Context. The average Doppler shift shown by spectral lines formed from the chromosphere to the corona reveals important information on the mass and energy balance of the solar atmosphere, providing an important observational constraint to any models of the solar corona. Previous spectroscopic observations of vacuum ultra-violet (VUV) lines have revealed a persistent average wavelength shift of lines formed at temperatures up to 1 MK. At higher temperatures, the behaviour is still essentially unknown. Aims. Here we analyse combined SUMER (Solar Ultraviolet Measurements of Emitted Radiation)/SoHO (Solar and Heliospheric Observatory) and EIS (EUV Imaging Spectrometer)/Hinode observations of the quiet Sun around disk centre to determine, for the first time, the average Doppler shift of several spectral lines formed between 1 and 2 MK, where the largest part of the quiet coronal emission is formed. Methods. The measurements are based on a novel technique applied to EIS spectra to measure the difference in Doppler shift between lines formed at different temperatures. Simultaneous wavelength-calibrated SUMER spectra allow establishing the absolute value at the reference temperature of T ≈ 1 MK. Results. The average line shifts at 1 MK < T < 1.8 MK are modestly, but clearly bluer than those observed at 1 MK. By accepting an average blue shift of about (−1.8 ± 0.6) km s −1 at 1 MK (as provided by SUMER measurements), this translates into a maximum Doppler shift of (−4.4 ± 2.2) km s −1 around 1.8 MK. The measured value appears to decrease to about (−1.3 ± 2.6) km s −1 at the Fe xv formation temperature of 2.1 MK. Conclusions. The measured average Doppler shift between 0.01 and 2.1 MK, for which we provide a parametrisation, appears to be qualitatively and roughly quantitatively consistent with what foreseen by 3D coronal models where heating is produced by dissipation of currents induced by photospheric motions and by reconnection with emerging magnetic flux.

The moss is the area at the footpoint of the hot (3 to 5 MK) loops forming the core of the active region where emission is believed to result from the heat flux conducted down to the transition region from the hot loops. Studying the variation of Doppler shift as a function of line formation temperatures over the moss area can give clues on the heating mechanism in the hot loops in the core of the active regions. We investigate the absolute Doppler shift of lines formed at temperatures between 1 MK and 2 MK in a moss area within active region NOAA 11243 using a novel technique that allows determining the absolute Doppler shift of EUV lines by combining observations from the SUMER and EIS spectrometers. The inner (brighter and denser) part of the moss area shows roughly constant blue shift (upward motions) of 5 km s −1 in the temperature range of 1 MK to 1.6 MK. For hotter lines the blue shift decreases and reaches 1 km s −1 for Fe xv 284 Å (∼2 MK). The measurements are discussed in relation to models of the heating of hot loops.The results for the hot coronal lines seem to support the quasi-steady heating models for nonsymmetric hot loops in the core of active regions.

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

In this study, the properties of wave functions of the MHD oscillations for a single and a system of straight flux tubes are investigated. Magnetic flux tubes with a straight magnetic field and longitudinal density stratification were considered in zero‐β approximation. A single three‐dimensional wave equation (eigenvalue problem) is solved for longitudinal component of the perturbed magnetic field using the finite element method. Wave functions (eigenfunction of wave equation) of the MHD oscillations are categorized into sausage, kink, helical kink, and fluting modes. Exact recognition of the wave functions and the frequencies of oscillations can be used in coronal seismology and also helps to the future high‐resolution instruments that would be designed for studying the properties of the solar loop oscillations in details. The properties of collective oscillations of nonidentical and identical system of flux tubes and their interactions are studied. The ratios of frequencies, the oscillation frequencies of a system of flux tubes to their equivalent monolithic tube ( trueω~sys/trueω~mono), are obtained between 0.748 and 0.841 for a system of nonidentical tubes, whereas the related ratios of frequencies for a system of identical flux tubes are fluctuated around 0.761.