arXiv subjects

Luis Linan

Publications and source records attributed to Luis Linan.

17 recordsLinked to original sources

arXiv2026

COCONUT: Toward practical time-evolving Sun-to-Earth magnetohydrodynamic modeling

Due to computational efficiency and numerical stability limitations, coronal simulations constrained by static magnetograms are typically performed first and then used to drive inner-heliosphere (IH) models. In this paper, we calculate the Sun-to-Earth coronal and wind evolutions using a single time-evolving MHD model, showing that implicit MHD models have the potential to meaningfully simplify and improve the overall Sun-to-Earth modelling pipeline. We extend the implicit time-evolving coronal MHD model COCONUT out to 1 AU, and utilise it to investigate solar coronal and wind evolutions around a solar maximum Carrington rotation (CR). We compare quasi-steady-state and time-evolving Sun-to-Earth simulations to evaluate the impact of the inner-boundary magnetic field evolution, which is neglected in steady-state simulations, on background plasma parameters. Comparisons with commonly used coupled Sun-to-Earth simulations are also conducted to further validate and assess the Sun-to-Earth model COCONUT. The results show that the time-evolving implicit MHD modelling approach yields noticeable differences compared to oversimplified steady-state simulations, and is efficient enough for practical applications. Modelling the solar corona and wind using a single MHD model simplifies the modelling pipeline and avoids uncertainties associated with coupling different coronal and IH models. The noticeable differences in the temporal evolution of plasma parameters at the L1 and L5 points highlight the need to use continuously evolving, synchronised magnetic field observations to improve global coronal and solar wind simulations, whereas the overall consistent evolutionary trend reveals the reliability of using L5 observations to forecast solar wind conditions near Earth about four days in advance.

astro-ph.SR↗

arXiv2026

MHD modeling of magnetic flux evolution around solar maximum by the coronal model COCONUT

In this paper, we simulate the magnetic flux evolution at different heliocentric distances during two solar-maximum Carrington rotations (CRs) using the time-evolving coronal magnetohydrodynamic (MHD) model COCONUT to investigate the ``open flux problem". The simulated open magnetic flux (OMF) near the solar surface is comparable to that derived from \textit{in situ} observations by PSP and WIND satellites, and is about 5 times larger than that derived from SDO coronal hole (CH) observations, and the variation in the simulated radial solar wind speed is consistent with the evolution of the OMF evaluated around the corresponding solar disk center. We find that the OMF is reduced by up to $45\%$ from 1.01~$R_s$ to 0.1~AU and increases with a higher-resolution mesh. The OMF decreases mainly within 3~$R_s$, where the closed magnetic flux drops more rapidly, from about $60\%$ of the total magnetic flux at 1.01~$R_s$ to about $4\%$ at 3~$R_s$. Moderate adjustment of the heating source term can effectively regulate the simulated OMF. Preprocessing the photospheric magnetograms with a potential field solver that removes many high-order spherical harmonic components reduces the OMF in the low corona, while having little impact beyond 3~$R_s$. Additionally, the ratio of the maximum to the minimum OMF can reach 1.4 during a single solar maximum CR. These findings highlight the necessity of considering higher grid resolution, more realistic heating mechanisms, and the time-evolving regime of coronal MHD modeling when further addressing the ``open flux problem".

astro-ph.SR↗

arXiv2025

Rotation of flux ropes in the low corona

Eruptions of filaments are defined by different parameters, specially, sigmoid handedness and direction of the eruption, which are important parameters for forecasting the geoeffectiveness of consequent interplanetary coronal mass ejection (ICME) or magnetic cloud. Solar filaments often exhibit rotation and deflection during eruptions, which would significantly affect the geoeffectiveness of the coronal mass ejections (CMEs). Therefore, understanding the mechanisms that lead to such lateral displacement of filaments is a great concern to space weather forecasting. Two case studies are discussed. Firstly, the events of September 8 and September 10 2014, were analyzed from the Sun to the Earth. The numerical heliospheric simulation EUHFORIA shows that the handedness of the EUV sigmoid deduced from coronagraph observations was different from the tilt of the ICME at 1~au, suggesting a rotation of the CME in the low corona. A potential undetected low coronal rotation led to erroneous space weather prediction. The second event concerns a filament observed on August 20 2021, which underwent a rotation of 73 degrees during its eruption, implying a significant lateral drifting of the filament material. A data-constrained magnetohydrodynamic (MHD) simulation confirms such a rotation. These two studies reinforce the idea that CMEs are subjected to more significant rotation and deflection in the low corona than during their journey in the heliosphere.

astro-ph.SR↗

arXiv2025

COCONUT: A coronal model with an energy decomposition strategy

In this paper, we propose an energy decomposition method combined with an HLL Riemann solver that includes an additional dissipation term in the energy equation to improve the numerical stability of the fully implicit, time-evolving coronal model COCONUT and extend its applicability to solar-maximum phases. In MHD simulations that evolve conservative variables in time, the thermal pressure is typically computed by subtracting the magnetic and kinetic energies from the total energy. In low-beta (the ratio of thermal to magnetic pressure; $< 10^{-3}$) regions, discretization errors of magnetic energy can be comparable to the thermal pressure, potentially leading to negative thermal pressure and causing the simulation to crash. Therefore, we update the decomposed energy, excluding the magnetic energy, at each time step. It avoids subtracting a large magnetic energy from the total energy to obtain a very small thermal pressure in low-$\beta$ regions, thereby improving the numerical stability of MHD models. We validate the algorithm using a time-evolving solar-maximum Carrington rotation simulation in 2025, which the previous code failed to run to completion. We also perform quasi-steady-state coronal simulations and 2D benchmark tests to further assess the algorithm's performance. The simulation results show that the algorithm produces results nearly identical to those obtained using the traditional full energy equation during solar minimum, while significantly improving COCONUT's ability to simulate coronal evolution under strong magnetic fields, even including fields exceeding 100 Gauss with $\beta<10^{-3}$. This method provides a promising approach for performing quasi-realistic coronal simulations during solar maxima.

astro-ph.SR↗

arXiv2025

Modelling gyrosynchrotron emission from coronal energetic electrons in a CME flux rope

Solar flares and coronal mass ejections (CMEs) can accelerate electrons, causing bursts such as type IV emissions in the solar radio continuum. Although radio spectroscopy is a powerful diagnostic tool for the corona, the origin and mechanisms of type IV bursts remain uncertain. In situ measurements can occasionally shed some light on these mechanisms, but they are limited in space and time. Sophisticated numerical modelling offers the best approach to improve our understanding of the physical processes involved. This research examines type IV radio bursts, exploring the effects of various electron distribution properties and CMEs on their generation and characteristics. To transcend idealised assumptions, we employ realistic, anisotropic electron distributions - obtained from particle transport simulations within complex magnetohydrodynamic (MHD) environments - as input for radio emission models. We use the 3D MHD model COCONUT to generate coronal background configurations, including a CME modelled as a modified Titov-D\'{e}moulin magnetic flux rope (MFR). These MHD simulations are used by the PARADISE particle transport code, which injects energetic electrons into the MFR and tracks their evolution. Finally, we feed the electron distributions and solar wind parameters into the Ultimate Fast Gyrosynchrotron (GS) Codes to compute radio emission along lines of sight. Electrons injected close to the MFR's central axis remain largely confined, producing a GS emission spectrum resembling observed type IV characteristics. Varying observer positions, CME properties, and spectral indices of the electron energy distributions modify the intensities and durations of the observed bursts. The strongest GS emission is observed to originate from the CME flanks. Our results indicate that GS emission is the major component in type IV spectra, although additional contributors cannot be ruled out.

astro-ph.SR↗

arXiv2025

SIP-IFVM: An observation-based magnetohydrodynamic model of coronal mass ejection

Currently, achieving a balance between computational efficiency, accuracy, and numerical stability in CME simulations, particularly in the sub-Alfv{'e}nic coronal region, remains a significant challenge. This paper aims to address the challenge by integrating observational data and developing advanced numerical algorithms, focusing on reproducing large-scale CME evolutions that are consistent with observations in the coronal region. Based on the recently developed fully implicit thermodynamic MHD coronal model (Wang et al. 2025a), we further use an observation-based RBSL flux rope to trigger a CME event during CR 2111. Additionally, we improve the temporal accuracy using a 2nd-order accurate ESDIRK2 method, with the intermediate stage solutions computed by the 2nd-order accurate BDF2 pseudo-time marching method. To enhance the numerical stability of ESDIRK2, we apply approximate linearisation in the implicitly solved intermediate stages. Furthermore, we adjust the time-evolving magnetic field B1 to zero at the end of each physical time step to further validate the extended magnetic field decomposition approach proposed by (Wang et al. 2025a). It is noticed that the model successfully reproduces the CME evolution consistent with white-light coronagraph observations, enables faster-than-real-time CME propagation simulations from solar surface to 0.1 AU using only a few dozen CPU cores on approximately 1 million grid cells, and remains numerically stable in CME simulations involving low-\b{eta} regions. The simulation results show that this novel MHD coronal model, combined with an observation-based magnetic flux rope, is sufficiently numerically stable and computationally efficient to reproduce real CME events propagating through the sub-Alfv{\'e}nic coronal region. Thus, the observation-based CME model is well suited for practical applications in daily space weather forecasting.

astro-ph.SR↗

arXiv2025

Time-evolving coronal modelling of the solar maximum around the solar storms in May 2024 by COCONUT

Time-evolving MHD coronal models deliver more realistic results than traditional quasi-steady-state models. The fully implicit time-evolving coronal model COCONUT performs efficiently enough for real-time coronal simulations during solar minimum. However, during solar maxima, the coronal magnetic field is more complex and stronger, and coronal structures evolve more rapidly than during solar minima. Time-evolving MHD coronal modelling of solar maxima often struggles with poor numerical stability and low computational efficiency. We enhanced the numerical stability of the time-evolving coronal model COCONUT to mitigate these issues with the aim to evaluate the differences between the time-evolving and quasi-steady-state coronal simulation results, and to assess the impact of the spatial resolution on global MHD coronal modelling of solar maxima. After enhancing the positivity-preserving property of COCONUT, we employed it to simulate the evolution of coronal structures within 0.1 AU in an inertial coordinate system over two CRs around the solar storms in May 2024. These simulations were performed on unstructured geodesic meshes containing 6.06, 1.52, and 0.38 M cells. We also conducted a quasi-steady-state coronal simulation that treated the solar surface as a rigidly rotating spherical shell. A comparison with observations further validated the reliability of the time-evolving coronal modelling technique. It shows that incorporating the evolution of the magnetic field on the solar surface can significantly improve the fidelity of global MHD coronal simulations around a solar maximum. A simulated magnetic field strength using a mesh with 6.06 M cells can be stronger by more than 40% than that in a mesh with 0.38 M cells. The fully implicit time-evolving model COCONUT shows promise for accurately conducting real-time global coronal simulations of solar maxima.

astro-ph.SR↗

arXiv2025

SIP-IFVM: A time-evolving coronal model with an extended magnetic field decomposition strategy

Time-evolving magnetohydrodynamic (MHD) coronal modeling, driven by a series of time-dependent photospheric magnetograms, represents a new generation of coronal simulations. This approach offers greater realism compared to traditional coronal models constrained by a static magnetogram. However, its practical application is seriously limited by low computational efficiency and poor numerical stability. Therefore, we propose an extended magnetic field decomposition strategy and implement it in the implicit MHD model to develop a coronal model that is both efficient and numerically stable enough for simulating the long-term evolutions of the global corona. The traditional decomposition strategies split the magnetic field into a time-invariant potential field and a time-dependent component $\mathbf{B}_1$. It works well for quasi-steady-state coronal simulations where $\left|\mathbf{B}_1\right|$ is typically small. However, as the inner-boundary magnetic field evolves, $\left|\mathbf{B}_1\right|$ can grow significantly larger and its discretization errors often lead to nonphysical negative thermal pressure, ultimately causing the code to crash. In this paper, we mitigate such undesired situations by introducing a temporally piecewise-constant variable to accommodate part of the non-potential field and remain $\left|\mathbf{B}_1\right|$ consistently small throughout the simulations. We incorporate this novel magnetic field decomposition strategy into our implicit MHD coronal model and apply it to simulate the evolution of coronal structures within 0.1 AU over two solar-maximum Carrington rotations. The results show that this coronal model effectively captures observations and performs more than 80 times faster than real time using only 192 CPU cores, making it well-suited for practical applications in simulating the time-evolving corona.

astro-ph.SR↗

arXiv2024

Cross-Field Diffusion Effects on Particle Transport in a Solar Coronal Flux Rope

Solar energetic particles (SEPs) associated with solar flares and coronal mass ejections (CMEs) are key agents of space weather phenomena, posing severe threats to spacecraft and astronauts. Recent observations by Parker Solar Probe (PSP) indicate that the magnetic flux ropes of a CME can trap energetic particles and act as barriers, preventing other particles from crossing. In this paper, we introduce the novel COCONUT+PARADISE model to investigate the confinement of energetic particles within a flux rope and the effects of cross-field diffusion (CFD) on particle transport in the solar corona, particularly in the presence of a CME. Using the global magnetohydrodynamic coronal model COCONUT, we generate background configurations containing a CME modeled as a Titov-D\'emoulin flux rope (TDFR). We then utilize the particle transport code PARADISE to inject monoenergetic 100 keV protons inside one of the TDFR legs near its footpoint and evolve the particles through the COCONUT backgrounds. To study CFD, we employ two different approaches regarding the perpendicular proton mean free path (MFP): a constant MFP and a Larmor radius-dependent MFP. We contrast these results with those obtained without CFD. While particles remain fully trapped within the TDFR without CFD, we find that even relatively small perpendicular MFP values allow particles on the outer layers to escape. In contrast, the initially interior trapped particles stay largely confined. Finally, we highlight how our model and this paper's results are relevant for future research on particle acceleration and transport in an extended domain encompassing both the corona and inner heliosphere.

astro-ph.SR↗

arXiv2024

Efficient magnetohydrodynamic modelling of the time-evolving corona by COCONUT

Compared to quasi-steady-state corona models that are constrained by a time-invariant magnetogram over a CR period, time-evolving corona models driven by time-varying photospheric magnetograms are more realistic and can maintain more useful information to accurately describe solar wind evolution and forecast CME propagation. This paper demonstrate that time-evolving corona simulations can be performed efficiently and accurately using an implicit method with relatively large time steps. We also evaluate differences between coronal structures captured by time-evolving and quasi-steady simulations over a CR period during solar minimum. We used a series of hourly updated photospheric magnetograms to drive the evolution of coronal structures from the solar surface to $25\; R_s$ during two CRs around the 2019 eclipse in an inertial coordinate system. We compare the time-evolving and quasi-steady simulations to demonstrate that the differences in these two types of coronal modelling can be obvious even for a solar minimum. The relative differences in radial velocity and density can be over $15 \%$ and $25 \%$ at 20$\;R_s$ during one CR period. We also evaluated the impact of time steps on the simulation results. Using a time step of approximately 10 minutes balances efficiency and necessary numerical stability and accuracy for time-evolving corona simulations around solar minima, with coronal evolution during a full CR simulated within only 9 hours (using 1080 CPU cores for 1.5M grid cells). The simulation results demonstrate that time-evolving MHD coronal simulations can be performed efficiently and accurately using an implicit method, offering a more realistic alternative to quasi-steady-state simulations. The fully implicit time-evolving corona model thus promises to simulate the time-evolving corona accurately in practical space weather forecasting.

astro-ph.SR↗

arXiv2024

Toroidal modified Miller-Turner CME model in EUHFORIA: II. Validation and comparison with flux rope and spheromak

Rising concerns about the impact of space weather-related disruptions demand modelling and reliable forecasting of coronal mass ejection (CME) impacts. In this study, we demonstrate the application of the modified Miller-Turner (mMT) model implemented in EUropean Heliospheric FORecasting Information Asset (EUHFORIA), to forecast the geo-effectiveness of observed coronal mass ejection (CME) events in the heliosphere. The goal is to develop a model that not only has a global geometry to improve overall forecasting but is also fast enough for operational space weather forecasting. We test the original full torus implementation and introduce a new three-fourth Torus version called the Horseshoe CME model. This new model has a more realistic CME geometry, and it overcomes the inaccuracies of the full torus geometry. We constrain the torus geometrical and magnetic field parameters using observed signatures of the CMEs before, during, and after the eruption. The assessment of the model's capability to predict the most important Bz component is performed using the advanced Dynamic Time Warping technique. The Horseshoe model prediction of CME arrival time and geo-effectiveness for both validation events compare well to the observations and are weighed with the results obtained with the spheromak and FRi3D models that were already available in EUHFORIA. The runtime of the Horseshoe model simulations is close to that of the spheromak model, which is suitable for operational space weather forecasting. Yet, the capability of the magnetic field prediction at 1~AU of the Horseshoe model is close to that of the FRi3D model. In addition, we demonstrate that the Horseshoe CME model can be used for simulating successive CMEs in EUHFORIA, overcoming a limitation of the FRi3D model.

physics.space-ph↗

arXiv2024

The operationally ready full three-dimensional magnetohydrodynamic (3D MHD) model from the Sun to Earth: COCONUT+Icarus

Solar wind modelling has become a crucial area of study due to the increased dependence of modern society on technology, navigation, and power systems. Accurate space weather forecasts can predict upcoming threats to Earth's geospace. In this study, we examine a novel full magnetohydrodynamic (MHD) chain from the Sun to Earth. The goal of this study is to demonstrate the capabilities of the full MHD modelling chain from the Sun to Earth by finalising the implementation of the full MHD coronal model into the COolfluid COroNa UnsTructured (COCONUT) model and coupling it to the MHD heliospheric model Icarus. The resulting coronal model has significant advantages compared to the pre-existing polytropic alternative, as it models a more realistic bi-modal wind, which is crucial for heliospheric studies. In this study, only thermal conduction, radiative losses, and approximated coronal heating function were considered in the energy equation. A realistic specific heat ratio was applied. The output of the coronal model was used to onset the 3D MHD heliospheric model Icarus. A minimum solar activity case was chosen as the first test case for the full MHD model. The numerically simulated data in the corona and the heliosphere were compared to observational products. We present a first attempt to obtain the full MHD chain from the Sun to Earth with COCONUT and Icarus. The coronal model has been upgraded to a full MHD model for a realistic bi-modal solar wind configuration. The approximated heating functions have modelled the wind reasonably well, but simple approximations are not enough to obtain a realistic density-speed balance or realistic features in the low corona and farther, near the outer boundary. The full MHD model was computed in 1.06 h on 180 cores of the Genius cluster of the Vlaams Supercomputing Center, which is only 1.8 times longer than the polytropic simulation.

astro-ph.SR↗

arXiv2020

Additivity of relative magnetic helicity in finite volumes

Relative magnetic helicity is conserved by magneto-hydrodynamic evolution even in the presence of moderate resistivity. For that reason, it is often invoked as the most relevant constraint to the dynamical evolution of plasmas in complex systems, such as solar and stellar dynamos, photospheric flux emergence, solar eruptions, and relaxation processes in laboratory plasmas. However, such studies often indirectly imply that relative magnetic helicity in a given spatial domain can be algebraically split into the helicity contributions of the composing subvolumes, i.e., that it is an additive quantity. A limited number of very specific applications have shown that this is not the case. Progress in understanding the non-additivity of relative magnetic helicity requires removal of restrictive assumptions in favour of a general formalism that can be used both in theoretical investigations as well as in numerical applications. We derive the analytical gauge-invariant expression for the partition of relative magnetic helicity between contiguous finite-volumes, without any assumptions on either the shape of the volumes and interface, or the employed gauge. The non-additivity of relative magnetic helicity in finite volumes is proven in the most general, gauge-invariant formalism, and verified numerically. More restrictive assumptions are adopted to derive known specific approximations, yielding a unified view of the additivity issue. As an example, the case of a flux rope embedded in a potential field shows that the non-additivity term in the partition equation is, in general, non-negligible. The relative helicity partition formula can be applied to numerical simulations to precisely quantify the effect of non-additivity on global helicity budgets of complex physical processes.

astro-ph.SR↗

arXiv2020

Energy and helicity fluxes in line-tied eruptive simulations

Based on a decomposition of the magnetic field into potential and nonpotential components, magnetic energy and relative helicity can both also be decomposed into two quantities: potential and free energies, and volume-threading and current-carrying helicities. In this study, we perform a coupled analysis of their behaviors in a set of parametric 3D magnetohydrodynamic (MHD) simulations of solar-like eruptions. We present the general formulations for the time-varying components of energy and helicity in resistive MHD. We calculated them numerically with a specific gauge, and compared their behaviors in the numerical simulations, which differ from one another by their imposed boundary-driving motions. Thus, we investigated the impact of different active regions surface flows on the development of the energy and helicity-related quantities. Despite general similarities in their overall behaviors, helicities and energies display different evolutions that cannot be explained in a unique framework. While the energy fluxes are similar in all simulations, the physical mechanisms that govern the evolution of the helicities are markedly distinct from one simulation to another: the evolution of volume-threading helicity can be governed by boundary fluxes or helicity transfer, depending on the simulation. The eruption takes place for the same value of the ratio of the current-carrying helicity to the total helicity in all simulations. However, our study highlights that this threshold can be reached in different ways, with different helicity-related processes dominating for different photospheric flows. This means that the details of the pre-eruptive dynamics do not influence the eruption-onset helicity-related threshold. Nevertheless, the helicity-flux dynamics may be more or less efficient in changing the time required to reach the onset of the eruption.

astro-ph.SR↗

arXiv2019

On the reliability of magnetic energy and helicity computations based on nonlinear force-free coronal magnetic field models

We demonstrate the sensitivity of magnetic energy and helicity computations regarding the quality of the underlying coronal magnetic field model. We apply the method of Wiegelmann & Inhester (2010) to a series of SDO/HMI vector magnetograms, and discuss nonlinear force-free (NLFF) solutions based on two different sets of the free model parameters. The two time series differ from each other concerning their force-free and solenoidal quality. Both force- and divergence-freeness are required for a consistent NLFF solution. Full satisfaction of the solenoidal property is inherent in the definition of relative magnetic helicity in order to insure gauge-independence. We apply two different magnetic helicity computation methods (Thalmann et al. 2011; Valori et al. 2012) to both NLFF time series and find that the output is highly dependent on the level to which the NLFF magnetic fields satisfy the divergence-free condition, with the computed magnetic energy being less sensitive than the relative helicity. Proxies for the non-potentiality and eruptivity derived from both quantities are also shown to depend strongly on the solenoidal property of the NLFF fields. As a reference for future applications, we provide quantitative thresholds for the force- and divergence-freeness, for the assurance of reliable computation of magnetic energy and helicity, and of their related eruptivity proxies.

astro-ph.SR↗

arXiv2018

Time variations of the non-potential and volume-threading magnetic helicities

Relative magnetic helicity is a gauge invariant quantity suitable for the study of the magnetic helicity content of heliospheric plasmas. Relative magnetic helicity can be decomposed uniquely into two gauge invariant quantities, the magnetic helicity of the non-potential component of the field, and a complementary volume-threading helicity. Recent analysis of numerical experiments simulating the generation of solar eruptions have shown that the ratio of the non-potential helicity to the total relative helicity is a clear marker of the eruptivity of the magnetic system, and that the high value of that quantity could be a sufficient condition for the onset of the instability generating the eruptions. The present study introduces the first analytical examination of the time variations of these non-potential and volume-threading helicities. The validity of the analytical formulas derived are confirmed with analysis of three-dimensional (3D) magnetohydrodynamics (MHD) simulations of solar coronal dynamics. Both the analytical investigation, and the numerical application show that, unlike magnetic helicity, the non-potential and the volume-threading helicities are not conserved quantities, even in the ideal MHD regime. A term corresponding to the transformation between the non-potential and volume-threading helicities frequently dominates their dynamics. This finding has an important consequence for their estimation in the solar corona: unlike with relative helicity, their volume coronal evolution cannot be ascertained by the flux of these quantities through the volume's boundaries. Only techniques extrapolating the 3D coronal field will enable both the proper study of the non-potential and volume-threading helicities, and the observational analysis of helicity-based solar-eruptivity proxies.

astro-ph.SR↗

arXiv2018

Threshold of non-potential magnetic helicity ratios at the onset of solar eruptions

The relative magnetic helicity is a quantity that is often used to describe the level of entanglement of non-isolated magnetic fields, such as the magnetic field of solar active regions.The aim of this paper is to investigate how different kinds of photospheric boundary flows accumulate relative magnetic helicity in the corona and if and how-well magnetic helicity related quantities identify the onset of an eruption. We use a series of three-dimensional, parametric magnetohydrodynamic simulations of the formation and eruption of magnetic flux ropes. All the simulations are performed on the same grid, using the same parameters, but they are characterized by different driving photospheric flows, i.e., shearing, convergence, stretching, peripheral- and central- dispersion flows. For each of the simulations, the instant of the onset of the eruption is carefully identified by using a series of relaxation runs. We find that magnetic energy and total relative helicity are mostly injected when shearing flows are applied at the boundary, while the magnetic energy and helicity associated with the coronal electric currents increase regardless of the kind of photospheric flows. We also find that, at the onset of the eruptions, the ratio between the non-potential magnetic helicity and the total relative magnetic helicity has the same value for all the simulations, suggesting the existence of a threshold in this quantity. Such threshold is not observed for other quantities as, for example, those related to the magnetic energy.

astro-ph.SR↗