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 4,227ARs 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 "small-world network". 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.Corresponding author: Hossein Safari safari@znu.ac.ir Daei, Safari, and Dadashi

Context. Alfvén-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 Alfvén waves. This requires us to understand the propagation and evolution of Alfvén waves in the solar wind in order to develop an understanding of the relationship between turbulent heating and solar-wind parameters. Aims. We aim to study the response of the solar wind upon injecting monochromatic single-frequency Alfvén waves at the base of the corona for various magnetic flux-tube geometries. Methods. We used an ideal magnetohydrodynamic model using an adiabatic equation of state. An Alfvén pump wave was injected into the quiet solar wind by perturbing the transverse magnetic field and velocity components. Results. Alfvén 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.

Context. The data-driven and time-dependent modeling of coronal magnetic fields is crucial for understanding solar eruptions. These efforts are complicated by the challenges of finding a balance between physical realism and computing efficiency. One possible technique is to couple two modeling approaches. Aims. Our aim here is to showcase our progress in using time-dependent magnetofrictional model (TMFM) results as input to dynamical magnetohydrodynamic (MHD) simulations. However, due to the different evolution processes in these two models, using TMFM snapshots in an MHD simulation is nontrivial. We address these issues, both physically and numerically, discuss the incompatibility of the TMFM output to serve as the initial condition in MHD simulations, and show our methods of mitigating this. The evolution of the flux systems and the cause of the eruption are investigated. Methods. TMFM is a prevalent approach that has proven to be a very useful tool in the study of the formation of unstable structures in the solar corona. In particular, it is capable of incorporating observational data as initial and boundary conditions and requires shorter computational time compared to MHD simulations. To leverage the efficiency of data-driven TMFM and also to simulate eruptive events in the MHD framework, one can apply TMFM up to a certain time before the expected eruption(s) and then proceed with the simulation in the full or ideal MHD regime in order to more accurately capture the eruption process. Results. We show the results of a benchmark test case with a linked TMFM and MHD simulation to study the evolution of NOAA active region 12673. A rise of a twisted flux bundle through the MHD simulation domain is observed, but we find that the rate of the rise and the altitude reached depends on the time of the TMFM snapshot that was used to initialize the MHD simulation and the helicity injected into the system. The analysis suggested that torus instability and slip-running reconnection could play an important role in the eruption. Conclusions. The results show that the linkage of TMFM and zero-β MHD models can be successfully used to model the eruptive coronal magnetic fields.

Context. Meter-wavelength type II solar radio bursts are thought to be the signatures of shock-accelerated electrons in the corona. Studying these bursts can give information about the initial kinematics, dynamics, and energetics of coronal mass ejections (CMEs) in the absence of white-light observations. Aims. We investigate the occurrence of type II bursts in solar cycles 23 and 24 and their association with CMEs. We also explore whether type II bursts might occur in the absence of a CME. Methods. We performed a statistical analysis of type II bursts that occurred between 200 and 25 MHz in solar cycles 23 and 24 and determined the temporal association of these radio bursts with CMEs. We categorized the CMEs based on their linear speed and angular width and studied the distribution of type II bursts with fast (≥500 km s−1), slow (< 500 km s−1), wide (≥60°), and narrow (< 60°) CMEs. We explored the dependence of type II bursts occurrence on the phases of the solar cycle. Results. Our analysis shows that during solar cycles 23 and 24, 768 and 435 type II bursts occurred, respectively. Of these, 79% were associated with CMEs in solar cycle 23, and 95% were associated with CMEs in solar cycle 24. However, only 4% and 3% of the total number of CMEs were accompanied by type II bursts in solar cycle 23 and 24, respectively. Most of the type II bursts in both cycles were related to fast and wide CMEs (48%). We also determined the typical drift rate and duration for type II bursts, which is 0.06 MHz s−1 and 9 min. Our results suggest that type II bursts dominate at heights ≈1.7 − 2.3 ± 0.3 R⊙. A clear majority have an onset height around 1.7 ± 0.3 R⊙ assuming the four-fold Newkirk model. Conclusions. The results indicate that most of the type II bursts had a white-light CME counterpart, but a few type II bursts lacked a clear CME association. There were more CMEs in cycle 24 than in cycle 23. However, cycle 24 contained fewer type II radio bursts than cycle 23. The onset heights of type II bursts and their association with wide CMEs reported in this study indicate that the early lateral expansion of CMEs may play a key role in the generation of these radio bursts.