Empirical Optimization of the Source-surface Height in the Potential Field Source Surface Extrapolation

We constructed global coronal magnetic fields of the Sun during the Total Solar Eclipse (TSE) 9 March 2016 by using Potential Field Source Surface (PFSS) model. Synoptic photospheric magnetogram data from Helioseismic and Magnetic Imager (HMI) onboard Solar Dynamics Observatory (SDO) was used as a boundary condition to extrapolate the coronal magnetic fields of the Sun. This extrapolated structure was analyzed by comparing the alignment of the fields from the model with coronal structure from the observation. We also used observational data of coronal structure during the total solar eclipse to know how well the model agree with the observation. As a result, we could identify several coronal streamers which were produced by the large closed loops in the lower regime of the corona. This result verified that the PFSS extrapolation can be used as a tool to model the inner corona with several constraints. We also discussed how the coronal structure can be used to deduce the phase of the solar cycle.

Magnetic fields generated in the Sun’s interior by the dynamo mechanism drive solar activity over a range of time-scales. Direct sunspot observations exist for a few centuries; reconstructed variations based on cosmogenic isotopes in the solar open flux and cosmic ray flux exist over thousands of years. While such reconstructions indicate the presence of extreme solar activity fluctuations in the past, causal links between millennia scale dynamo activity, consequent coronal field, solar wind, open flux and cosmic ray flux variations remain elusive; a lack of coronal field observations compounds this issue. By utilizing a stochastically forced solar dynamo model and potential field source surface extrapolation, we perform long-term simulations to illuminate how dynamo generated magnetic fields govern the structure of the solar corona and the state of the heliosphere – as indicated by variations in the open flux and cosmic ray modulation potential. We establish differences in the nature of the large-scale structuring of the solar corona during grand maximum, minimum, and regular solar activity phases and simulate how the open flux and cosmic ray modulation potential vary across these different phases of activity. We demonstrate that the power spectrum of simulated and observationally reconstructed solar open flux time series are consistent with each other. Our study provides the theoretical foundation for interpreting long-term solar cycle variations inferred from cosmogenic isotope based reconstructions and establishes causality between solar internal variations to the forcing of the state of the heliosphere.

A significant number of interplanetary shocks (∼17%) during cycle 23 were not followed by drivers. The number of such “driverless” shocks steadily increased with the solar cycle with 15%, 33%, and 52% occurring in the rise, maximum, and declining phase of the solar cycle. The solar sources of 15% of the driverless shocks were very close the central meridian of the Sun (within ∼15°), which is quite unexpected. More interestingly, all the driverless shocks with their solar sources near the solar disk center occurred during the declining phase of solar cycle 23. When we investigated the coronal environment of the source regions of driverless shocks, we found that in each case there was at least one coronal hole nearby, suggesting that the coronal holes might have deflected the associated coronal mass ejections (CMEs) away from the Sun‐Earth line. The presence of abundant low‐latitude coronal holes during the declining phase further explains why CMEs originating close to the disk center mimic the limb CMEs, which normally lead to driverless shocks due to purely geometrical reasons. We also examined the solar source regions of shocks with drivers. For these, the coronal holes were located such that they either had no influence on the CME trajectories, or they deflected the CMEs toward the Sun‐Earth line. We also obtained the open magnetic field distribution on the Sun by performing a potential field source surface extrapolation to the corona. It was found that the CMEs generally move away from the open magnetic field regions. The CME–coronal hole interaction must be widespread in the declining phase and may have a significant impact on the geoeffectiveness of CMEs.

Context. Impulsive solar energetic particle events in the inner heliosphere show the long-lasting enrichment of 3He. Aims. We study the source regions of long-lasting 3He-rich solar energetic particle (SEP) events Methods. We located the responsible open magnetic field regions, we combined potential field source surface extrapolations (PFSS) with the Parker spiral, and compared the magnetic field of the identified source regions with in situ magnetic fields. The candidate open field regions are active region plages. The activity was examined by using extreme ultraviolet (EUV) images from the Solar Dynamics Observatory (SDO) and STEREO together with radio observations from STEREO and WIND. Results. Multi-day periods of 3He-rich SEP events are associated with ion production in single active region. Small flares or coronal jets are their responsible solar sources. We also find that the 3He enrichment may depend on the occurrence rate of coronal jets.

The 2015 March 15 coronal mass ejection as one of the two that together drove the largest geomagnetic storm of solar cycle 24 so far was associated with sympathetic filament eruptions. We investigate the relations between the different filaments involved in the eruption. A surge-like small-scale filament motion is confirmed as the trigger that initiated the erupting filament with multi-wavelength observations and using a forced magnetic field extrapolation method. When the erupting filament moved to an open magnetic field region, it experienced an obvious acceleration process and was accompanied by a C-class flare and the rise of another larger filament that eventually failed to erupt. We measure the decay index of the background magnetic field, which presents a critical height of 118 Mm. Combining with a potential field source surface extrapolation method, we analyze the distributions of the large-scale magnetic field, which indicates that the open magnetic field region may provide a favorable condition for F2 rapid acceleration and have some relation with the largest solar storm. The comparison between the successful and failed filament eruptions suggests that the confining magnetic field plays an important role in the preconditions for an eruption.

Three-dimensional (3-d) magnetohydrodynamics (MHD) modeling is a key method for studying the interplanetary solar wind. In this article, In this paper, we introduce a new 3-d MHD solar wind model driven by the self-consistent boundary condition obtained from multiple observations and Artificial Neural Network (ANN) machine learning technique. At the inner boundary, the magnetic field is derived using the magnetogram and potential field source surface extrapolation; the electron density is derived from the polarized brightness (pB) observations, the velocity can be deduced by an ANN using both the magnetogram and pB observations, and the temperature is derived from the magnetic field and electron density by a self-consistent method. Then, the 3-d interplanetary solar wind from CR2057 to CR2062 are modeled by the new model with the self-consistent boundary conditions. The modeling results present various observational characteristics at different latitudes, and are in good agreement with both the OMNI and Ulysses observations.

The aim of this work is to provide a physical explanation for the genesis of multiple coronal mass ejections (CMEs) in an asymmetric coronal field configuration. We analyze STEREO observations of a multiple eruption and compare the results from the data analysis with predictions provided by magnetohydrodynamic (MHD) simulations. To this end, the multiple CMEs (MCMEs) observed on 21 – 22 September 2009 were selected. Both eruptions originated from the same source region and showed approximately the same latitudinal deflection, by more than 15 degrees, toward the heliospheric current sheet (HCS) during their propagation in the COR1 field of view. Numerical MHD simulations of the MCMEs have been performed, starting from an asymmetric coronal field configuration that mimics the potential field source surface extrapolation for 21 September 2009. The results demonstrate that, by shearing the footpoints at the base of the southern arcade, we were able to reproduce the observed dynamics of the MCMEs. Both CMEs are deflected toward the HCS due to an imbalance in the magnetic pressure and tension forces; the global field strength turns out to be a crucial parameter in order to release two subsequent eruptions, and hence to reproduce the observed evolution.

Solar wind modeling with the 3D MHD model EUHFORIA (EUropean Heliospheric FORecasting Information Asset; Pomoell & Poedts, 2018) revealed discrepancy with in situ observations by the Parker Solar Probe (PSP) at near-Sun distances . The default coronal model employed in EUHFORIA consists of the potential field source surface extrapolation (PFSS), Schatten current sheet (SCS) model and semi-empirical WSA model, which simulate the plasma and magnetic conditions at the inner boundary (0.1 AU). Parameters such as the PFSS source surface height (RSS), which is the outer boundary of PFSS, and the inner boundary of SCS model influence the modelled coronal hole areas and the associated open flux areas. A default RSS value of 2.6 R⊙, as per McGregor et al. (2008), is used in EUHFORIA for solar wind simulations. Lowering the RSS value has been reported to better capture coronal hole areas (Asvestari et al., 2019), improve the reconstruction of small-scale features (Badman et al., 2020), and more accurately reflect coronal magnetic field topologies during different phases of solar cycles (Lee et al., 2011; Arden et al., 2014).In this parameter study we investigate the possible systematic effects of changing the outer boundary of the PFSS model and the inner boundary of the SCS model, while keeping default values for other parameters. The resulting solar wind simulations are compared to those obtained using all default parameters in the model, by evaluating their agreement with the in situ observations from PSP for its first ten perihelion encounters. Although we found improved modeling accuracy for several time intervals, first results do not show clear systematic improvements in the accuracy of the modeled solar wind.

Context.A complex and long-lasting solar eruption on 17 April 2021 produced a widespread solar energetic particle (SEP) event that was observed by five longitudinally well-separated observers in the inner heliosphere that covered distances to the Sun from 0.42 to 1 au: BepiColombo, Parker Solar Probe, Solar Orbiter, STEREO A, and near-Earth spacecraft. The event was the second widespread SEP event detected in solar cycle 25, and it produced relativistic electrons and protons. It was associated with a long-lasting solar hard X-ray flare that showed multiple hard X-ray peaks over a duration of one hour. The event was further accompanied by a medium-fast coronal mass ejection (CME) with a speed of 880 km s−1that drove a shock, an extreme ultraviolet wave, and long-lasting and complex radio burst activity that showed four distinct type III burst groups over a period of 40 min.Aims.We aim to understand the reason for the wide spread of elevated SEP intensities in the inner heliosphere as well as identify the underlying source regions of the observed energetic electrons and protons.Methods.We applied a comprehensive multi-spacecraft analysis of remote-sensing observations and in situ measurements of the energetic particles and interplanetary context to attribute the SEP observations at the different locations to the various potential source regions at the Sun. We used an ENLIL simulation to characterize the complex interplanetary state and its role in the energetic particle transport. The magnetic connection between each spacecraft and the Sun was determined using ballistic backmapping in combination with potential field source surface extrapolations in the lower corona. Using also a reconstruction of the coronal shock front, we then determined the times when the shock establishes magnetic connections with the different observers. Radio observations were used to characterize the directivity of the four main injection episodes, which were then employed in a 2D SEP transport simulation to test the importance of these different injection episodes.Results.A comprehensive timing analysis of the inferred solar injection times of the SEPs observed at each spacecraft suggests different source processes being important for the electron and proton events. Comparison among the characteristics and timing of the potential particle sources, such as the CME-driven shock or the flare, suggests a stronger shock contribution for the proton event and a more likely flare-related source for the electron event.Conclusions.In contrast to earlier studies on widespread SEP events, we find that in this event an important ingredient for the wide SEP spread was the wide longitudinal range of about 110° covered by distinct SEP injections, which is also supported by our SEP transport modeling.

Since Parker, the existence of the solar wind has been ascribed to the fact that the solar corona is not in hydrostatic equilibrium and thus is constantly expanding. However, the mechanism responsible for accelerating/heating the solar wind is widely debated, even though there is evidence that it is magnetic in nature. New space missions like Parker Solar Probe (PSP), Solar Orbiter (SolO) and BepiColombo (BC), being much closer to the Sun, allow observations of less evolved and less mixed solar wind. Thus, for example, the observed streams can be easily back-propagated to their source on the Sun, allowing generally more accurate characterizations. These new observations revealed that the measured magnetic field is highly structured close to the Sun, exhibiting patches of large and intermittent reversals associated with jets of plasma. Jetting activity reveals that the solar wind emission is discrete in nature rather than homogeneous, leading to intermittent/impulsive outflow from the corona driven by small-scale magnetic reconnection. In a recent work, it has been shown that super granulation structure at the coronal base remains imprinted in the near-Sun solar wind, resulting in the magnetic polarity inversions known as switchback. Farther from the Sun, however, switchbacks are less frequent, probably due to mixing and turbulent decay.According to the Potential Field Source Surface extrapolation between 6th and 7th October 2021, BC and SolO were connected to the same region on the Sun. BC and SolO were located at 0.36 AU and 0.67 AU, respectively. Both spacecraft detected a patch of switchbacks, offering the opportunity to investigate their evolution with solar wind propagation. Our findings highlight the potential of BC for synergistic studies with PSP and SolO, despite its primary focus on Mercury’s environment.

Context. Although the most likely source regions of fast solar wind relate to coronal holes, the exact acceleration mechanism that drives the fast solar wind is still not fully understood. An important approach that can improve our understanding involves the combination of remote sensing and in situ measurements, often referred to as linkage analysis. This linkage tries to identify the source location of the in situ solar wind with a process called back-mapping. Typically, back-mapping is a combination of ballistic mapping, where the solar wind draws the magnetic field into the Parker Spiral at larger radial distances, and magnetic mapping, where the solar wind follows the magnetic field line topology from the solar surface to a point in the corona where the solar wind starts to expand radially. Aims. By examining the different model ingredients that can affect the derived back-mapped position, we aim to provide a more precise estimate of the source location and a measure of confidence in the mapping procedure. This can be used to improve the connection between remote sensing and in situ measurements. Methods. For the ballistic mapping, we created velocity profiles based on Parker wind approximations. These profiles are constrained by observations of the fast solar wind close to the Sun and are used to examine the mapping uncertainty. The coronal magnetic field topology from the solar surface up to an outer surface (the source surface) radius RSS is modeled with a potential field source surface extrapolation (PFSS). As inputs, the PFSS takes a photospheric synoptic magnetogram and a value for the source surface radius, where this latter is defined as the boundary after which the magnetic field becomes radial. The sensitivity of the extrapolated field is examined by adding reasonable noise to the input magnetogram and performing a Monte Carlo simulation, where we calculate the source position of the solar wind for multiple noise realizations. Next, we examine the effect of free parameters –such as the height of the source surface– and derive statistical estimates. We used Gaussian Mixture clustering to group the back-mapped points associated with different sources of uncertainty, and provide a confidence area for the source location of the solar wind. Furthermore, we computed a number of metrics to evaluate the back-mapping results and assessed their statistical significance by examining three high-speed stream events. Finally, we explored the effect of corotation close to the Sun on the derived source region of the solar wind. Results. For back-mapping with a PFSS corona and ballistic solar wind, our results show that the height of the source surface produces the largest uncertainty in the source region of the fast solar wind, followed by the noise in the input magnetogram, and the choice of the velocity profile. Additionally, we display the ability to derive a confidence area on the solar surface that represents the potential source region of the in situ-measured fast solar wind.

Some key physical processes that impact the evolution of Earth's atmosphere on time-scale from days to millennia, such as the EUV emissions, are determined by the solar magnetic field. However, observations of the solar spectral irradiance are restricted to the last few solar cycles and are subject to large uncertainties. We present a physics-based model to reconstruct short-term solar spectral irradiance (SSI) variability. The coronal magnetic field is estimated to employ the Potential Field Source Surface extrapolation (PFSS) based on observational synoptic charts and magnetic flux transport model. The emission is estimated to employ the CHIANTI atomic database 8.0. The performance of the model is compared to the emission observed by TIMED/SORCE.

A coronal hole formed as a result of a quiet-Sun filament eruption close to the solar disk center on 2014 June 25. We studied this formation using images from the Atmospheric Imaging Assembly (AIA), magnetograms from the Helioseismic and Magnetic Imager, and a differential emission measure analysis derived from the AIA images. The coronal hole developed in three stages: (1) formation, (2) migration, and (3) stabilization. In the formation phase, the emission measure (EM) and temperature started to decrease 6 hr before the filament erupted. Then, the filament erupted and a large coronal dimming formed over the following 3 hr. Subsequently, in a phase lasting 15.5 hr, the coronal dimming migrated by ≈150 ″ from its formation site to a location where potential field source surface extrapolations indicate the presence of open magnetic field lines, marking the transition into a coronal hole. During this migration, the coronal hole drifted across quasi-stationary magnetic elements in the photosphere, implying the occurrence of magnetic interchange reconnection at the boundaries of the coronal hole. In the stabilization phase, the magnetic properties and area of the coronal hole became constant. The EM of the coronal hole decreased, which we interpret as a reduction in plasma density due to the onset of plasma outflow into interplanetary space. As the coronal hole rotated toward the solar limb, it merged with a nearby preexisting coronal hole. At the next solar rotation, the coronal hole was still apparent, indicating a lifetime of >1 solar rotation.

<p>Although the sources of the fast solar wind are known (the coronal holes), the exact acceleration mechanism of the fast solar wind is still not fully understood. An important factor that can improve our understanding is the combination of remote sensing and in-situ measurements.</p><p>In order to combine them, it is necessary to accurately identify the source location of the in-situ solar wind with a process called back-mapping. Back-mapping consists mainly of two parts.<br>The first one is the ballistic mapping where the solar wind radially draws the magnetic field into the Parker Spiral, down to a point in the outer corona. <br>The second one is the magnetic mapping where the solar wind follows the magnetic field line topology down to the solar surface. The magnetic field in this region is derived from a global model, like the potential field source surface extrapolations (PFSS).</p><p>In this study we focus on this back-mapping of the fast solar wind and try to determine all the uncertainties and sources of error that can affect the final location deduced on the solar surface. We compare different models for the ballistic mapping and also for the magnetic mapping and explore which free parameters have the greatest effect in the back-mapped locations.<br>Finally, we provide an uncertainty estimation for the back-mapped footpoints and compare our results with existing frameworks, like the Connectivity-Tool of IRAP.</p><div></div>

Three-dimensional (3-d) magnetohydrodynamics (MHD) modeling is a key method for studying the interplanetary solar wind. In this paper, we introduce a new 3-d MHD solar wind model driven by the self-consistent boundary condition obtained from multiple observations and the Artificial Neural Network (ANN) machine learning technique. At the inner boundary, the magnetic field is derived using the magnetogram and potential field source surface extrapolation; the electron density is derived from the polarized brightness (pB) observations, the velocity can be deduced by an ANN using both the magnetogram and pB observations, and the temperature is derived from the magnetic field and electron density by a self-consistent method. Then, the 3-d interplanetary solar wind from CR2057 to CR2062 is modeled by the new model with the self-consistent boundary conditions. The modeling results present various observational characteristics at different latitudes, and are in better agreement with both the OMNI and Ulysses observations compared to our previous MHD model based only on photospheric magnetic field observations.