arXiv subjects

M. K. Georgoulis

Publications and source records attributed to M. K. Georgoulis.

At least 19 recordsLinked to original sources

arXiv2026

Height-dependent thermal properties of extreme-ultraviolet campfires in the quiet Sun

Small-scale impulsive energy-release events are widely considered a key ingredient of quiet-Sun coronal heating. We quantified the thermal-energy content of extreme-ultraviolet (EUV) campfires, examined their impulsive heating characteristics, and investigated how their properties vary with atmospheric height. We analysed 1,468 campfires from an observing sequence on 30 May 2020 with Solar Orbiter/EUI HRIEUV at 174 A. Temperatures and emission measures were adopted from SDO/AIA diagnostics, and geometric uncertainties were explored using multiple volume models. Statistical properties were characterised using cumulative distribution functions and maximum-likelihood techniques and compared with Solar Orbiter/STIX microflares and SDO/AIA nanoflare-like events. Campfire durations show a clear dependence on height: short-duration events occur at all heights, whereas longer-lived brightenings are preferentially associated with chromospheric layers. Emitting volumes and thermal energies, by contrast, show no comparable height dependence. Background-subtracted thermal energies span approximately 10^20-10^24 erg, with rare events reaching approximately 5 x 10^24 erg. The statistically robust power-law regime extends over approximately 10^22-10^24 erg. Directly detected campfires contribute a sub-percent fraction of the canonical quiet-Sun heating requirement; approximate corrections for the detection threshold and DEM completeness could raise this contribution to a value of order a few percent. EUV campfires extend the flare energy distribution towards lower energies and provide height-resolved constraints on impulsive heating in the quiet Sun. The height dependence of event durations, combined with broadly invariant energy and volume distributions, indicates that atmospheric stratification primarily modulates cooling and dissipation timescales rather than the characteristic energy scale.

astro-ph.SR↗

arXiv2026

Advancing Heliophysics and Space Weather Modeling through Open Science

We present a community-wide effort to develop a strategy and action plan to advance heliophysics and space weather modeling through open science. While open science has the potential to enhance the quality and pace of scientific discovery, its application to scientific modeling requires more careful consideration regarding open data and open software guidelines, as scientific models differ significantly from data analysis software. We gathered feedback from modeling teams worldwide through a living survey and discussion sessions at the 2024 Open Science Workshop in College Park, USA, and at the 2025 COSPAR ISWAT Working Meeting in Cape Canaveral, USA. We complement these findings with lessons learned from almost 25 years of experience at the Community Coordinated Modeling Center in enabling open use of models. We identify key roadblocks in current open science practices and guidelines and offer recommendations for future progress across four overlapping themes: open use of models and simulation results, open validation, open development, and open collaboration. An essential outcome of the discussion is the need for model developers and model users to speak with a united voice and promote the role of models in future open science efforts. We introduce a new cross-domain community initiative called the Heliophysics Open Modeling Environment (HOME), which will be integrated as an overarching activity within COSPAR ISWAT. HOME will serve as a platform for modelers and model users to work together, facilitate community modeling, improve the scientific return on modeling investment, and advance understanding, modeling, and forecasting in heliophysics and space weather.

physics.space-ph↗

arXiv2024

Magnetic helicity and energy budgets of jet events from an emerging solar active region

Using photospheric vector magnetograms obtained by the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory and a magnetic connectivity-based method, we compute the magnetic helicity and free magnetic energy budgets of a simple bipolar solar active region (AR) during its magnetic flux emergence phase which lasted $\sim$47 hrs. The AR did not produce any coronal mass ejections (CMEs) or flares with an X-ray class above C1.0 but it was the site of 60 jet events during its flux emergence phase. The helicity and free energy budgets of the AR were below established eruption-related thresholds throughout the interval we studied. However, in addition to their slowly-varying evolution, each of the time profiles of the helicity and free energy budgets showed discrete localized peaks, with eight pairs of them occurring at times of jets emanating from the AR. These jets featured larger base areas and longer durations than the other jets of the AR. We estimated, for the first time, the helicity and free magnetic energy changes associated with these eight jets which were in the ranges of $0.5-7.1 \times 10^{40}$ Mx$^2$ and $1.1-6.9 \times 10^{29}$ erg, respectively. Although these values are one to two orders of magnitude smaller than those usually associated with CMEs, the relevant percentage changes were significant and ranged from 13% to 76% for the normalized helicity and from 9% to 57% for the normalized free magnetic energy. Our study indicates that occasionally jets may have a significant imprint in the evolution of helicity and free magnetic energy budgets of emerging active regions.

astro-ph.SR↗

arXiv2024

The temporal evolution of non-neutralized electric currents and the complexity of solar active regions

We study the evolution of electric currents during the emergence of magnetic flux in the solar photosphere and the differences exhibited between solar active regions of different Hale complexity classes. A sample of 59 active regions was analyzed using a method based on image segmentation and error analysis to determine the total amount of non-neutralized electric current along their magnetic polarity inversion lines. The time series of the total unsigned non-neutralized electric current, $I_{NN,tot}$, exhibit intricate structure in the form of distinct peaks and valleys. This information is largely missing in the respective time series of the total unsigned vertical electric current $I_z$. Active regions with $δ$- spots stand out, exhibiting 1.9 times higher flux emergence rate and 2.6 times higher $I_{NN,tot}$ increase. The median value of their peak $I_{NN,tot}$ is equal to $3.6\cdot10^12$ A, which is more than three times higher than that of the other regions of the sample. An automated detection algorithm was also developed to pinpoint the injection events of non-neutralized electric current. The injection rates and duration of these events were higher with increasing complexity of active regions, with regions containing $δ$-spots exhibiting the strongest and longest events. These events do not necessarily coincide with increasing magnetic flux, although they exhibit moderate correlation. We conclude that net electric currents are injected during flux emergence, but are also shaped drastically by the incurred photospheric evolution, as active regions grow and evolve.

astro-ph.SR↗

arXiv2023

Magnetic Helicity and Free Magnetic Energy as Tools to Probe Eruptions in two Differently Evolving Solar Active Regions

Using vector magnetograms from the HMI/SDO and a magnetic connectivity-based method, we calculate the instantaneous relative magnetic helicity and free magnetic energy budgets for several days in two solar active regions (ARs), AR11890 and AR11618, both with complex photospheric magnetic field configurations. The ARs produced several major eruptive flares while their photospheric magnetic field exhibited primarily flux decay in AR11890 and primarily flux emergence in AR11618. Throughout much of their evolution both ARs featured substantial budgets of free magnetic energy and of both positive and negative helicity. In fact, the imbalance between the signed components of their helicity was as low as in the quiet Sun and their net helicity eventually changed sign 14-19 hours after their last major flare. Despite such incoherence, the eruptions occurred at times of net helicity peaks that were co-temporal with peaks in the free magnetic energy. The losses associated with the eruptive flares in the normalized free magnetic energy were in the range 10-60%. For the helicity, changes ranged from 25% to the removal of the entire excess helicity of the prevailing sign, leading a roughly zero net helicity, but with significant equal and opposite budgets of both helicity senses. The removal of the slowly varying background component of the free energy and helicity timeseries revealed that all eruption-related peaks of both quantities exceeded the 2$σ$ levels of their detrended timeseries. There was no eruption when only one or none of these quantities exceeded its 2$σ$ level. Our results indicate that differently evolving ARs may produce major eruptive flares even when, in addition to the accumulation of significant free magnetic energy budgets, they accumulate large amounts of both negative and positive helicity without a strong dominance of one handedness over the other.

astro-ph.SR↗

arXiv2022

Automatic detection of small-scale EUV brightenings observed by the Solar Orbiter/EUI

Context. Accurate detections of frequent small-scale extreme ultraviolet (EUV) brightenings are essential to the investigation of the physical processes heating the corona. Aims. We detected small-scale brightenings, termed campfires, using their morphological and intensity structures as observed in coronal EUV imaging observations for statistical analysis. Methods. We applied a method based on Zernike moments and a support vector machine classifier to automatically identify and track campfires observed by Solar Orbiter/Extreme Ultraviolet Imager (EUI) and SDO/AIA. Results. This method detected 8678 campfires (with length scales between 400 km and 4000 km) from a sequence of 50 High Resolution EUV telescope (HRIEUV) 174Å images. From 21 near co-temporal AIA images covering the same field of view as EUI, we found 1131 campfires, 58% of which were also detected in HRIEUV images. In contrast, about 16% of campfires recognized in HRIEUV were detected by AIA. We obtain a campfire birthrate of 2*10-16m-2s-1. About 40% of campfires show a duration longer than 5 s, having been observed in at least two HRIEUV images. We find that 27% of campfires were found in coronal bright points and the remaining 73% have occurred out of coronal bright points. We detected 23 EUI campfires with a duration greater than 245 s. We found that about 80% of campfires are formed at supergranular boundaries, and the features with the highest total intensities are generated at network junctions and intense H I Lyman-α emission regions observed by EUI/HRILya. The probability distribution functions for the total intensity, peak intensity, and projected area of campfires follow a power law behavior with absolute indices between 2 and 3. This self-similar behavior is a possible signature of self-organization, or even self-organized criticality, in the campfire formation process.

astro-ph.SR↗

arXiv2021

Magnetic helicity estimations in models and observations of the solar magnetic field. Part IV: Application to solar observations

In this ISSI-supported series of studies on magnetic helicity in the Sun, we systematically implement different magnetic helicity calculation methods on high-quality solar magnetogram observations. We apply finite-volume, discrete flux tube (in particular, connectivity-based) and flux-integration methods to data from Hinode's Solar Optical Telescope. The target is NOAA active region 10930 during a ~1.5 day interval in December 2006 that included a major eruptive flare (SOL2006-12-13T02:14X3.4). Finite-volume and connectivity-based methods yield instantaneous budgets of the coronal magnetic helicity, while the flux-integration methods allow an estimate of the accumulated helicity injected through the photosphere. The objectives of our work are twofold: A cross-validation of methods, as well as an interpretation of the complex events leading to the eruption. To the first objective, we find (i) strong agreement among the finite-volume methods, (ii) a moderate agreement between the connectivity-based and finite-volume methods, (iii) an excellent agreement between the flux-integration methods, and (iv) an overall agreement between finite-volume and flux-integration based estimates regarding the predominant sign and magnitude of the helicity. To the second objective, we are confident that the photospheric helicity flux significantly contributed to the coronal helicity budget, and that a right-handed structure erupted from a predominantly left-handed corona during the X-class flare. Overall, we find that the use of different methods to estimate the (accumulated) coronal helicity may be necessary in order to draw a complete picture of an active-region corona, given the careful handling of identified data (preparation) issues, which otherwise would mislead the event analysis and interpretation.

astro-ph.SR↗

arXiv2021

The Flare Likelihood and Region Eruption Forecasting (FLARECAST) Project: Flare forecasting in the big data & machine learning era

The EU funded the FLARECAST project, that ran from Jan 2015 until Feb 2018. FLARECAST had a R2O focus, and introduced several innovations into the discipline of solar flare forecasting. FLARECAST innovations were: first, the treatment of hundreds of physical properties viewed as promising flare predictors on equal footing, extending multiple previous works; second, the use of fourteen (14) different ML techniques, also on equal footing, to optimize the immense Big Data parameter space created by these many predictors; third, the establishment of a robust, three-pronged communication effort oriented toward policy makers, space-weather stakeholders and the wider public. FLARECAST pledged to make all its data, codes and infrastructure openly available worldwide. The combined use of 170+ properties (a total of 209 predictors are now available) in multiple ML algorithms, some of which were designed exclusively for the project, gave rise to changing sets of best-performing predictors for the forecasting of different flaring levels. At the same time, FLARECAST reaffirmed the importance of rigorous training and testing practices to avoid overly optimistic pre-operational prediction performance. In addition, the project has (a) tested new and revisited physically intuitive flare predictors and (b) provided meaningful clues toward the transition from flares to eruptive flares, namely, events associated with coronal mass ejections (CMEs). These leads, along with the FLARECAST data, algorithms and infrastructure, could help facilitate integrated space-weather forecasting efforts that take steps to avoid effort duplication. In spite of being one of the most intensive and systematic flare forecasting efforts to-date, FLARECAST has not managed to convincingly lift the barrier of stochasticity in solar flare occurrence and forecasting: solar flare prediction thus remains inherently probabilistic.

astro-ph.SR↗

arXiv2020

Differential Emission Measure Evolution as a Precursor of Solar Flares

We analyse the temporal evolution of the Differential Emission Measure (DEM) of solar active regions and explore its usage in solar flare prediction. The DEM maps are provided by the Gaussian Atmospheric Imaging Assembly (GAIA-DEM) archive, calculated assuming a Gaussian dependence of the DEM on the logarithmic temperature. We analyse time-series of sixteen solar active regions and a statistically significant sample of 9454 point-in-time observations corresponding to hundreds of regions observed during solar cycle 24. The time-series analysis shows that the temporal derivatives of the Emission Measure dEM/dt and the maximum DEM temperature dTmax/dt frequently exhibit high positive values a few hours before M- and X-class flares, indicating that flaring regions become brighter and hotter as the flare onset approaches. From the point-in-time observations we compute the conditional probabilities of flare occurrences using the distributions of positive values of the dEM/dt, and dTmax/dt and compare them with corresponding flaring probabilities of the total unsigned magnetic flux, a conventionally used, standard flare predictor. For C-class flares, conditional probabilities have lower or similar values with the ones derived for the unsigned magnetic flux, for 24 and 12 hours forecast windows. For M- and X-class flares, these probabilities are higher than those of the unsigned flux for higher parameter values. Shorter forecast windows improve the conditional probabilities of dEM/dt, and dTmax/dt in comparison to those of the unsigned magnetic flux. We conclude that flare forerunner events such as preflare heating or small flare activity prior to major flares reflect on the temporal evolution of EM and Tmax. Of these two, the temporal derivative of the EM could conceivably be used as a credible precursor, or short-term predictor, of an imminent flare.

astro-ph.SR↗

arXiv2020

Decoding the Pre-Eruptive Magnetic Field Configurations of Coronal Mass Ejections

A clear understanding of the nature of the pre-eruptive magnetic field configurations of Coronal Mass Ejections (CMEs) is required for understanding and eventually predicting solar eruptions. Only two, but seemingly disparate, magnetic configurations are considered viable; namely, sheared magnetic arcades (SMA) and magnetic flux ropes (MFR). They can form via three physical mechanisms (flux emergence, flux cancellation, helicity condensation) . Whether the CME culprit is an SMA or an MFR, however, has been strongly debated for thirty years. We formed an International Space Science Institute (ISSI) team to address and resolve this issue and report the outcome here. We review the status of the field across modeling and observations, identify the open and closed issues, compile lists of SMA and MFR observables to be tested against observations and outline research activities to close the gaps in our current understanding. We propose that the combination of multi-viewpoint multi-thermal coronal observations and multi-height vector magnetic field measurements is the optimal approach for resolving the issue conclusively. We demonstrate the approach using MHD simulations and synthetic coronal images. Our key conclusion is that the differentiation of pre-eruptive configurations in terms of SMAs and MFRs seems artificial. Both observations and modeling can be made consistent if the pre-eruptive configuration exists in a hybrid state that is continuously evolving from an SMA to an MFR. Thus, the 'dominant' nature of a given configuration will largely depend on its evolutionary stage (SMA-like early-on, MFR-like near the eruption).

astro-ph.SR↗

arXiv2020

The Solar Orbiter Science Activity Plan: translating solar and heliospheric physics questions into action

Solar Orbiter is the first space mission observing the solar plasma both in situ and remotely, from a close distance, in and out of the ecliptic. The ultimate goal is to understand how the Sun produces and controls the heliosphere, filling the Solar System and driving the planetary environments. With six remote-sensing and four in-situ instrument suites, the coordination and planning of the operations are essential to address the following four top-level science questions: (1) What drives the solar wind and where does the coronal magnetic field originate? (2) How do solar transients drive heliospheric variability? (3) How do solar eruptions produce energetic particle radiation that fills the heliosphere? (4) How does the solar dynamo work and drive connections between the Sun and the heliosphere? Maximising the mission's science return requires considering the characteristics of each orbit, including the relative position of the spacecraft to Earth (affecting downlink rates), trajectory events (such as gravitational assist manoeuvres), and the phase of the solar activity cycle. Furthermore, since each orbit's science telemetry will be downloaded over the course of the following orbit, science operations must be planned at mission level, rather than at the level of individual orbits. It is important to explore the way in which those science questions are translated into an actual plan of observations that fits into the mission, thus ensuring that no opportunities are missed. First, the overarching goals are broken down into specific, answerable questions along with the required observations and the so-called Science Activity Plan (SAP) is developed to achieve this. The SAP groups objectives that require similar observations into Solar Orbiter Observing Plans (SOOPs), resulting in a strategic, top-level view of the optimal opportunities for science observations during the mission lifetime.

astro-ph.SR↗

arXiv2020

Solar Flare Prediction Using Magnetic Field Diagnostics Above the Photosphere

In this article, we present the application of the weighted horizontal gradient of magnetic field (WGM) flare prediction method to 3-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 WGM is best exploited. The optimal height is where flare prediction, by means of the WGM method, is achieved earlier than at the photospheric level. 3D magnetic structures, based on potential and non-linear 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 WGM 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 WGM method between 1000 and 1800 km above the solar surface would improve the prediction of the flare onset time by around 2-8 hours.Certain caveats and an outlook for future work along these lines are also discussed.

astro-ph.SR↗

arXiv2018

On the evolution of pre-flare patterns of a 3-dimensional model of AR 11429

We apply a novel pre-flare tracking of sunspot groups towards improving the estimation of flare onset time by focusing on the evolution of the 3D magnetic field construction of AR 11429. The 3D magnetic structure is based on potential field extrapolation encompassing a vertical range from the photosphere through the chromosphere and transition region into the low corona. The basis of our proxy measure of activity prediction is the so-called weighted horizontal gradient of magnetic field (WG_M) defined between spots of opposite polarities close to the polarity inversion line of an active region. The temporal variation of the distance of the barycenter of the opposite polarities is also found to possess potentially important diagnostic information about the flare onset time estimation as function of height similar to its counterpart introduced initially in an application at the photosphere only in Korsos et al. (2015). We apply the photospheric pre-flare behavioural patterns of sunspot groups to the evolution of their associated 3D-constructed AR 11429 as function of height. We found that at a certain height in the lower solar atmosphere the onset time may be estimated much earlier than at the photosphere or at any other heights. Therefore, we present a tool and recipe that may potentially identify the optimum height for flare prognostic in the solar atmosphere allowing to improve our flare prediction capability and capacity.

astro-ph.SR↗

arXiv2017

A Helicity-Based Method to Infer the CME Magnetic Field Magnitude in Sun and Geospace: Generalization and Extension to Sun-Like and M-Dwarf Stars and Implications for Exoplanet Habitability

Patsourakos et al. (Astrophys. J. 817, 14, 2016) and Patsourakos and Georgoulis (Astron. Astrophys. 595, A121, 2016) introduced a method to infer the axial magnetic field in flux-rope coronal mass ejections (CMEs) in the solar corona and farther away in the interplanetary medium. The method, based on the conservation principle of magnetic helicity, uses the relative magnetic helicity of the solar source region as input estimates, along with the radius and length of the corresponding CME flux rope. The method was initially applied to cylindrical force-free flux ropes, with encouraging results. We hereby extend our framework along two distinct lines. First, we generalize our formalism to several possible flux-rope configurations (linear and nonlinear force-free, non-force-free, spheromak, and torus) to investigate the dependence of the resulting CME axial magnetic field on input parameters and the employed flux-rope configuration. Second, we generalize our framework to both Sun-like and active M-dwarf stars hosting superflares. In a qualitative sense, we find that Earth may not experience severe atmosphere-eroding magnetospheric compression even for eruptive solar superflares with energies ~ 10^4 times higher than those of the largest Geostationary Operational Environmental Satellite (GOES) X-class flares currently observed. In addition, the two recently discovered exoplanets with the highest Earth-similarity index, Kepler 438b and Proxima b, seem to lie in the prohibitive zone of atmospheric erosion due to interplanetary CMEs (ICMEs), except when they possess planetary magnetic fields that are much higher than that of Earth.

astro-ph.SR↗

arXiv2016

Near-Sun and 1 AU magnetic field of coronal mass ejections: A parametric study

Aims. The magnetic field of coronal mass ejections (CMEs) determines their structure, evolution, and energetics, as well as their geoeffectiveness. However, we currently lack routine diagnostics of the near-Sun CME magnetic field, which is crucial for determining the subsequent evolution of CMEs. Methods. We recently presented a method to infer the near-Sun magnetic field magnitude of CMEs and then extrapolate it to 1 AU. This method uses relatively easy to deduce observational estimates of the magnetic helicity in CME-source regions along with geometrical CME fits enabled by coronagraph observations. We hereby perform a parametric study of this method aiming to assess its robustness. We use statistics of active region (AR) helicities and CME geometrical parameters to determine a matrix of plausible near-Sun CME magnetic field magnitudes. In addition, we extrapolate this matrix to 1 AU and determine the anticipated range of CME magnetic fields at 1 AU representing the radial falloff of the magnetic field in the CME out to interplanetary (IP) space by a power law with index aB. Results. The resulting distribution of the near-Sun (at 10 Rs ) CME magnetic fields varies in the range [0.004, 0.02] G, comparable to, or higher than, a few existing observational inferences of the magnetic field in the quiescent corona at the same distance. We also find that a theoretically and observationally motivated range exists around aB = -1.6 +-0.2, thereby leading to a ballpark agreement between our estimates and observationally inferred field magnitudes of magnetic clouds (MCs) at L1. Conclusions. In a statistical sense, our method provides results that are consistent with observations.

astro-ph.SR↗

arXiv2016

A Comparison of Flare Forecasting Methods, I: Results from the "All-Clear" Workshop

Solar flares produce radiation which can have an almost immediate effect on the near-Earth environment, making it crucial to forecast flares in order to mitigate their negative effects. The number of published approaches to flare forecasting using photospheric magnetic field observations has proliferated, with varying claims about how well each works. Because of the different analysis techniques and data sets used, it is essentially impossible to compare the results from the literature. This problem is exacerbated by the low event rates of large solar flares. The challenges of forecasting rare events have long been recognized in the meteorology community, but have yet to be fully acknowledged by the space weather community. During the interagency workshop on "all clear" forecasts held in Boulder, CO in 2009, the performance of a number of existing algorithms was compared on common data sets, specifically line-of-sight magnetic field and continuum intensity images from MDI, with consistent definitions of what constitutes an event. We demonstrate the importance of making such systematic comparisons, and of using standard verification statistics to determine what constitutes a good prediction scheme. When a comparison was made in this fashion, no one method clearly outperformed all others, which may in part be due to the strong correlations among the parameters used by different methods to characterize an active region. For M-class flares and above, the set of methods tends towards a weakly positive skill score (as measured with several distinct metrics), with no participating method proving substantially better than climatological forecasts.

astro-ph.SR↗

arXiv2014

Validation of the magnetic energy vs. helicity scaling in solar magnetic structures

We assess the validity of the free magnetic energy - relative magnetic helicity diagram for solar magnetic structures. We used two different methods of calculating the free magnetic energy and the relative magnetic helicity budgets: a classical, volume-calculation nonlinear force-free (NLFF) method applied to finite coronal magnetic structures and a surface-calculation NLFF derivation that relies on a single photospheric or chromospheric vector magnetogram. Both methods were applied to two different data sets, namely synthetic active-region cases obtained by three-dimensional magneto-hydrodynamic (MHD) simulations and observed active-region cases, which include both eruptive and noneruptive magnetic structures. The derived energy--helicity diagram shows a consistent monotonic scaling between relative helicity and free energy with a scaling index 0.84$\pm$0.05 for both data sets and calculation methods. It also confirms the segregation between noneruptive and eruptive active regions and the existence of thresholds in both free energy and relative helicity for active regions to enter eruptive territory. We consider the previously reported energy-helicity diagram of solar magnetic structures as adequately validated and envision a significant role of the uncovered scaling in future studies of solar magnetism.

astro-ph.SR↗

arXiv2014

Validation and Benchmarking of a Practical Free Magnetic Energy and Relative Magnetic Helicity Budget Calculation in Solar Magnetic Structures

In earlier works we introduced and tested a nonlinear force-free (NLFF) method designed to self-consistently calculate the free magnetic energy and the relative magnetic helicity budgets of the corona of observed solar magnetic structures. The method requires, in principle, only a single, photospheric or low-chromospheric, vector magnetogram of a quiet-Sun patch or an active region and performs calculations in the absence of three-dimensional magnetic and velocity-field information. In this work we strictly validate this method using three-dimensional coronal magnetic fields. Benchmarking employs both synthetic, three-dimensional magnetohydrodynamic simulations and nonlinear force-free field extrapolations of the active-region solar corona. We find that our time-efficient NLFF method provides budgets that differ from those of more demanding semi-analytical methods by a factor of ~3, at most. This difference is expected from the physical concept and the construction of the method. Temporal correlations show more discrepancies that, however, are soundly improved for more complex, massive active regions, reaching correlation coefficients of the order of, or exceeding, 0.9. In conclusion, we argue that our NLFF method can be reliably used for a routine and fast calculation of free magnetic energy and relative magnetic helicity budgets in targeted parts of the solar magnetized corona. As explained here and in previous works, this is an asset that can lead to valuable insight into the physics and the triggering of solar eruptions.

astro-ph.SR↗