IMF), indicating that reconnection with IMF has influences on particle precipitation in the Jovian magnetosphere.

The most violent space weather events (eruptive solar flares and coronal mass ejections) are driven by the release of free magnetic energy stored in the solar corona. Energy can build up on timescales of hours to days, and then may be suddenly released in the form of a magnetic eruption, which then propagates through interplanetary space, possibly impacting the Earth's space environment. Can we use the observed evolution of the magnetic and velocity fields in the solar photosphere to model the evolution of the overlying solar coronal field, including the storage and release of magnetic energy in such eruptions? The objective of CGEM, the Coronal Global Evolutionary Model, funded by the NASA/NSF Space Weather Modeling program, is to develop and evaluate such a model for the evolution of the coronal magnetic field. The evolving coronal magnetic field can then be used as a starting point for magnetohydrodynamic (MHD) models of the corona, which can then be used to drive models of heliospheric evolution and predictions of magnetic field and plasma density conditions at 1AU., Comment: 7 pages, 2 figures. Feature article in Space Weather 13

Time-dependent three-dimensional magnetohydrodynamics (MHD) simulation modules are implemented at the Joint Science Operation Center (JSOC) of Solar Dynamics Observatory (SDO). The modules regularly produce three-dimensional data of the time-relaxed minimum-energy state of the solar corona using global solar-surface magnetic-field maps created from Helioseismic Magnetic Imager (HMI) full-disk magnetogram data. With the assumption of polytropic gas with specific heat ratio of 1.05, three types of simulation products are currently generated: i) simulation data with medium spatial resolution using the definitive calibrated synoptic map of the magnetic field with a cadence of one Carrington rotation, ii) data with low spatial resolution using the definitive version of the synchronic frame format of the magnetic field, with a cadence of one day, and iii) low-resolution data using near-real-time (NRT) synchronic format of the magnetic field on daily basis. The MHD data available in the JSOC database are three-dimensional, covering heliocentric distances from 1.025 to 4.975 solar radii, and contain all eight MHD variables: the plasma density, temperature and three components of motion velocity, and three components of the magnetic field. This article describes details of the MHD simulations as well as the production of the input magnetic-field maps, and details of the products available at the JSOC database interface. In order to assess the merits and limits of the model, we show the simulated data in early 2011 and compare with the actual coronal features observed by the Atmospheric Imaging Assembly (AIA) and the near-Earth in-situ data., Comment: Accepted for publication in Solar Physics

Solar active regions (ARs) are thought to be formed by magnetic fields from the convection zone. Our flux emergence simulations revealed that a strong horizontal divergent flow (HDF) of unmagnetized plasma appears at the photosphere before the flux begins to emerge. In our earlier study, we analyzed HMI data for a single AR and confirmed presence of this precursor plasma flow in the actual Sun. In this paper, as an extension of our earlier study, we conducted a statistical analysis of the HDFs to further investigate their characteristics and better determine the properties. From SDO/HMI data, we picked up 23 flux emergence events over a period of 14 months, the total flux of which ranges from 10^{20} to 10^{22} Mx. Out of 23 selected events, 6 clear HDFs were detected by the method we developed in our earlier study, and 7 HDFs detected by visual inspection were added to this statistic analysis. We found that the duration of the HDF is on average 61 minutes and the maximum HDF speed is on average 3.1 km s^{-1}. We also estimated the rising speed of the subsurface magnetic flux to be 0.6-1.4 km s^{-1}. These values are highly consistent with our previous one-event analysis as well as our simulation results. The observation results lead us to the conclusion that the HDF is rather a common feature in the earliest phase of AR emergence. Moreover, our HDF analysis has capability of determining the subsurface properties of emerging fields that cannot be directly measured., Comment: 40 pages, 8 figures, 3 tables, accepted for publication in ApJ. A high-quality version can be found at http://www-space.eps.s.u-tokyo.ac.jp/~toriumi/toriumi2014apj.pdf

A new data product from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) called Space-weather HMI Active Region Patches (SHARPs) is now available. SDO/HMI is the first space-based instrument to map the full-disk photospheric vector magnetic field with high cadence and continuity. The SHARP data series provide maps in patches that encompass automatically tracked magnetic concentrations for their entire lifetime; map quantities include the photospheric vector magnetic field and its uncertainty, along with Doppler velocity, continuum intensity, and line-of-sight magnetic field. Furthermore, keywords in the SHARP data series provide several parameters that concisely characterize the magnetic-field distribution and its deviation from a potential-field configuration. These indices may be useful for active-region event forecasting and for identifying regions of interest. The indices are calculated per patch and are available on a twelve-minute cadence. Quick-look data are available within approximately three hours of observation; definitive science products are produced approximately five weeks later. SHARP data are available at http://jsoc.stanford.edu and maps are available in either of two different coordinate systems. This article describes the SHARP data products and presents examples of SHARP data and parameters., Comment: 27 pages, 7 figures. Accepted to Solar Physics

The Helioseismic and Magnetic Imager (HMI) began near-continuous full-disk solar measurements on 1 May 2010 from the Solar Dynamics Observatory (SDO). An automated processing pipeline keeps pace with observations to produce observable quantities, including the photospheric vector magnetic field, from sequences of filtergrams. The primary 720s observables were released in mid 2010, including Stokes polarization parameters measured at six wavelengths as well as intensity, Doppler velocity, and the line-of-sight magnetic field. More advanced products, including the full vector magnetic field, are now available. Automatically identified HMI Active Region Patches (HARPs) track the location and shape of magnetic regions throughout their lifetime. The vector field is computed using the Very Fast Inversion of the Stokes Vector (VFISV) code optimized for the HMI pipeline; the remaining 180 degree azimuth ambiguity is resolved with the Minimum Energy (ME0) code. The Milne-Eddington inversion is performed on all full-disk HMI observations. The disambiguation, until recently run only on HARP regions, is now implemented for the full disk. Vector and scalar quantities in the patches are used to derive active region indices potentially useful for forecasting; the data maps and indices are collected in the SHARP data series, hmi.sharp_720s. Patches are provided in both CCD and heliographic coordinates. HMI provides continuous coverage of the vector field, but has modest spatial, spectral, and temporal resolution. Coupled with limitations of the analysis and interpretation techniques, effects of the orbital velocity, and instrument performance, the resulting measurements have a certain dynamic range and sensitivity and are subject to systematic errors and uncertainties that are characterized in this report., Comment: 42 pages, 19 figures, accepted to Solar Physics

Solar active regions (ARs) are thought to be formed by magnetic fields from the convection zone. Our flux emergence simulations revealed that a strong horizontal divergent flow (HDF) of unmagnetized plasma appears at the photosphere before the flux begins to emerge. In our earlier study, we analyzed HMI data for a single AR and confirmed presence of this precursor plasma flow in the actual Sun. In this paper, as an extension of our earlier study, we conducted a statistical analysis of the HDFs to further investigate their characteristics and better determine the properties. From SDO/HMI data, we picked up 23 flux emergence events over a period of 14 months, the total flux of which ranges from 10^{20} to 10^{22} Mx. Out of 23 selected events, 6 clear HDFs were detected by the method we developed in our earlier study, and 7 HDFs detected by visual inspection were added to this statistic analysis. We found that the duration of the HDF is on average 61 minutes and the maximum HDF speed is on average 3.1 km s^{-1}. We also estimated the rising speed of the subsurface magnetic flux to be 0.6-1.4 km s^{-1}. These values are highly consistent with our previous one-event analysis as well as our simulation results. The observation results lead us to the conclusion that the HDF is rather a common feature in the earliest phase of AR emergence. Moreover, our HDF analysis has capability of determining the subsurface properties of emerging fields that cannot be directly measured., Comment: 40 pages, 8 figures, 3 tables, accepted for publication in ApJ. A high-quality version can be found at http://www-space.eps.s.u-tokyo.ac.jp/~toriumi/toriumi2014apj.pdf

The Helioseismic and Magnetic Imager (HMI) began near-continuous full-disk solar measurements on 1 May 2010 from the Solar Dynamics Observatory (SDO). An automated processing pipeline keeps pace with observations to produce observable quantities, including the photospheric vector magnetic field, from sequences of filtergrams. The primary 720s observables were released in mid 2010, including Stokes polarization parameters measured at six wavelengths as well as intensity, Doppler velocity, and the line-of-sight magnetic field. More advanced products, including the full vector magnetic field, are now available. Automatically identified HMI Active Region Patches (HARPs) track the location and shape of magnetic regions throughout their lifetime. The vector field is computed using the Very Fast Inversion of the Stokes Vector (VFISV) code optimized for the HMI pipeline; the remaining 180 degree azimuth ambiguity is resolved with the Minimum Energy (ME0) code. The Milne-Eddington inversion is performed on all full-disk HMI observations. The disambiguation, until recently run only on HARP regions, is now implemented for the full disk. Vector and scalar quantities in the patches are used to derive active region indices potentially useful for forecasting; the data maps and indices are collected in the SHARP data series, hmi.sharp_720s. Patches are provided in both CCD and heliographic coordinates. HMI provides continuous coverage of the vector field, but has modest spatial, spectral, and temporal resolution. Coupled with limitations of the analysis and interpretation techniques, effects of the orbital velocity, and instrument performance, the resulting measurements have a certain dynamic range and sensitivity and are subject to systematic errors and uncertainties that are characterized in this report., Comment: 42 pages, 19 figures, accepted to Solar Physics

A new data product from the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) called Space-weather HMI Active Region Patches (SHARPs) is now available. SDO/HMI is the first space-based instrument to map the full-disk photospheric vector magnetic field with high cadence and continuity. The SHARP data series provide maps in patches that encompass automatically tracked magnetic concentrations for their entire lifetime; map quantities include the photospheric vector magnetic field and its uncertainty, along with Doppler velocity, continuum intensity, and line-of-sight magnetic field. Furthermore, keywords in the SHARP data series provide several parameters that concisely characterize the magnetic-field distribution and its deviation from a potential-field configuration. These indices may be useful for active-region event forecasting and for identifying regions of interest. The indices are calculated per patch and are available on a twelve-minute cadence. Quick-look data are available within approximately three hours of observation; definitive science products are produced approximately five weeks later. SHARP data are available at http://jsoc.stanford.edu and maps are available in either of two different coordinate systems. This article describes the SHARP data products and presents examples of SHARP data and parameters., Comment: 27 pages, 7 figures. Accepted to Solar Physics

We report one of several homologous non-radial eruptions from NOAA active region (AR) 11158 that are strongly modulated by the local magnetic field as observed with the Solar Dynamic Observatory (SDO). A small bipole emerged in the sunspot complex and subsequently created a quadrupolar flux system. Non-linear force-free field (NLFFF) extrapolation from vector magnetograms reveals its energetic nature: the fast-shearing bipole accumulated ~2e31 erg free energy (10% of AR total) over just one day despite its relatively small magnetic flux (5% of AR total). During the eruption, the ejected plasma followed a highly inclined trajectory, over 60 degrees with respect to the radial direction, forming a jet-like, inverted-Y shaped structure in its wake. Field extrapolation suggests complicated magnetic connectivity with a coronal null point, which is favorable of reconnection between different flux components in the quadrupolar system. Indeed, multiple pairs of flare ribbons brightened simultaneously, and coronal reconnection signatures appeared near the inferred null. Part of the magnetic setting resembles that of a blowout-type jet; the observed inverted-Y structure likely outlines the open field lines along the separatrix surface. Owing to the asymmetrical photospheric flux distribution, the confining magnetic pressure decreases much faster horizontally than upward. This special field geometry likely guided the non-radial eruption during its initial stage., Comment: 10 pages, 7 figures, 4 movies. Accepted for publication in ApJ

We report the evolution of magnetic field and its energy in NOAA active region 11158 over 5 days based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Fast flux emergence and strong shearing motion led to a quadrupolar sunspot complex that produced several major eruptions, including the first X-class flare of Solar Cycle 24. Extrapolated non-linear force-free coronal fields show substantial electric current and free energy increase during early flux emergence near a low-lying sigmoidal filament with sheared kilogauss field in the filament channel. The computed magnetic free energy reaches a maximum of ~2.6e32 erg, about 50% of which is stored below 6 Mm. It decreases by ~0.3e32 erg within 1 hour of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, the photospheric field changed rapidly: horizontal field was enhanced by 28% in the core region, becoming more inclined and more parallel to the polarity inversion line. Such change is consistent with the conjectured coronal field "implosion", and is supported by the coronal loop retraction observed by the Atmospheric Imaging Assembly (AIA). The extrapolated field becomes more "compact" after the flare, with shorter loops in the core region, probably because of reconnection. The coronal field becomes slightly more sheared in the lowest layer, relaxes faster with height, and is overall less energetic., Comment: Eq. (A1) corrected

We report one of several homologous non-radial eruptions from NOAA active region (AR) 11158 that are strongly modulated by the local magnetic field as observed with the Solar Dynamic Observatory (SDO). A small bipole emerged in the sunspot complex and subsequently created a quadrupolar flux system. Non-linear force-free field (NLFFF) extrapolation from vector magnetograms reveals its energetic nature: the fast-shearing bipole accumulated ~2e31 erg free energy (10% of AR total) over just one day despite its relatively small magnetic flux (5% of AR total). During the eruption, the ejected plasma followed a highly inclined trajectory, over 60 degrees with respect to the radial direction, forming a jet-like, inverted-Y shaped structure in its wake. Field extrapolation suggests complicated magnetic connectivity with a coronal null point, which is favorable of reconnection between different flux components in the quadrupolar system. Indeed, multiple pairs of flare ribbons brightened simultaneously, and coronal reconnection signatures appeared near the inferred null. Part of the magnetic setting resembles that of a blowout-type jet; the observed inverted-Y structure likely outlines the open field lines along the separatrix surface. Owing to the asymmetrical photospheric flux distribution, the confining magnetic pressure decreases much faster horizontally than upward. This special field geometry likely guided the non-radial eruption during its initial stage., Comment: 10 pages, 7 figures, 4 movies. Accepted for publication in ApJ

We report the evolution of magnetic field and its energy in NOAA active region 11158 over 5 days based on a vector magnetogram series from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO). Fast flux emergence and strong shearing motion led to a quadrupolar sunspot complex that produced several major eruptions, including the first X-class flare of Solar Cycle 24. Extrapolated non-linear force-free coronal fields show substantial electric current and free energy increase during early flux emergence near a low-lying sigmoidal filament with sheared kilogauss field in the filament channel. The computed magnetic free energy reaches a maximum of ~2.6e32 erg, about 50% of which is stored below 6 Mm. It decreases by ~0.3e32 erg within 1 hour of the X-class flare, which is likely an underestimation of the actual energy loss. During the flare, the photospheric field changed rapidly: horizontal field was enhanced by 28% in the core region, becoming more inclined and more parallel to the polarity inversion line. Such change is consistent with the conjectured coronal field "implosion", and is supported by the coronal loop retraction observed by the Atmospheric Imaging Assembly (AIA). The extrapolated field becomes more "compact" after the flare, with shorter loops in the core region, probably because of reconnection. The coronal field becomes slightly more sheared in the lowest layer, relaxes faster with height, and is overall less energetic., Comment: Eq. (A1) corrected

The Helioseismic and Magnetic Imager (HMI) has just started producing data that will help determine what the sources and mechanisms of variability in the Sun's interior are. The instrument measures the Doppler shift and the polarization of the Fe I 6173 A line, on the entire solar disk at a relatively-high cadence, in order to study the oscillations and the evolution of the full vector magnetic field of the solar Photosphere. After the data are properly calibrated, they are given to a Milne-Eddington inversion code (VFISV, Borrero et al. 2010) whose purpose is to infer certain aspects of the physical conditions in the Sun's Photosphere, such as the full 3-D topology of the magnetic field and the line-of-sight velocity at the solar surface. We will briefly describe the characteristics of the inversion code, its advantages and limitations --both in the context of the model atmosphere and the actual nature of the data--, and other aspects of its performance on such a remarkable data load. Also, a cross-comparison with near-simultaneous maps from the Spectro-Polarimeter (SP) onboard Hinode will be made., Comment: Proceedings of the Solar Polarization Workshop 6 held in Maui (May 31- June 4)

The Helioseismic and Magnetic Imager (HMI) has just started producing data that will help determine what the sources and mechanisms of variability in the Sun's interior are. The instrument measures the Doppler shift and the polarization of the Fe I 6173 A line, on the entire solar disk at a relatively-high cadence, in order to study the oscillations and the evolution of the full vector magnetic field of the solar Photosphere. After the data are properly calibrated, they are given to a Milne-Eddington inversion code (VFISV, Borrero et al. 2010) whose purpose is to infer certain aspects of the physical conditions in the Sun's Photosphere, such as the full 3-D topology of the magnetic field and the line-of-sight velocity at the solar surface. We will briefly describe the characteristics of the inversion code, its advantages and limitations --both in the context of the model atmosphere and the actual nature of the data--, and other aspects of its performance on such a remarkable data load. Also, a cross-comparison with near-simultaneous maps from the Spectro-Polarimeter (SP) onboard Hinode will be made., Comment: Proceedings of the Solar Polarization Workshop 6 held in Maui (May 31- June 4)