Solar Coronal Magnetic Field Research Articles

Testing a Data-driven Active Region Evolution Model with Boundary Data at Different Heights from a Solar Magnetic Flux Emergence Simulation

Abstract A data-driven active region evolution (DARE) model has been developed to study the complex structures and dynamics of solar coronal magnetic fields. The model is configured with a typical coronal environment of tenuous gas governed by strong magnetic field, and thus its lower boundary is set at the base of the corona, but driven by magnetic fields observed in the photosphere. A previous assessment of the model using data from a flux emergence simulation (FES) showed that the DARE failed to reproduce the coronal magnetic field in the FES, which is attributed to the fact that the photospheric data in the FES has a very strong Lorentz force and therefore spurious flows are generated in the DARE model. Here we further test the DARE by using three sets of data from the FES sliced at incremental heights, which correspond to the photosphere, the chromosphere, and the base of the corona. It is found that the key difference in the three sets of data is the extent of the Lorentz force, which makes the data-driven model perform very differently. At the two higher levels above the photosphere, the Lorentz force decreases substantially, and the DARE model attains results in much better agreement with the FES, confirming that the Lorentz force in the boundary data is a key issue affecting the results of the DARE model. However, unlike the FES data, the photospheric field from SDO/HMI observations has recently been found to be very close to force-free. Therefore, we suggest that it is still reasonable to use the photospheric magnetic field as an approximation of the field at the coronal base to drive the DARE model.

Global maps of the magnetic field in the solar corona.

Understanding many physical processes in the solar atmosphere requires determination of the magnetic field in each atmospheric layer. However, direct measurements of the magnetic field in the Sun's corona are difficult to obtain. Using observations with the Coronal Multi-channel Polarimeter, we have determined the spatial distribution of the plasma density in the corona and the phase speed of the prevailing transverse magnetohydrodynamic waves within the plasma. We combined these measurements to map the plane-of-sky component of the global coronal magnetic field. The derived field strengths in the corona, from 1.05 to 1.35 solar radii, are mostly 1 to 4 gauss. Our results demonstrate the capability of imaging spectroscopy in coronal magnetic field diagnostics.

Abrupt Shrinking of Solar Corona in the Late 1990s

Abstract We derive the longest uniform record of rotational intensities solar coronal magnetic field since 1968 and compare it with the heliospheric magnetic field (HMF) observed at the Earth. We scale the Mount Wilson Observatory and Wilcox Solar Observatory observations of the photospheric magnetic field to the level of the Synoptic Optical Long-term Investigations of the Sun/Vector Spectro Magnetograph and apply the potential field source surface model to calculate the coronal magnetic field. We find that the evolution of the coronal magnetic field during the last 50 yr agrees with the HMF observed at the Earth only if the effective coronal size, the distance of the coronal source surface of the HMF, is allowed to change in time. We calculate the optimum source surface distance for each rotation and find that it experienced an abrupt decrease in the late 1990s. The effective volume of the solar corona shrunk to less than one half during a short period of only a few years. We note that this abrupt shrinking coincides with other changes in solar magnetic fields that are likely related to the decrease of the overall solar activity, i.e., the demise of the Grand Modern Maximum.

Coronagraphic Observations of Si x λ14301 and Fe xiii λ10747 Linearly Polarized Spectra Using the SOLARC Telescope

Abstract The forbidden Si x emission line at 14301 Å has been identified as a potentially valuable polarized diagnostic for solar coronal magnetic fields; however, the only polarized Si x measurements achieved to date have been during eclipses and at comparatively low spatial and spectral resolution. Here we report spectropolarimetric observations of both the Si x 14301 Å and more well-established Fe xiii 10747 Å coronal lines acquired with the 0.45 m aperture SOLARC coronagraph atop Haleakalā. Using its fiber-based integral field spectropolarimeter, we derive observations sampled at radial intervals of 0.05 (i.e., ∼50″) with a spectral resolving power of ≈36,000. Results for both lines, which represent averages over different active and nonactive regions of the corona, indicate a relatively flat radial variation for the line widths and line centers and a factor of ≈2–3 decrease in polarized brightness between 1.05 and 1.45 . Averaging over all the measurements the mean and standard deviations of line properties for Si x 14301 Å and Fe xiii 10747 Å are, respectively, FWHM of 3.0 ± 0.4 Å and 1.6 ± 0.1 Å, line-integrated polarized brightness of 0.07 ± 0.03 and 0.3 ± 0.3 erg s−2 cm−2 sr−1, where the uncertainty quoted reflects a large sample variance, and line center wavelengths 14300.7 ± 0.2 Å and 10746.3 ± 0.1 Å. The polarized brightness for both lines may be underestimated by up to a factor of 5 due to limitations in the photometric calibration. When accounting for this uncertainty we find consistency between our observations and previous measurements of the two lines as well as theoretical calculations and affirm the potential of the Si x line as a polarized diagnostic of the solar corona.

Automatic detection of coronal loops using guided filtering and wavelet transform

The corona is the outer layer of the solar asmosphere. The bright loop-like structures in the corona, which are called coronal loops, are hot plasma to be bound to the solar coronal magnetic fields. Studying these magnetic features can help to better understand the dynamics of coronal magnetic fields and coronal oscillations, and further clearify the debate of coronal heating. Accurate identifying coronal loops are crucial for the relevant studies. However, due to the complexity of the coronal magnetic fields, it is very difficult to identify and extract the loop-like structures. In this case, we propose a novel algorithm based on guided filtering and wavelet transform modulus maxima to automatically detect and extract them. The steps are as follows: we use (1) a fuzzy function to enhance the contrast of solar corona images; (2) guided filtering to highlight the edges of coronal loops; (3) wavelet transform modulus maxima to identitify the edges of coronal loops; (4) image binarization to extract coronal loops; (5) morphological operate to remove those non-loop structures. The images observed by the Transition and Coronal Explorer (TRACE) and the Atmospheric Imaging Assembly on the Solar Dynamics (SDO/AIA) intruments in the 171 A channel are selected to illustrate the porcess and further evaluate the performance of the algorithm. The results demonstrate that the proposed algorithm has significant advantages over provious identification methods and the detected and extracted structures can be further applied to scientific researchs.

Nonlocal heat flux effects on temperature evolution of the solar atmosphere

Context. Heat flux is one of the main energy transport mechanisms in the weakly collisional plasma of the solar corona. There, rare binary collisions let hot electrons travel over long distances and influence other regions along magnetic field lines. Thus, the fully collisional heat flux models might not describe transport well enough since they consider only the local contribution of electrons. The heat flux in weakly collisional plasmas at high temperatures with large mean free paths has to consider the nonlocality of the energy transport in the frame of nonlocal models in order to treat energy balance in the solar atmosphere properly. Aims. We investigate the impact of nonlocal heat flux on the thermal evolution and dynamics of the solar atmosphere by implementing a nonlocal heat flux model in a 3D magnetohydrodynamic simulation of the solar corona. Methods. We simulate the evolution of solar coronal plasma and magnetic fields considering both a local collision dominated and a nonlocal heat flux model. The initial magnetic field is obtained by a potential extrapolation of the observed line-of-sight magnetic field of AR11226. The system is perturbed by moving the plasma at the photosphere. We compared the simulated evolution of the solar atmosphere in its dependence on the heat flux model. Results. The main differences for the average temperature profiles were found in the upper chromosphere/transition region. In the nonlocal heat transport model case, thermal energy is transported more efficiently to the upper chromosphere and lower transition region and leads to an earlier heating of the lower atmosphere. As a consequence, the structure of the solar atmosphere is affected with the nonlocal simulations producing on average a smoother temperature profile and the transition region placed about 500 km higher. Using a nonlocal heat flux also leads to two times higher temperatures in some of the regions in the lower corona. Conclusions. The results of our 3D MHD simulations considering nonlocal heat transport supports the previous results of simpler 1D two-fluid simulations. They demonstrated that it is important to consider a nonlocal formulation for the heat flux when there is a strong energy deposit, like the one observed during flares, in the solar corona.

Addendum to: Strength of the Solar Coronal Magnetic Field – A Comparison of Independent Estimates Using Contemporaneous Radio and White-Light Observations

Addendum to: Strength of the Solar Coronal Magnetic Field – A Comparison of Independent Estimates Using Contemporaneous Radio and White-Light Observations

Strength of the Solar Coronal Magnetic Field – A Comparison of Independent Estimates Using Contemporaneous Radio and White-Light Observations

We estimated the coronal magnetic field strength ($B$) during the 23 July 2016 coronal mass ejection (CME) event using i) the flux rope structure of the CME in the whitelight coronagraph images and ii) the band splitting in the associated type {\sc II} burst. No models were assumed for the coronal electron density ($N(r)$) used in the estimation.The results obtained using the above two independent methods correspond to different heliocentric distances ($r$) in the range $\approx$\,2.5\,--\,4.5$\rm R_{\odot}$, but they show excellent consistency and could be fitted with a single power-law distribution of the type $B(r)=5.7r^{-2.6}$ \textrm{G}, which is applicable in the aforementioned distance range. The power law index i.e. $-2.6$) is in good agreement with the results obtained in previous studies by different methods.

Precipitation and Release of Solar Energetic Particles from the Solar Coronal Magnetic Field

Abstract Most solar energetic particles (SEPs) are produced in the corona. They propagate through complex coronal magnetic fields subject to scattering and diffusion across the averaged field lines by turbulence. We examine the behaviors of particle transport using a stochastic 3D focused transport simulation in a potential field source surface model of coronal magnetic field. The model is applied to an SEP event on 2010 February 7. We study three scenarios of particle injection at (i) the compact solar flare site, (ii) the coronal mass ejection (CME) shock, and (iii) the EUV wave near the surface. The majority of particles injected on open field lines are able to escape the corona. We found that none of our models can explain the observations of wide longitudinal SEP spread without perpendicular diffusion. If the perpendicular diffusion is about 10% of what is derived from the random walk of field lines at the rate of supergranular diffusion, particles injected at the compact solar flare site can spread to a wide range of longitude and latitude, very similar to the behavior of particles injected at a large CME shock. Stronger pitch-angle scattering results in a little more lateral spread by holding the particles in the corona for longer periods of time. Some injected particles eventually end up precipitating onto the solar surface. Even with a very small perpendicular diffusion, the pattern of the particle precipitation can be quite complicated depending on the detailed small-scale coronal magnetic field structures, which could be seen with future sensitive gamma-ray telescopes.

Comparison of Two Coronal Magnetic Field Models to Reconstruct a Sigmoidal Solar Active Region with Coronal Loops

Abstract Magnetic field extrapolation is an important tool to study the three-dimensional (3D) solar coronal magnetic field, which is difficult to directly measure. Various analytic models and numerical codes exist, but their results often drastically differ. Thus, a critical comparison of the modeled magnetic field lines with the observed coronal loops is strongly required to establish the credibility of the model. Here we compare two different non-potential extrapolation codes, a nonlinear force-free field code (CESE–MHD–NLFFF) and a non-force-free field (NFFF) code, in modeling a solar active region (AR) that has a sigmoidal configuration just before a major flare erupted from the region. A 2D coronal-loop tracing and fitting method is employed to study the 3D misalignment angles between the extrapolated magnetic field lines and the EUV loops as imaged by SDO/AIA. It is found that the CESE–MHD–NLFFF code with preprocessed magnetogram performs the best, outputting a field that matches the coronal loops in the AR core imaged in AIA 94 Å with a misalignment angle of ∼10°. This suggests that the CESE–MHD–NLFFF code, even without using the information of the coronal loops in constraining the magnetic field, performs as good as some coronal-loop forward-fitting models. For the loops as imaged by AIA 171 Å in the outskirts of the AR, all the codes including the potential field give comparable results of the mean misalignment angle (∼30°). Thus, further improvement of the codes is needed for a better reconstruction of the long loops enveloping the core region.

Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. III. Twist Number Method

Abstract We study the writhe, twist, and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov–Démoulin equilibrium solution, non-force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger–Prior formula, which is suitable for arbitrary geometry and both force-free and non-force-free models. The magnetic helicity is estimated by the twist multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field.

Magnetohydrodynamic Modeling of Solar Coronal Dynamics with an Initial Non-force-free Magnetic Field

Abstract The magnetic fields in the solar corona are generally neither force-free nor axisymmetric and have complex dynamics that are difficult to characterize. Here we simulate the topological evolution of solar coronal magnetic field lines (MFLs) using a magnetohydrodynamic model. The simulation is initialized with a non-axisymmetric non-force-free magnetic field that best correlates with the observed vector magnetograms of solar active regions (ARs). To focus on these ideas, simulations are performed for the flaring AR 11283 noted for its complexity and well-documented dynamics. The simulated dynamics develops as the initial Lorentz force pushes the plasma and facilitates successive magnetic reconnections at the two X-type null lines present in the initial field. Importantly, the simulation allows for the spontaneous development of mass flow, unique among contemporary works, that preferentially reconnects field lines at one of the X-type null lines. Consequently, a flux rope consisting of low-lying twisted MFLs, which approximately traces the major polarity inversion line, undergoes an asymmetric monotonic rise. The rise is attributed to a reduction in the magnetic tension force at the region overlying the rope, resulting from the reconnection. A monotonic rise of the rope is in conformity with the standard scenario of flares. Importantly, the simulated dynamics leads to bifurcations of the flux rope, which, being akin to the observed filament bifurcation in AR 11283, establishes the appropriateness of the initial field in describing ARs.

Testing the Accuracy of Data-driven MHD Simulations of Active Region Evolution

Abstract Models for the evolution of the solar coronal magnetic field are vital for understanding solar activity, yet the best measurements of the magnetic field lie at the photosphere, necessitating the development of coronal models which are “data-driven” at the photosphere. We present an investigation to determine the feasibility and accuracy of such methods. Our validation framework uses a simulation of active region (AR) formation, modeling the emergence of magnetic flux from the convection zone to the corona, as a ground-truth data set, to supply both the photospheric information and to perform the validation of the data-driven method. We focus our investigation on how the accuracy of the data-driven model depends on the temporal frequency of the driving data. The Helioseismic and Magnetic Imager on NASA’s Solar Dynamics Observatory produces full-disk vector magnetic field measurements at a 12-minute cadence. Using our framework we show that ARs that emerge over 25 hr can be modeled by the data-driving method with only ∼1% error in the free magnetic energy, assuming the photospheric information is specified every 12 minutes. However, for rapidly evolving features, under-sampling of the dynamics at this cadence leads to a strobe effect, generating large electric currents and incorrect coronal morphology and energies. We derive a sampling condition for the driving cadence based on the evolution of these small-scale features, and show that higher-cadence driving can lead to acceptable errors. Future work will investigate the source of errors associated with deriving plasma variables from the photospheric magnetograms as well as other sources of errors, such as reduced resolution, instrument bias, and noise.

Particle Acceleration Due to Coronal Non-null Magnetic Reconnection

Various topological features, for example magnetic null points and separators, have been inferred as likely sites of magnetic reconnection and particle acceleration in the solar atmosphere. In fact, magnetic reconnection is not constrained to solely take place at or near such topological features and may also take place in the absence of such features. Studies of particle acceleration using non-topological reconnection experiments embedded in the solar atmosphere are uncommon. We aim to investigate and characterise particle behaviour in a model of magnetic reconnection which causes an arcade of solar coronal magnetic field to twist and form an erupting flux rope, crucially in the absence of any common topological features where reconnection is often thought to occur. We use a numerical scheme that evolves the gyro-averaged orbit equations of single electrons and protons in time and space, and simulate the gyromotion of particles in a fully analytical global field model. We observe and discuss how the magnetic and electric fields of the model and the initial conditions of each orbit may lead to acceleration of protons and electrons up to 2 MeV in energy (depending on model parameters). We describe the morphology of time-dependent acceleration and impact sites for each particle species and compare our findings to those recovered by topologically based studies of three-dimensional (3D) reconnection and particle acceleration. We also broadly compare aspects of our findings to general observational features typically seen during two-ribbon flare events.

Nonlinear Force-free Coronal Magnetic Stereoscopy

Abstract Insights into the 3D structure of the solar coronal magnetic field have been obtained in the past by two completely different approaches. The first approach are nonlinear force-free field (NLFFF) extrapolations, which use photospheric vector magnetograms as boundary condition. The second approach uses stereoscopy of coronal magnetic loops observed in EUV coronal images from different vantage points. Both approaches have their strengths and weaknesses. Extrapolation methods are sensitive to noise and inconsistencies in the boundary data, and the accuracy of stereoscopy is affected by the ability of identifying the same structure in different images and by the separation angle between the view directions. As a consequence, for the same observational data, the 3D coronal magnetic fields computed with the two methods do not necessarily coincide. In an earlier work (Paper I) we extended our NLFFF optimization code by including stereoscopic constrains. The method was successfully tested with synthetic data, and within this work, we apply the newly developed code to a combined data set from SDO/HMI, SDO/AIA, and the two STEREO spacecraft. The extended method (called S-NLFFF) contains an additional term that monitors and minimizes the angle between the local magnetic field direction and the orientation of the 3D coronal loops reconstructed by stereoscopy. We find that when we prescribe the shape of the 3D stereoscopically reconstructed loops, the S-NLFFF method leads to a much better agreement between the modeled field and the stereoscopically reconstructed loops. We also find an appreciable decrease by a factor of two in the angle between the current and the magnetic field. This indicates the improved quality of the force-free solution obtained by S-NLFFF.

High-latitude Conic Current Sheets in the Solar Wind

Abstract We provide observational evidence for the existence of large-scale cylindrical (or conic-like) current sheets (CCSs) at high heliolatitudes. Long-lived CCSs were detected by Ulysses during its passages over the South Solar Pole in 1994 and 2007. The characteristic scale of these tornado-like structures is several times less than a typical width of coronal holes within which the CCSs are observed. CCS crossings are characterized by a dramatic decrease in the solar wind speed and plasma beta typical for predicted profiles of CCSs. Ulysses crossed the same CCS at different heliolatitudes at 2–3 au several times in 1994, as the CCS was declined from the rotation axis and corotated with the Sun. In 2007, a CCS was detected directly over the South Pole, and its structure was strongly highlighted by the interaction with comet McNaught. Restorations of solar coronal magnetic field lines reveal the occurrence of conic-like magnetic separators over the solar poles in both 1994 and 2007. Such separators exist only during solar minima. Interplanetary scintillation data analysis confirms the presence of long-lived low-speed regions surrounded by the typical polar high-speed solar wind in solar minima. Energetic particle flux enhancements up to several MeV/nuc are observed at edges of the CCSs. We built simple MHD models of a CCS to illustrate its key features. The CCSs may be formed as a result of nonaxiality of the solar rotation axis and magnetic axis, as predicted by the Fisk–Parker hybrid heliospheric magnetic field model in the modification of Burger and coworkers.

THE POSSIBLE IMPACT OF L5 MAGNETOGRAMS ON NON-POTENTIAL SOLAR CORONAL MAGNETIC FIELD SIMULATIONS

ABSTRACT The proposed Carrington-L5 mission would bring instruments to the L5 Lagrange point to provide us with crucial data for space weather prediction. To assess the importance of including a magnetograph, we consider the possible differences in non-potential solar coronal magnetic field simulations when magnetograph observations are available from the L5 point, compared with an L1-based field of view (FOV). A timeseries of synoptic radial magnetic field maps is constructed to capture the emergence of two active regions from the L5 FOV. These regions are initially absent in the L1 magnetic field maps, but are included once they rotate into the L1 FOV. Non-potential simulations for these two sets of input data are compared in detail. Within the bipolar active regions themselves, differences in the magnetic field structure can exist between the two simulations once the active regions are included in both. These differences tend to reduce within 5 days of the active region being included in L1. The delayed emergence in L1 can, however, lead to significant persistent differences in long-range connectivity between the active regions and the surrounding fields, and also in the global magnetic energy. In particular, the open magnetic flux and the location of open magnetic footpoints, are sensitive to capturing the real-time of emergence. These results suggest that a magnetograph at L5 could significantly improve predictions of the non-potential corona, the interplanetary magnetic field, and of solar wind source regions on the Sun.

Eyecciones coronales de masa solar a 1 unidad astronómica

La presente investigación concluye estadísticamente que las eyecciones coronales de masa solar (CME) por sus siglas en inglés, son grandes erupciones de campos magnéticos coronales solares y plasma (considerado el cuarto estado de la materia), que alcanzan la órbita de la Tierra con características especiales de velocidad, en este caso específico estudiado, se convierten en tormentas geomagnéticas, de alta o baja velocidad, según las CME.Para desarrollar la presente investigación se estudiaron los datos de eyecciones coronales de masa solar con propiedades delimitadas: de velocidad, masa y diferentes tipos de energía del año 1990 al 2012 que pudieron convertirse en tormentas geomagnéticas. Se enfocó la investigación en eventos rápidos con un rango de tiempo mayor o igual a 0.5 días y menor o igual a 1 día, para calcular el tiempo de llegada al planeta Tierra en días; se usó la distancia promedio entre nuestro planeta y el Sol.De los datos de CME de altas velocidades, tenemos como resultados pocas fluctuaciones del campo magnético, o sea, pocas tormentas geomagnéticas; pero se observaron valores de índices k desde 0 a 9. En general, haciendo un análisis comparativo de los resultados de la caracterización de eyecciones coronales con la actividad solar, se observó que los ciclos de máxima actividad fueron atípicos, concluyendo que realmente los ciclos mínimos se han prolongado, se resalta la tendencia decreciente en la actividad solar y como consecuencia también hay tendencia decreciente en la ocurrencia de eyecciones coronales de masa que son la principal causa de las tormentas geomagnéticas.Revista Ciencia y Tecnología No. 17, diciembre 2015 pp.179-194

A small mission concept to the Sun–Earth Lagrangian L5 point for innovative solar, heliospheric and space weather science

We present a concept for a small mission to the Sun–Earth Lagrangian L5 point for innovative solar, heliospheric and space weather science. The proposed INvestigation of Solar-Terrestrial Activity aNd Transients (INSTANT) mission is designed to identify how solar coronal magnetic fields drive eruptions, mass transport and particle acceleration that impact the Earth and the heliosphere. INSTANT is the first mission designed to (1) obtain measurements of coronal magnetic fields from space and (2) determine coronal mass ejection (CME) kinematics with unparalleled accuracy. Thanks to innovative instrumentation at a vantage point that provides the most suitable perspective view of the Sun–Earth system, INSTANT would uniquely track the whole chain of fundamental processes driving space weather at Earth. We present the science requirements, payload and mission profile that fulfill ambitious science objectives within small mission programmatic boundary conditions.

COMPARISON OF CORONAL EXTRAPOLATION METHODS FOR CYCLE 24 USING HMI DATA

ABSTRACT Two extrapolation models of the solar coronal magnetic field are compared using magnetogram data from the Solar Dynamics Observatory/Helioseismic and Magnetic Imager instrument. The two models, a horizontal current–current sheet–source surface (HCCSSS) model and a potential field–source surface (PFSS) model, differ in their treatment of coronal currents. Each model has its own critical variable, respectively, the radius of a cusp surface and a source surface, and it is found that adjusting these heights over the period studied allows for a better fit between the models and the solar open flux at 1 au as calculated from the Interplanetary Magnetic Field (IMF). The HCCSSS model provides the better fit for the overall period from 2010 November to 2015 May as well as for two subsets of the period: the minimum/rising part of the solar cycle and the recently identified peak in the IMF from mid-2014 to mid-2015 just after solar maximum. It is found that an HCCSSS cusp surface height of 1.7 R ⊙ provides the best fit to the IMF for the overall period, while 1.7 and 1.9 R ⊙ give the best fits for the two subsets. The corresponding values for the PFSS source surface height are 2.1, 2.2, and 2.0 R ⊙ respectively. This means that the HCCSSS cusp surface rises as the solar cycle progresses while the PFSS source surface falls.