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We generalize a magnetogram-matching Biot-Savart law (BSL) from planar to spherical geometry. For a given coronal current density $\bf{J}$, this law determines the corresponding magnetic field $\tilde{\bf B}$ under the condition that its radial component vanishes at the surface. The superposition of $\tilde{\bf B}$ with a potential magnetic field defined by the given surface radial field, $B_r$, provides the entire magnetic configuration, in which $B_r$ remains unchanged by the currents. Using this approach, we (1) upgrade our regularized BSLs for constructing coronal magnetic flux ropes (MFRs) and (2) propose a new method for decomposing a measured photospheric magnetic field as ${\bf B} = {\bf B}_{\mathrm{pot}} + {\bf B}_T + {\bf B}_{\tilde{S}}$, where the potential, ${\bf B}_{\mathrm{pot}}$, toroidal, ${\bf B}_T$, and tangential poloidal, ${\bf B}_{\tilde{S}}$, fields are determined by $B_r$, $J_r$, and the surface divergence of ${\bf B} - {\bf B}_{\mathrm{pot}}$, respectively, all derived from magnetic data. Our ${\bf B}_T$ is identical to the one in the alternative decomposition by Schuck et al. (2022), while ${\bf B}_{\mathrm{pot}}$ and ${\bf B}_{\tilde{S}}$ are very different from their poloidal fields ${\bf B}_{\mathrm{P}<}$ and ${\bf B}_{\mathrm{P}>}$, which are {\it potential} and refer to {\it different} surface sides. In contrast, our ${\bf B}_{\tilde{S}}$ is generally {\it nonpotential} and, as ${\bf B}_{\mathrm{pot}}$ and ${\bf B}_T$, refers to the {\it same} upper side of the surface, rendering our decomposition more complete and consistent. We demonstrate that it allows one to identify the footprints and projected surface-location of MFRs, as well as the direction and connectivity of their currents, especially for weak or complex configurations, which is very important for modeling and analyzing observed pre-eruptive configurations and their eruptions., Comment: 25 pages, 8 figures, submitted to ApJ

Observations have shown a clear association of filament/prominence eruptions with the emergence of magnetic flux in or near filament channels. Magnetohydrodynamic (MHD) simulations have been employed to systematically study the conditions under which such eruptions occur. These simulations to date have modeled filament channels as two-dimensional (2D) flux ropes or 3D uniformly sheared arcades. Here we present MHD simulations of flux emergence into a more realistic configuration consisting of a bipolar active region containing a line-tied 3D flux rope. We use the coronal flux-rope model of Titov et al. (2014) as the initial condition and drive our simulations by imposing boundary conditions extracted from a flux-emergence simulation by Leake et al. (2013). We identify three mechanisms that determine the evolution of the system: (i) reconnection displacing foot points of field lines overlying the coronal flux rope, (ii) changes of the ambient field due to the intrusion of new flux at the boundary, and (iii) interaction of the (axial) electric currents in the pre-existing and newly emerging flux systems. The relative contributions and effects of these mechanisms depend on the properties of the pre-existing and emerging flux systems. Here we focus on the location and orientation of the emerging flux relative to the coronal flux rope. Varying these parameters, we investigate under which conditions an eruption of the latter is triggered., Comment: 18 pages, 8 figures, accepted for publication by The Astrophysical Journal

The slow solar wind belt in the quiet corona, observed with the Metis coronagraph on board Solar Orbiter on May 15, 2020, during the activity minimum of the cycle 24, in a field of view extending from 3.8 $R_\odot$ to 7.0 $R_\odot$, is formed by a slow and dense wind stream running along the coronal current sheet, accelerating in the radial direction and reaching at 6.8 $R_\odot$ a speed within 150 km s$^{-1}$ and 190 km s$^{-1}$, depending on the assumptions on the velocity distribution of the neutral hydrogen atoms in the coronal plasma. The slow stream is separated by thin regions of high velocity shear from faster streams, almost symmetric relative to the current sheet, with peak velocity within 175 km s$^{-1}$ and 230 km s$^{-1}$ at the same coronal level. The density-velocity structure of the slow wind zone is discussed in terms of the expansion factor of the open magnetic field lines that is known to be related to the speed of the quasi-steady solar wind, and in relation to the presence of a web of quasi separatrix layers, S-web, the potential sites of reconnection that release coronal plasma into the wind. The parameters characterizing the coronal magnetic field lines are derived from 3D MHD model calculations. The S-web is found to coincide with the latitudinal region where the slow wind is observed in the outer corona and is surrounded by thin layers of open field lines expanding in a non-monotonic way.

The solar wind consists of continuous streams of charged particles that escape into the heliosphere from the Sun, and is split into fast and slow components, with the fast wind emerging from the interiors of coronal holes. Near the ecliptic plane, the fast wind from low-latitude coronal holes is interspersed with a highly structured slow solar wind, the source regions and drivers of which are poorly understood. Here we report extreme-ultraviolet observations that reveal a spatially complex web of magnetized plasma structures that persistently interact and reconnect in the middle corona. Coronagraphic white-light images show concurrent emergence of slow wind streams over these coronal web structures. With advanced global MHD coronal models, we demonstrate that the observed coronal web is a direct imprint of the magnetic separatrix web (S-web). By revealing a highly dynamic portion of the S-web, our observations open a window into important middle-coronal processes that appear to play a key role in driving the structured slow solar wind., Comment: This version of the article has been accepted for publication, after peer review but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1038/s41550-022-01834-5

The investigation of the wind in the solar corona initiated with the observations of the resonantly scattered UV emission of the coronal plasma obtained with UVCS-SOHO, designed to measure the wind outflow speed by applying the Doppler dimming diagnostics. Metis on Solar Orbiter complements the UVCS spectroscopic observations, performed during solar activity cycle 23, by simultaneously imaging the polarized visible light and the HI Ly-alpha corona in order to obtain high-spatial and temporal resolution maps of the outward velocity of the continuously expanding solar atmosphere. The Metis observations, on May 15, 2020, provide the first HI Ly-alpha images of the extended corona and the first instantaneous map of the speed of the coronal plasma outflows during the minimum of solar activity and allow us to identify the layer where the slow wind flow is observed. The polarized visible light (580-640 nm), and the UV HI Ly-alpha (121.6 nm) coronal emissions, obtained with the two Metis channels, are combined in order to measure the dimming of the UV emission relative to a static corona. This effect is caused by the outward motion of the coronal plasma along the direction of incidence of the chromospheric photons on the coronal neutral hydrogen. The plasma outflow velocity is then derived as a function of the measured Doppler dimming. The static corona UV emission is simulated on the basis of the plasma electron density inferred from the polarized visible light. This study leads to the identification, in the velocity maps of the solar corona, of the high-density layer about +/-10 deg wide, centered on the extension of a quiet equatorial streamer present at the East limb where the slowest wind flows at about (160 +/- 18) km/s from 4 Rs to 6 Rs. Beyond the boundaries of the high-density layer, the wind velocity rapidly increases, marking the transition between slow and fast wind in the corona.

The so-called regularized Biot-Savart laws (RBSLs) provide an efficient and flexible method for modeling pre-eruptive magnetic configurations of coronal mass ejections (CMEs) whose characteristics are constrained by observational images and magnetic-field data. This method allows one to calculate the field of magnetic flux ropes (MFRs) with small circular cross-sections and an arbitrary axis shape. The field of the whole configuration is constructed as a superposition of (1) such a flux-rope field and (2) an ambient potential field derived, for example, from an observed magnetogram. The RBSL kernels are determined from the requirement that the MFR field for a straight cylinder must be exactly force-free. For a curved MFR, however, the magnetic forces are generally unbalanced over the whole path of the MFR. To minimize these forces, we apply a modified Gauss-Newton method to find optimal MFR parameters. This is done by iteratively adjusting the MFR axis path and axial current. We then try to relax the resulting optimized configuration in a subsequent line-tied zero-beta magnetohydrodynamic simulation toward a force-free equilibrium. By considering two models of the sigmoidal pre-eruption configuration for the 2009 February 13 CME, we demonstrate how this approach works and what it is capable of. We show, in particular, that the building blocks of the core magnetic structure described by these models match to morphological features typically observed in such type of configurations. Our method will be useful for both the modeling of particular eruptive events and theoretical studies of idealized pre-eruptive MFR configurations., Comment: 21 pages, 11 figures, accepted to ApJS

Many scientists use coronal hole (CH) detections to infer open magnetic flux. Detection techniques differ in the areas that they assign as open, and may obtain different values for the open magnetic flux. We characterize the uncertainties of these methods, by applying six different detection methods to deduce the area and open flux of a near-disk center CH observed on 9/19/2010, and applying a single method to five different EUV filtergrams for this CH. Open flux was calculated using five different magnetic maps. The standard deviation (interpreted as the uncertainty) in the open flux estimate for this CH was about 26%. However, including the variability of different magnetic data sources, this uncertainty almost doubles to 45%. We use two of the methods to characterize the area and open flux for all CHs in this time period. We find that the open flux is greatly underestimated compared to values inferred from in-situ measurements (by 2.2-4 times). We also test our detection techniques on simulated emission images from a thermodynamic MHD model of the solar corona. We find that the methods overestimate the area and open flux in the simulated CH, but the average error in the flux is only about 7%. The full-Sun detections on the simulated corona underestimate the model open flux, but by factors well below what is needed to account for the missing flux in the observations. Under-detection of open flux in coronal holes likely contributes to the recognized deficit in solar open flux, but is unlikely to resolve it., Comment: 28 pages, 10 figures, submitted to ApJ

GPU accelerators have had a notable impact on high-performance computing across many disciplines. They provide high performance with low cost/power, and therefore have become a primary compute resource on many of the largest supercomputers. Here, we implement multi-GPU acceleration into our Solar MHD code (MAS) using OpenACC in a fully portable, single-source manner. Our preliminary implementation is focused on MAS running in a reduced physics "zero-beta" mode. While valuable on its own, our main goal is to pave the way for a full physics, thermodynamic MHD implementation. We describe the OpenACC implementation methodology and challenges. "Time-to-solution" performance results of a production-level flux rope eruption simulation on multi-CPU and multi-GPU systems are shown. We find that the GPU-accelerated MAS code has the ability to run "zero-beta" simulations on a single multi-GPU server at speeds previously requiring multiple CPU server-nodes of a supercomputer., Comment: 13 pages, 9 figures

Seven different models are applied to the same problem of simulating the Sun's coronal magnetic field during the solar eclipse on 2015 March 20. All of the models are non-potential, allowing for free magnetic energy, but the associated electric currents are developed in significantly different ways. This is not a direct comparison of the coronal modelling techniques, in that the different models also use different photospheric boundary conditions, reflecting the range of approaches currently used in the community. Despite the significant differences, the results show broad agreement in the overall magnetic topology. Among those models with significant volume currents in much of the corona, there is general agreement that the ratio of total to potential magnetic energy should be approximately 1.4. However, there are significant differences in the electric current distributions; while static extrapolations are best able to reproduce active regions, they are unable to recover sheared magnetic fields in filament channels using currently available vector magnetogram data. By contrast, time-evolving simulations can recover the filament channel fields at the expense of not matching the observed vector magnetic fields within active regions. We suggest that, at present, the best approach may be a hybrid model using static extrapolations but with additional energization informed by simplified evolution models. This is demonstrated by one of the models., Comment: 29 pages, 11 figures, accepted for publication in Space Science Reviews

The heliospheric magnetic field is of pivotal importance in solar and space physics. The field is rooted in the Sun's photosphere, where it has been observed for many years. Global maps of the solar magnetic field based on full disk magnetograms are commonly used as boundary conditions for coronal and solar wind models. Two primary observational constraints on the models are (1) the open field regions in the model should approximately correspond to coronal holes observed in emission, and (2) the magnitude of the open magnetic flux in the model should match that inferred from in situ spacecraft measurements. In this study, we calculate both MHD and PFSS solutions using fourteen different magnetic maps produced from five different types of observatory magnetograms, for the time period surrounding July, 2010. We have found that for all of the model/map combinations, models that have coronal hole areas close to observations underestimate the interplanetary magnetic flux, or, conversely, for models to match the interplanetary flux, the modeled open field regions are larger than coronal holes observed in EUV emission. In an alternative approach, we estimate the open magnetic flux entirely from solar observations by combining automatically detected coronal holes for Carrington rotation 2098 with observatory synoptic magnetic maps. This approach also underestimates the interplanetary magnetic flux. Our results imply that either typical observatory maps underestimate the Sun's magnetic flux, or a significant portion of the open magnetic flux is not rooted in regions that are obviously dark in EUV and X-ray emission.

We describe a method for the automatic mapping of coronal holes (CH) using simultaneous multi-instrument EUV imaging data. Synchronized EUV images from STEREO/EUVI A&B 195A and SDO/AIA 193A are preprocessed, including PSF deconvolution and the application of data-derived intensity corrections that account for center-to-limb variations (limb brightening) and inter-instrument intensity normalization. We systematically derive a robust limb-brightening correction that takes advantage of unbiased long-term averages of data and respects the physical nature of the problem. The new preprocessing greatly assists in CH detection, allowing for the use of a simplified variable-connectivity two-threshold region growing image segmentation algorithm to obtain consistent detection results. We generate synchronic EUV and CH maps, and show a preliminary analysis of CH evolution. Several data and code products are made available to the community (www.predsci.com/chd): For the period of this study (06/10/2010 to 08/18/14) we provide synchronic EUV and coronal hole map data at 6-hour cadence, data-derived limb-brightening corrections for STEREO/EUVI A&B 195A and SDO/AIA 193A, and inter-instrument correction factors to equate their intensities. We also provide the coronal hole image segmentation code module (ezseg) implemented in both FORTRAN OpenMP and GPU-accelerated C-CUDA. A complete implementation of our coronal hole detection pipeline in the form of a ready-to-use MATLAB driver script euv2chm utilizing ezseg is also made available., Comment: 37 pages, 24 figures

EUV images of Comet Lovejoy (C/2011 W3) from the AIA show striations related to the magnetic field structure in both open and closed magnetic regions. The brightness contrast implies coronal density contrasts of at least a factor of 6 between neighboring flux tubes over scales of a few thousand km. These density structures imply variations in the Alfven speed on a similar scale. They will drastically affect the propagation and dissipation of Alfven waves, and that should be taken into account in models of coronal heating and solar wind acceleration. In each striation, the cometary emission moves along the magnetic field and broadens with time. The speed and the rate of broadening are related to the parallel and perpendicular components of the velocities of the cometary neutrals when they become ionized. We use an MHD model of the coronal magnetic field and the theory of pickup ions to compare the measurements with theoretical predictions, in particular with the energy lost to Alfven waves as the cometary ions isotropize., Comment: Accepted for publication in the Astrophysical Journal. 7 pages (emulateapj style), 6 figures

We study the influence of the spatial resolution on scales of $5\deg$ and smaller of solar surface magnetic field maps on global magnetohydrodynamic solar wind models, and on a model of coronal heating and X-ray emission. We compare the solutions driven by a low-resolution Wilcox Solar Observatory magnetic map, the same map with spatial resolution artificially increased by a refinement algorithm, and a high-resolution Solar and Heliospheric Observatory Michelson Doppler Imager map. We find that both the wind structure and the X-ray morphology are affected by the fine-scale surface magnetic structure. Moreover, the X-ray morphology is dominated by the closed loop structure between mixed polarities on smaller scales and shows significant changes between high and low resolution maps. We conclude that three-dimensional modeling of coronal X-ray emission has greater surface magnetic field spatial resolution requirements than wind modeling, and can be unreliable unless the dominant mixed polarity magnetic flux is properly resolved., Comment: 26 pages, 6 figures, accepted for publication in ApJ

We present a numerical investigation of the coronal evolution of a coronal mass ejection (CME) on 2005 August 22 using a 3-D thermodynamics magnetohydrodynamic model, the SWMF. The source region of the eruption was anemone active region (AR) 10798, which emerged inside a coronal hole. We validate our modeled corona by producing synthetic extreme ultraviolet (EUV) images, which we compare to EIT images. We initiate the CME with an out-of-equilibrium flux rope with an orientation and chirality chosen in agreement with observations of a H-alpha filament. During the eruption, one footpoint of the flux rope reconnects with streamer magnetic field lines and with open field lines from the adjacent coronal hole. It yields an eruption which has a mix of closed and open twisted field lines due to interchange reconnection and only one footpoint line-tied to the source region. Even with the large-scale reconnection, we find no evidence of strong rotation of the CME as it propagates. We study the CME deflection and find that the effect of the Lorentz force is a deflection of the CME by about 3 deg/Rsun towards the East during the first 30 minutes of the propagation. We also produce coronagraphic and EUV images of the CME, which we compare with real images, identifying a dimming region associated with the reconnection process. We discuss the implication of our results for the arrival at Earth of CMEs originating from the limb and for models to explain the presence of open field lines in magnetic clouds., Comment: 14 pages, 8 Figures, accepted to Astrophysical Journal

We perform a numerical study of the evolution of a Coronal Mass Ejection (CME) and its interaction with the coronal magnetic field based on the May 12, 1997, CME event using a global MagnetoHydroDynamic (MHD) model for the solar corona. The ambient solar wind steady-state solution is driven by photospheric magnetic field data, while the solar eruption is obtained by superimposing an unstable flux rope onto the steady-state solution. During the initial stage of CME expansion, the core flux rope reconnects with the neighboring field, which facilitates lateral expansion of the CME footprint in the low corona. The flux rope field also reconnects with the oppositely orientated overlying magnetic field in the manner of the breakout model. During this stage of the eruption, the simulated CME rotates counter-clockwise to achieve an orientation that is in agreement with the interplanetary flux rope observed at 1 AU. A significant component of the CME that expands into interplanetary space comprises one of the side lobes created mainly as a result of reconnection with the overlying field. Within 3 hours, reconnection effectively modifies the CME connectivity from the initial condition where both footpoints are rooted in the active region to a situation where one footpoint is displaced into the quiet Sun, at a significant distance ($\approx 1R_\odot$) from the original source region. The expansion and rotation due to interaction with the overlying magnetic field stops when the CME reaches the outer edge of the helmet streamer belt, where the field is organized on a global scale. The simulation thus offers a new view of the role reconnection plays in rotating a CME flux rope and transporting its footpoints while preserving its core structure., Comment: Accepted to JGR Space Physics, 15 pages, 8 figures

We present EXAFS data at the Mn K and Tb L3 edges that provide upper limits on the possible displacements of any atoms in TbMnO3. The displacements must be less than 0.005-0.01A for all atoms which eliminates the possibility of moderate distortions (0.02A) with a small c-axis component, but for which the displacements in the ab plane average to zero. Assuming the polarization arises from a displacement of the O2 atoms along the c-axis, the measured polarization then leads to an O2 displacement that is at least 6X10^{-4}A, well below our experimental limit. Thus a combination of the EXAFS and the measured electrical polarization indicate that the atomic displacements likely lie in the range 6X10^{-4} - 5X10^{-3}A., Comment: submitted to PRB; 11 pages (preprint form) 7 figures