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We investigate the effect of data-driving on flux rope eruptivity in magnetic field simulations by analysing fully data-driven modelling results of active region (AR) 12473 and AR11176, as well as preforming relaxation runs for AR12473 (found to be eruptive). Here, the driving is switched off systematically at different time steps. We analyse the behaviour of fundamental quantities, essential for understanding the eruptivity of magnetic flux ropes (MFRs). The data-driven simulations are carried out with the time-dependent magnetofrictional model (TMFM) for AR12473 and AR11176. For the relaxation runs, we employ the magnetofrictional method (MFM) and a zero-beta magnetohydrodynamic (MHD) model to investigate how significant the differences between the two relaxation procedures are when started from the same initial conditions. To determine the eruptivity of the MFRs, we calculate characteristic geometric properties, such as the cross-section, MFR height along with stability parameters, such as MFR twist and the decay index. For eruptive cases, we investigate the effect of sustained driving beyond the point of eruptivity on the MFR properties. We find that the fully-driven AR12473 MFR is eruptive while the AR11176 MFR is not. For the relaxation runs, we find that the MFM MFRs are eruptive when the driving is stopped around the flare time or later, while the MHD MFRs show eruptive behaviour even if the driving is switched off one and a half days before the flare occurs. We find that characteristic MFR properties can vary greatly even for the eruptive cases of different relaxation simulations. The results suggest that data driving can significantly influence the evolution of the eruption, with differences appearing even when the relaxation time is set to later stages of the simulation when the MFRs have already entered an eruptive phase., Comment: Accepted for publication at A&A

Investigating the early-stage evolution of an erupting flux rope from the Sun is important to understand the mechanisms of how it looses its stability and its space weather impacts. Our aim is to develop an efficient scheme for tracking the early dynamics of erupting solar flux ropes and use the algorithm to analyse its early-stage properties. The algorithm is tested on a data-driven simulation of an eruption that took place in active region AR12473. We investigate the modelled flux rope's footpoint movement and magnetic flux evolution and compare with observational data from the Solar Dynamics Observatory's Atmospheric Imaging Assembly in the 211 $\unicode{x212B}$ and 1600 $\unicode{x212B}$ channels. To carry out our analysis, we use the time-dependent data-driven magnetofrictional model (TMFM). We also perform another modelling run, where we stop the driving of the TMFM midway through the flux rope's rise through the simulation domain and evolve it instead with a zero-beta magnetohydrodynamic (MHD) approach. The developed algorithm successfully extracts a flux rope and its ascend through the simulation domain. We find that the movement of the modelled flux rope footpoints showcases similar trends in both TMFM and relaxation MHD run: they recede from their respective central location as the eruption progresses and the positive polarity footpoint region exhibits a more dynamic behaviour. The ultraviolet brightenings and extreme ultraviolet dimmings agree well with the models in terms of their dynamics. According to our modelling results, the toroidal magnetic flux in the flux rope first rises and then decreases. In our observational analysis, we capture the descending phase of toroidal flux. In conclusion, the extraction algorithm enables us to effectively study the flux rope's early dynamics and derive some of its key properties such as footpoint movement and toroidal magnetic flux., Comment: Accepted for publication in Astronomy & Astrophysics

Alfv\'en-wave turbulence has emerged as an important heating mechanism to accelerate the solar wind. The generation of this turbulent heating is dependent on the presence and subsequent interaction of counter-propagating alfv\'en waves. This requires us to understand the propagation and evolution of alfv\'en waves in the solar wind in order to develop an understanding of the relationship between turbulent heating and solar-wind parameters. We aim to study the response of the solar wind upon injecting monochromatic single-frequency alfv\'en waves at the base of the corona for various magnetic flux-tube geometries. We used an ideal magnetohydrodynamic (MHD) model using an adiabatic equation of state. An Alfv\'en pump wave was injected into the quiet solar wind by perturbing the transverse magnetic field and velocity components. Alfv\'en waves were found to be reflected due to the development of the parametric decay instability (PDI). Further investigation revealed that the PDI was suppressed both by efficient reflections at low frequencies as well as magnetic flux-tube geometries., Comment: 10 pages, 7 figures. Accepted for publication in Astronomy & Astrophysics

Modeling fast solar wind based on the kinetic theory is an important task for scientists. In this paper, we present a two-fluid model for fast solar wind with anisotropic Kappa-Maxwellian electrons and Bi-Maxwellian protons. In the simulation, the energy exchange between the plasma particles and low-frequency Alfv\'en waves is considered. A set of eleven coupled equations is derived by applying the zeroth- to fourth-order moments of the Vlasov equation and the modified electromagnetic Maxwell equations. A characteristic of the Kappa distribution (indicated by $\kappa$ index) is explicit in the equation for the parallel component of the electron heat flux (parallel to the ambient magnetic field line) and differs from the equation derived for the proton heat flux due to the different nature of the distributions. Within the large $\kappa$ index, the equations for the two-fluid model tend to the equations obtained by the Maxwellian distribution. Using an iterated Crank-Nicolson method, the coupled equations are numerically solved for the fast solar wind conditions. We show that at (0.3 - 1) AU from the Sun, the electron density, components of temperature, and components of heat flux follow the power-law behavior. We also showed that near the Earth, the flow speed (electron or proton) increases with decreasing $\kappa$. We concluded that applying the small $\kappa$ index (the non-Maxwellian distribution), the extraordinary nature of the solar atmosphere, with its temperature of several million kelvin temperature for electrons, has been captured., Comment: 37 pages, 7 figures

Here, we developed a complex network of solar active regions (ARs) to study various local and global properties of the network. The values of the Hurst exponent ($0.8-0.9$) were evaluated by both the detrended fluctuation analysis and the rescaled range analysis applied on the time series of the AR numbers. The findings suggest that ARs can be considered as a system of self-organized criticality. We constructed a growing network based on locations, occurrence times, and the lifetimes of 4,227 ARs recorded from 1 January 1999 to 14 April 2017. The behaviour of the clustering coefficient shows that the ARs network is not a random network. The logarithmic behaviour of the length scale has the characteristics of a so-called \textquotedblleft small-world network\textquotedblright. It is found that the probability distribution of the node degrees for undirected networks follows the power-law with exponents of about 3.7 to 4.2. This indicates the scale-free nature of the ARs network. The scale-free and small-world properties of the ARs network confirm that the system of ARs forms a system of self-organized criticality. Our results show that the occurrence probability of flares (classified by GOES class C $> 5$, M, and X flares) in the position of the ARs network hubs take values greater than that obtained for other nodes.