Potential Field Extrapolation Research Articles

Magnetic Eruption from a Three-ribbon Flare

We present observations and analysis of an eruptive M1.5 flare (SOL2014-08-01T18:13) in NOAA active region (AR) 12127, characterized by three flare ribbons, a confined filament between ribbons, and rotating sunspot motions as observed by the Solar Dynamics Observatory. The potential field extrapolation model shows a magnetic topology involving two intersecting quasi-separatrix layers (QSLs) forming a hyperbolic flux tube (HFT), which constitutes the fishbone structure for the three-ribbon flare. Two of the three ribbons show separation from each other, and the third ribbon is rather stationary at the QSL footpoints. The nonlinear force-free field extrapolation model implies the presence of a magnetic flux rope (MFR) structure between the two separating ribbons, which was unclear in the observation. This suggests that the standard reconnection scenario for eruptive flares applies to the two ribbons, and the QSL reconnection for the third ribbon. We find rotational flows around the sunspot, which may have caused the eruption by weakening the downward magnetic tension of the MFR. The confined filament is located in the region of relatively strong strapping field. The HFT topology and the accumulation of reconnected magnetic flux in the HFT may play a role in holding it from eruption. This eruption scenario differs from the one typically known for circular ribbon flares, which is mainly driven by a successful inside-out eruption of filaments. Our results demonstrate the diversity of solar magnetic eruption paths that arises from the complexity of the magnetic configuration.

Prediction of Solar Wind Speed Through Machine Learning From Extrapolated Solar Coronal Magnetic Field

AbstractAn accurate solar wind (SW) speed model is important for space weather predictions, catastrophic event warnings, and other issues concerning SW—magnetosphere interaction. In this work, we construct a model based on convolutional neural network (CNN) and Potential Field Source Surface (PFSS) magnetic field maps, considering a SW source surface of RSS = 2.5R⊙, aiming to predict the SW speed at the Lagrange‐1 (L1) point of the Sun‐Earth system. The input of our model consists of four PFSS magnetic field maps at RSS, which are three, four, five, and six days before the target epoch. Reduced maps are used to promote the model's efficiency. We use the Global Oscillation Network Group (GONG) photospheric magnetograms and the potential field extrapolation model to generate PFSS magnetic field maps at the source surface. The model provides predictions of the quasi‐continuous test data set, which is generated by randomly assigning 120 data segments that are individually continuous in time, with an averaged correlation coefficient (CC) of 0.53 ± 0.07 and a root mean square error (RMSE) of 80.8 ± 4.8 km/s in an eight‐fold validation training scheme with the time resolution of the data as small as one hour. The model also has the potential to forecast high speed streams of the SW, which can be quantified with a general threat score of 0.39.

Identifying Coronal Sources of L1 Solar Wind Disturbances Using the Fisk Heliospheric Magnetic Field and Potential Field Extrapolations during Three Solar Minima

The solar minima between solar cycles 22–23, 23–24, and 24–25 are the best observed minima on record. In situ solar wind and interplanetary magnetic field measurements by the Wind and ACE spacecraft at L1 with 1 hr cadence are explored using wavelet analyses for the most quiescent year during each minimum. Times of local peaks in periodicities are identified in the solar wind velocity, magnetic field components, and proton number densities. The measured radial velocities at these times are used to trace magnetic field lines to the photosphere using two models. The first is the Fisk heliospheric magnetic field that traces field lines from L1 to the photosphere. They connect exclusively to solar poles and in 88% of instances to locations of polar coronal holes (PCHs). The second model uses the Parker spiral to trace from L1 to the solar source surface and potential-field extrapolations from the source surface to the photosphere. These field lines terminate at equatorial and midlatitude coordinates, of which some are located close to coronal holes (CHs). This study connects for the first time CH signatures in the ecliptic plane at L1 with PCHs using the Fisk field. It shows how sources from both the solar equator and poles influence the solar wind at L1 and how the two models complement each other to identify these sources.

Field Line Universal relaXer (FLUX): A Fluxon Approach to Coronal Magnetic Field Modeling

We describe a novel method for modeling the global, steady solar wind using photospheric magnetic fields as a driving boundary condition. Prior wind models in this class include both rapid heuristic methods that use potential field extrapolation and variants thereof, trading rigor for computation speed, and detailed 3D magnetohydrodynamic (MHD) models that attempt to simulate the entire solar corona with a degree of physical rigor, but require large amounts of computation. The Field Line Universal relaXer, an open-source numerical code that implements the “fluxon” semi-Lagrangian approach to MHD modeling, provides an intermediate approach between these two general classes. In particular, the fluxon approach to MHD describes the magnetic field through discrete analogs of magnetic field lines, relaxing these structures to a stationary state of force balance. In this work we introduce a 1D solar wind solution along each field line, providing an ensemble of solutions that are interpolated back onto a uniform grid at an outer boundary surface. This provides advantages in physical rigor over heuristic semianalytic techniques, and in computational efficiency over full 3D MHD techniques. Here we describe the underlying methodology and the FLUXPipe modeling pipeline process.

Two-sided Loop Solar Jet Driven by the Eruption of a Small Filament in a Big Filament Channel

Similar to the cases of anemone jets, two-sided loop solar jets can also be produced by either flux emergence from the solar interior or small-scale filament eruptions. Using high-quality data from the Solar Dynamics Observatory, we have analyzed a two-sided loop solar jet triggered by the eruption of a small filament. The jet occurred in a pre-existing big filament channel. The detailed processes involved in the eruption of the small filament, the interaction between the erupted filament and the big filament channel, and the launch of the two-sided loop jet are presented. The observations further revealed notable asymmetry between the two branches of the jet spire: the northeastern branch is narrow and short, while the southern branch is wide and long and accompanied by discernible untwisting motions. We explored the unique appearance of the jet by employing the method of local potential field extrapolation to calculate the coronal magnetic field configuration around the jet. The photospheric magnetic flux below the small filament underwent cancellation for approximately 7 hr before the filament eruption, and the negative flux near the southern footpoint of the filament decreased by about 56% during this interval. Therefore, we propose that the primary photospheric driver of the filament eruption and the associated two-sided loop jet in this event is flux cancellation rather than flux emergence.

Propagation Properties of Sunspots Umbral Oscillations in Horizontal and Vertical Directions

We present a study on investigating the propagation characteristics of umbral oscillations in sunspots. In sunspot 1 (located in NOAA AR 12127) with four umbrae, the analysis shows that the oscillations in different umbrae are correlated. The weak correlation (<20%) is attributed to the propagation of umbral oscillations across the umbral boundary to its adjacent umbra in the horizontal direction. We speculate that oscillations in two of the umbrae have a common origin in the sub-photosphere, resulting in a stronger correlation (>30%). Additionally, utilizing the TiO (photosphere), Hα (chromosphere) images provided by BBSO/GST, and the 304 Å (upper chromosphere and lower transition region), 171 Å (upper transition region), 193 Å (corona), and 211 Å (active region corona) images acquired by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO), we analyze the vertical propagation of oscillations in the sunspot umbra. Multi-channel observation shows that the umbral oscillations observed in the lower atmosphere of sunspot 1 cannot be detected in the upper atmosphere. However, in sunspot 2 (located in NOAA AR 12132), oscillations in the lower atmosphere can propagate to the upper atmosphere. Using photospheric magnetic field data provided by the Helioseismic and Magnetic Imager on board SDO, potential field extrapolation of the magnetic field for the two sunspots shows that open magnetic field structures allow sunspot oscillations to propagate to higher heights, while closed magnetic field structures do not.

Measuring local physical parameters in coronal loops with spatial seismology

Context. The method of spatial seismology can be applied to the amplitude profile of transverse coronal loop oscillations to constrain the distributions of physical parameters, such as the loop density, magnitude of the magnetic field, and so on. Aims. We intend to develop and apply a practical spatial seismology technique to detect physical parameters of plasma and validate its effectiveness by comparing it with other methods. Methods. A spatial seismology inversion was conducted by numerically optimizing a parametric dynamic model of the loop’s density stratification and magnetic field variation to best fit the measured amplitude profile of the loop. Results. The spatial seismology inversion technique developed here was applied to a transverse coronal loop oscillation that occurred on 2013 April 11, whose oscillation amplitude profile of both the fundamental mode and first overtone was reported in previous work. The consistency between the time domain analysis and spatial seismology has been verified. Meanwhile, we accounted for the asymmetric profile of the fundamental mode by forward modeling and we derived the magnetic field distribution by inverse modeling, which is coincident with that of the extrapolated one. In addition, spatial seismology inversion was applied to the transverse oscillation event on 2022 March 30 to obtain the distribution of the loop’s density and magnetic field, which are compared with the results derived from the differential emission measure (DEM) diagnostics and the direct potential field extrapolation. Conclusions. Spatial seismology inversion can be used as an effective method to independently measure various physical parameters, for example the density and magnetic field of coronal loops, which are consistent with the results obtained by DEM diagnostics and potential field extrapolation.

Data-constrained Solar Modeling with GX Simulator

To facilitate the study of solar flares and active regions, we have created a modeling framework, the freely distributed GX Simulator IDL package, that combines 3D magnetic and plasma structures with thermal and nonthermal models of the chromosphere, transition region, and corona. Its object-based modular architecture, which runs on Windows, Mac, and Unix/Linux platforms, offers the ability to either import 3D density and temperature distribution models, or to assign numerically defined coronal or chromospheric temperatures and densities, or their distributions, to each individual voxel. GX Simulator can apply parametric heating models involving average properties of the magnetic field lines crossing a given voxel, as well as compute and investigate the spatial and spectral properties of radio, (sub)millimeter, EUV, and X-ray emissions calculated from the model, and quantitatively compare them with observations. The package includes a fully automatic model production pipeline that, based on minimal users input, downloads the required SDO/HMI vector magnetic field data, performs potential or nonlinear force-free field extrapolations, populates the magnetic field skeleton with parameterized heated plasma coronal models that assume either steady-state or impulsive plasma heating, and generates non-LTE density and temperature distribution models of the chromosphere that are constrained by photospheric measurements. The standardized models produced by this pipeline may be further customized through specialized IDL scripts, or a set of interactive tools provided by the graphical user interface. Here, we describe the GX Simulator framework and its applications.

Role of Small-scale Impulsive Events in Heating the X-Ray Bright Points of the Quiet Sun

Small-scale impulsive events, known as nanoflares, are thought to be one of the prime candidates that can keep the solar corona hot at its multimillion-Kelvin temperature. Individual nanoflares are difficult to detect with the current generation of instruments; however, their presence can be inferred through indirect techniques such as Differential Emission Measure (DEM) analysis. Here, we employ this technique to investigate the possibility of nanoflare heating of the quiet corona during the minimum of solar cycle 24. We estimate the DEM of disk-integrated quiet Sun and X-ray bright points (XBP) using the observations from XSM on board the Chandrayaan-2 orbiter and AIA on board the Solar Dynamic Observatory. XBPs are found to be the dominant contributor to disk-integrated X-rays, with a radiative flux of ∼2 × 105 erg cm−2 s−1. XBPs consist of small-scale loops associated with bipolar magnetic fields. We simulate such XBP loops using the EBTEL hydrodynamic code. The lengths and magnetic field strengths of these loops are obtained through a potential field extrapolation of the photospheric magnetogram. Each loop is assumed to be heated by random nanoflares having an energy that depends on the loop properties. The composite nanoflare energy distribution for all the loops has a power-law slope close to −2.5. The simulation output is then used to obtain the integrated DEM. It agrees remarkably well with the observed DEM at temperatures above 1 MK, suggesting that the nanoflare distribution, as predicted by our model, can explain the XBP heating.

An Improved Magnetohydrodynamic Simulation of the 2006 December 13 Coronal Mass Ejection of NOAA Active Region 10930

We present a magnetohydrodynamic simulation of the coronal mass ejection on 2006 December 13 in the emerging δ-sunspot NOAA Active Region 10930, improving upon a previous simulation by Fan as follows. (1) Incorporate an ambient solar wind instead of using a static potential magnetic field extrapolation as the initial state. (2) In addition to imposing the emergence of a twisted flux rope, also impose at the lower boundary a random electric field that represents the effect of turbulent convection, which drives field-line braiding and produces resistive and viscous heating in the corona. With the inclusion of this heating, which depends on the magnetic field topology, we are able to model the synthetic soft X-ray images that would be observed by the X-Ray Telescope (XRT) of the Hinode satellite, produced by the simulated coronal magnetic field. We find that the simulated preeruption magnetic field with the buildup of a twisted magnetic flux rope produces synthetic soft X-ray emission that shows qualitatively similar morphology as that observed by the Hinode/XRT for both the ambient coronal loops of the active region and the central inverse S-shaped “sigmoid“ that sharpens just before the onset of the eruption. The synthetic postflare loop brightening also shows similar morphology to that seen in the Hinode/XRT image during the impulsive phase of the eruption. It is found that the kinematics of the erupting flux rope is significantly affected by the open magnetic fields and fast solar wind streams adjacent to the active region.

The Magnetic Field Environment of Active Region 12673 That Produced the Energetic Particle Events of September 2017

Forecasting solar energetic particles (SEPs), and identifying flares/coronal mass ejections (CMEs) from active regions (ARs) that will produce SEP events in advance is extremely challenging. We investigate the magnetic field environment of AR 12673, including the AR’s magnetic configuration, the surrounding field configuration in the vicinity of the AR, the decay index profile, and the footpoints of the Earth-connected magnetic field, around the time of four eruptive events. Two of the eruptive events are SEP productive (2017 September 4 at 20:00 UT and September 6 at 11:56 UT), while two are not (September 4 at 18:05 UT and September 7 at 14:33 UT). We analyzed a range of EUV and white-light coronagraph observations along with potential field extrapolations and find that the CMEs associated with the SEP-productive events either trigger null point reconnection that redirects flare-accelerated particles from the flare site to the Earth-connected field and/or have a significant expansion (and shock formation) into the open Earth-connected field. The rate of change of the decay index with height indicates that the region could produce a fast CME (v > 1500 km s−1), which it did during events 2 and 3. The AR’s magnetic field environment, including locations of open magnetic field and null points along with the magnetic field connectivity and propagation direction of the CMEs play an important role in the escape and arrival of SEPs at Earth. Other SEP-productive ARs should be investigated to determine whether their magnetic field environment and CME propagation direction are significant in the escape and arrival of SEPs at Earth.

Magnetic Helicity Flux Oscillations in the Atmospheres of Flaring and Nonflaring Active Regions

Analyzing the evolution of magnetic helicity flux at different atmospheric heights is key for identifying its role in the dynamics of active regions (ARs). The three-dimensional (3D) magnetic field of both flaring and nonflaring ARs is constructed using potential field extrapolations, enabling the derivation of emergence, shearing, and total magnetic helicity components at a range of atmospheric heights. An analysis of temporal oscillations of the derived components shows that the largest significant period of the three helicity fluxes are common (within ±2 hr) from the photosphere up to at least 1 Mm for flaring ARs—being consistent with the presence of a coupled oscillatory behavior that is absent in the nonflaring ARs. We suggest that large, energetic solar eruptions may have been produced in ARs when the vertical and horizontal helicity flux components became a coupled oscillatory system in the low solar atmosphere.

The Strength and Structure of the Magnetic Field in the Galactic Outflow of Messier 82

Abstract Galactic outflows driven by starbursts can modify the galactic magnetic fields and drive them away from the galactic planes. Here, we quantify how these fields may magnetize the intergalactic medium (IGM). We estimate the strength and structure of the fields in the starburst galaxy M82 using thermal polarized emission observations from the Stratospheric Observatory for Infrared Astronomy/High-resolution Airborne Wideband Camera-plus and a potential field extrapolation commonly used in solar physics. We modified the Davis–Chandrasekhar–Fermi method to account for the large-scale flow and the turbulent field. Results show that the observed magnetic fields arise from the combination of a large-scale ordered potential field associated with the outflow and a small-scale turbulent field associated with bow-shock-like features. Within the central 900 pc radius, the large-scale field accounts for 53 ± 4% of the observed turbulent magnetic energy with a median field strength of 305 ± 15 μG, while small-scale turbulent magnetic fields account for the remaining 40 ± 5% with a median field strength of 222 ± 19 μG. We estimate that the turbulent kinetic and turbulent magnetic energies are in close equipartition up to ∼2 kpc (measured), while the turbulent kinetic energy dominates at ∼7 kpc (extrapolated). We conclude that the fields are frozen into the ionized outflowing medium and driven away kinetically. The magnetic field lines in the galactic wind of M82 are open, providing a direct channel between the starburst core and the IGM. Our novel approach offers the tools needed to quantify the effects of outflows on galactic magnetic fields as well as their influence on the IGM and evolution of energetic particles.

Emerging Dimming as Coronal Heating Episodes

Abstract Emerging dimming occurs in isolated solar active regions (ARs) during the early stages of magnetic flux emergence. Observed by the Atmospheric Imaging Assembly, it features a rapid decrease in extreme-ultraviolet (EUV) emission in the 171 Å channel images, and a simultaneous increase in the 211 Å images. Here, we analyze the coronal thermodynamic and magnetic properties to probe its physical origin. We calculate the time-dependent differential emission measures for a sample of 18 events between 2010 and 2012. The emission measure (EM) decrease in the temperature range is well correlated with the EM increase in over eight orders of magnitude. This suggests that the coronal plasma is being heated from the quiet-Sun, sub-MK temperature to 1–2 MK, more typical for ARs. Potential field extrapolation indicates significant change in the local magnetic connectivity: the dimming region is now linked to the newly emerged flux via longer loops. We conclude that emerging dimming is likely caused by coronal heating episodes, powered by reconnection between the emerging and the ambient magnetic fields.

The chromospheric component of coronal bright points

Context. We investigate the chromospheric counterpart of small-scale coronal loops constituting a coronal bright point (CBP) and its response to a photospheric magnetic-flux increase accompanied by co-temporal CBP heating. Aims. The aim of this study is to simultaneously investigate the chromospheric and coronal layers associated with a CBP, and in so doing, provide further understanding on the heating of plasmas confined in small-scale loops. Methods. We used co-observations from the Atmospheric Imaging Assembly and Helioseismic Magnetic Imager on board the Solar Dynamics Observatory, together with data from the Fast Imaging Solar Spectrograph taken in the Hα and Ca II 8542.1 Å lines. We also employed both linear force-free and potential field extrapolation models to investigate the magnetic topology of the CBP loops and the overlying corona, respectively. We used a new multi-layer spectral inversion technique to derive the temporal variations of the temperature of the Hα loops (HLs). Results. We find that the counterpart of the CBP, as seen at chromospheric temperatures, is composed of a bundle of dark elongated features named in this work Hα loops, which constitute an integral part of the CBP loop magnetic structure. An increase in the photospheric magnetic flux due to flux emergence is accompanied by a rise of the coronal emission of the CBP loops, that is a heating episode. We also observe enhanced chromospheric activity associated with the occurrence of new HLs and mottles. While the coronal emission and magnetic flux increases appear to be co-temporal, the response of the Hα counterpart of the CBP occurs with a small delay of less than 3 min. A sharp temperature increase is found in one of the HLs and in one of the CBP footpoints estimated at 46% and 55% with respect to the pre-event values, also starting with a delay of less than 3 min following the coronal heating episode. The low-lying CBP loop structure remains non-potential for the entire observing period. The magnetic topological analysis of the overlying corona reveals the presence of a coronal null point at the beginning and towards the end of the heating episode. Conclusions. The delay in the response of the chromospheric counterpart of the CBP suggests that the heating may have occurred at coronal heights.

Mass of prominences experiencing failed eruptions

Abstract A number of solar filaments/prominences demonstrate failed eruptions, when a filament at first suddenly starts to ascend and then decelerates and stops at some greater height in the corona. The mechanism of the termination of eruptions is not clear yet. One of the confining forces able to stop the eruption is the gravity force. Using a simple model of a partial current-carrying torus loop anchored to the photosphere and photospheric magnetic field measurements as the boundary condition for the potential magnetic field extrapolation into the corona, we estimated masses of 15 eruptive filaments. The values of the filament mass show rather wide distribution in the range of $4\times10^{15}$ – $270\times10^{16}$ g. Masses of the most of filaments, laying in the middle of the range, are in accordance with estimations made earlier on the basis of spectroscopic and white-light observations.

Cause and Kinematics of a Jetlike CME

Abstract In this article, we present the multiviewpoint and multiwavelength analysis of an atypical solar jet based on data from Solar Dynamics Observatory, SOlar and Heliospheric Observatory, and Solar TErrestrial RElations Observatory. It is generally believed that coronal mass ejections (CMEs) develop from the large-scale solar eruptions in the lower atmosphere. However, the kinematical and spatial evolution of the jet on 2013 April 28 suggests that the jet was clearly associated with a narrow CME with a width of ≈25° and speed of ≈450 km s−1. To better understand the link between the jet and the CME, we performed a coronal potential field extrapolation from the line-of-sight magnetogram of the active region. The extrapolations suggest that the jet eruption follows the same path of the open magnetic field lines from the source region, which provides a route for the jet material to escape from the solar surface toward the outer corona.

The Minimal Helicity of Solar Coronal Magnetic Fields

Abstract Potential field extrapolations are widely used as minimum-energy models for the Sun’s coronal magnetic field. As the reference to which other magnetic fields are compared, they have—by any reasonable definition—no global (signed) magnetic helicity. Here we investigate the internal topological structure that is not captured by the global helicity integral, by splitting it into individual field line helicities. These are computed using potential field extrapolations from magnetogram observations over Solar Cycle 24, as well as for a simple illustrative model of a single bipolar region in a dipolar background. We find that localized patches of field line helicity arise primarily from linking between strong active regions and their overlying field, so that the total unsigned helicity correlates with the product of photospheric and open fluxes. Within each active region, positive and negative helicity may be unbalanced, but the signed helicity is only around a tenth of the unsigned helicity. Interestingly, in Cycle 24, there is a notable peak in unsigned helicity caused by a single large active region. On average, the total unsigned helicity at the resolution considered is approximately twice the typical signed helicity of a single real active region, according to non-potential models in the literature.

Solar Flare Prediction Using Magnetic Field Diagnostics above the Photosphere

Abstract In this article, we present the application of the weighted horizontal gradient of magnetic field (WG M ) flare prediction method to three-dimensional (3D) extrapolated magnetic configurations of 13 flaring solar active regions (ARs). The main aim is to identify an optimal height range, if any, in the interface region between the photosphere and lower corona, where the flare onset time prediction capability of WG M is best exploited. The optimal height is where flare prediction, by means of the WG M method, is achieved earlier than at the photospheric level. 3D magnetic structures, based on potential and nonlinear force-free field extrapolations, are constructed to study a vertical range from the photosphere up to the low corona with a 45 km step size. The WG M method is applied as a function of height to all 13 flaring AR cases that are subject to certain selection criteria. We found that applying the WG M method between 1000 and 1800 km above the solar surface would improve the prediction of the flare onset time by around 2–8 hr. Certain caveats and an outlook for future work along these lines are also discussed.

A distinct magnetic property of the inner penumbral boundary

Context. Analyses of sunspot observations revealed a fundamental magnetic property of the umbral boundary: the invariance of the vertical component of the magnetic field. Aims. We analyse the magnetic properties of the umbra-penumbra boundary in simulated sunspots and thus assess their similarity to observed sunspots. We also aim to investigate the role of the plasma β and the ratio of kinetic to magnetic energy in simulated sunspots in the convective motions because these quantities cannot be reliably determined from observations. Methods. We used a set of non-gray simulation runs of sunspots with the MURaM code. The setups differed in terms of subsurface magnetic field structure and magnetic field boundary imposed at the top of the simulation domain. These data were used to synthesize the Stokes profiles, which were then degraded to the Hinode spectropolarimeter-like observations. Then, the data were treated like real Hinode observations of a sunspot, and magnetic properties at the umbral boundaries were determined. Results. Simulations with potential field extrapolation produce a realistic magnetic field configuration on the umbral boundaries of the sunspots. Two simulations with a potential field upper boundary, but different subsurface magnetic field structures, differ significantly in the extent of their penumbrae. Increasing the penumbra width by forcing more horizontal magnetic fields at the upper boundary results in magnetic properties that are not consistent with observations. This implies that the size of the penumbra is given by the subsurface structure of the magnetic field, that is, by the depth and inclination of the magnetopause, which is shaped by the expansion of the sunspot flux rope with height. None of the sunspot simulations is consistent with the observed properties of the magnetic field and the direction of the Evershed flow at the same time. Strong outward-directed Evershed flows are only found in setups with an artificially enhanced horizontal component of the magnetic field at the top boundary that are not consistent with the observed magnetic field properties at the umbra-penumbra boundary. We stress that the photospheric boundary of simulated sunspots is defined by a magnetic field strength of equipartition field value.