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The universal properties of the geomagnetic/solar indices critically describe their time series’ dynamics. Here, we investigate the complexity behavior of the time series of the geomagnetic and solar activity indices Kp, DST, Ap, F10.7, , AE, AL, AU, pc, and R. To do this, we apply multiscale entropy (MSE) analysis, detrended fluctuation analysis (DFA), rescaled range (R/S) test, and visibility graph (VG) to the time series of indices recorded daily from January 1st, 1996 to January 1st, 2020. MSE analysis reveals that AE exhibits the lowest entropy (minimal complexity), followed by F10.7, , and R. Ap shows intermediate complexity, while AL, Dst, AU, and pc maintain higher entropy values. The range of Hurst exponents between 0.5 and 1 extracted from DFA and R/S analyses confirms the long-term memory of geomagnetic indices. In contrast, solar activity indices exhibit Hurst exponents consistent with pink noise or non-stationarity. VG analysis identifies AU, Dst, pc, and Kp as possessing “small-world” characteristics—corroborating strong long-range correlations. Synthesized results indicate that the indices Kp, Dst, AL, AU, and pc exhibit stronger evidence of long-term correlated memory, while the solar indices, along with the geomagnetic index AE, are comparatively suitable for studying transient phenomena.

Relying on the quantum tunnelling concept and Maxwell–Boltzmann–Gibbs statistics, Gamow shows that the star-burning process happens at temperatures comparable to a critical value, called the Gamow temperature (T) and less than the prediction of the classical framework. In order to highlight the role of the equipartition theorem in the Gamow argument, a thermal length scale is defined, and then the effects of non-extensivity on the Gamow temperature have been investigated by focusing on the Tsallis and Kaniadakis statistics. The results attest that while the Gamow temperature decreases in the framework of Kaniadakis statistics, it can be bigger or smaller than T when Tsallis statistics are employed.

The first gravitational-wave (GW) signal was detected in the year 2015 indicating tiny distortions of spacetime caused by accelerated masses. We focused on the GW signals consisting of a peak GW strain of 1.0×10−21 that shows merging pairs of large masses. We applied the generalized entropy known as multiscale entropy to the GW interval time series recorded by different observatories (H1, L1, and V1). This enables us to investigate the behavior of entropies on different scales as a method of studying complexity and organization. We found that the entropies of GW interval data with similar physical properties make the identical manner in different scales. Moreover, the results reveal that the signals collected by each observatory have approximately a similar trend in the multiscale analysis results. According to our findings, although different signals have different values for short-range correlations, the long-range correlations are not noticeable in most of them.

This study examines the possibility of starting the process of collapsing and forming stars from a fractional molecular cloud. Although the Verlinde’s approach is employed to derive the corresponding gravitational potential, the results are easily generalizable to other gravitational potential proposals for fractional systems. It is due to the fact that the different methods, despite the difference in the details of results, all obtain power forms for the potential in terms of radius. An essential result of this analysis is the derivation of the corresponding Jeans mass limit, which is a crucial parameter in understanding the formation of stars. The study shows that the Jeans mass of a cloud in fractional gravity is much smaller than the traditional value. In addition, the study also determines the burning temperature of the resulting star using the Gamow theory. This calculation provides insight into the complex processes that govern the evolution of these celestial bodies. Finally, the study briefly discusses the investigation of hydrostatic equilibrium, a crucial condition that ensures the stability of these fractional stars. It also addresses the corresponding Lane–Emden equation, which is pivotal in understanding this equilibrium.

With the exponential growth in data volume, especially in recent decades, the demand for data processing has surged across all scientific fields. Within astronomical datasets, the combination of solar space missions and ground-based telescopes has yielded high spatial and temporal resolutions for observing the Sun, thus fueling an increase in the utilization of automatic image processing approaches. Image processing methodologies play a pivotal role in analyzing solar data, a critical component in comprehending the Sun's behavior and its influence on Earth. This paper provides an overview of the utilization of diverse processing techniques applied to images captured from the solar photosphere. The introduction of our manuscript furnishes a description of the solar photosphere along with its primary characteristics. Subsequently, we endeavor to outline the significance of preprocessing photospheric images, a crucial prerequisite before engaging in any form of analysis. The subsequent section delves into an examination of numerous reputable sources that have employed image processing methodologies in their research pertaining to the Sun's surface. This section also encompasses discussions concerning recent advancements in image processing techniques for solar data analysis and their potential implications for future solar research. The final section deliberates on post-processing procedures as supplementary steps that are essential for deriving meaningful results from raw data. Effectively, this paper imparts vital information, offering concise explanations regarding the Sun's surface, the application of image processing techniques to various types of photospheric images, indispensable image preprocessing stages, and post-processing procedures aimed at transforming raw data into coherent and comprehensive insights.

We investigate the characteristics of the solar flares complex network. The limited predictability, non-linearity, and self-organized criticality of the flares allow us to study systems of flares in the field of the complex systems. Both the occurrence time and the location of flares detected from January 1, 2006 to July 21, 2016 are used to design the growing flares network. The solar surface is divided into cells with equal areas. The cells, which include flare(s), are considered as nodes of the network. The related links are equivalent to sympathetic flaring. The extracted features present that the network of flares follows quantitative measures of complexity. The power-law nature of the connectivity distribution with a degree exponent greater than three reveals that flares form a scale-free and small-world network. The great value of the clustering coefficient, small characteristic path length, and slowly change of the diameter are all characteristics of the flares network. We show that the degree correlation of the flares network has the characteristics of a disassortative network. About 11% of the large energetic flares (M and X types in GOES classification) that occurred in the network hubs cover 3% of the solar surface.

Aims: The statistics of the photospheric granulation pattern are investigated using continuum images observed by Solar Dynamic Observatory (SDO)/Helioseismic and Magnetic Imager (HMI) taken at 6713~\\AA. Methods: The supergranular boundaries can be extracted by tracking photospheric velocity plasma flows. The local ball-tracking method is employed to apply on the HMI data gathered over the years 2011-2015 to estimate the boundaries of the cells. The edge sharpening techniques are exerted on the output of ball-tracking to precisely identify the cells borders. To study the fractal dimensionality (FD) of supergranulation, the box counting method is used. Results: We found that both the size and eccentricity follow the log-normal distributions with peak values about 330 Mm\\(^2\\) and 0.85, respectively. The five-year mean value of the cells number appeared in half-hour sequences is obtained to be about 60 \\(\\pm\\) 6 within an area of \\(350^{\\prime\\prime}\\times350^{\\prime\\prime}\\). The cells orientation distribution presents the power-law behavior. Conclusions: The orientation of supergranular cells (\\(O\\)) and their size (\\(S\\)) follows a power-law function as \\(|O| \\propto S^{9.5}\\). We found that the non-roundish cells with smaller and larger sizes than 600 Mm\\(^2\\) are aligned and perpendicular with the solar rotational velocity on the photosphere, respectively. The FD analysis shows that the supergranular cells form the self-similar patterns.

The solar corona is the origin of very dynamic events that are mostly produced in active regions (AR) and coronal holes (CH). The exact location of these large-scale features can be determined by applying image-processing approaches to extreme-ultraviolet (EUV) data. We here investigate the problem of segmentation of solar EUV images into ARs, CHs, and quiet-Sun (QS) images in a firm Bayesian way. On the basis of Bayes' rule, we need to obtain both prior and likelihood models. To find the prior model of an image, we used a Potts model in non-local mode. To construct the likelihood model, we combined a mixture of a Markov-Gauss model and non-local means. After estimating labels and hyperparameters with the Gibbs estimator, cellular learning automata were employed to determine the label of each pixel. We applied the proposed method to a Solar Dynamics Observatory/ Atmospheric Imaging Assembly (SDO/AIA) dataset recorded during 2011 and found that the mean value of the filling factor of ARs is 0.032 and 0.057 for CHs. The power-law exponents of the size distribution of ARs and CHs were obtained to be -1.597 and -1.508, respectively, with the maximum likelihood estimator method. When we compare the filling factors of our method with a manual selection approach and the SPoCA algorithm, they are highly compatible.

Solar coronal loops represent the variety of fast, intermediate, and slow normal mode oscillations. In this study, the transverse oscillations of the loops with a few-minutes period and also with damping caused by the resonant absorption were analyzed using extreme ultraviolet (EUV) images of the Sun. We employed the 171 \\(\\AA\\) data recorded by Solar Dynamic Observatory (SDO)/Atmospheric Imaging Assembly (AIA) to analyze the parameters of coronal loop oscillations such as period, damping time, loop length, and loop width. For the loop observed on 11 October 2013, the period and the damping of this loop are obtained to be 19 and 70 minutes, respectively. The damping quality, the ratio of the damping time to the period, is computed about 3.6. The period and damping time for the extracted loop recorded on 22 January 2013 are about 81 and 6.79 minutes, respectively. The damping quality is also computed as 12. It can be concluded that the damping of the transverse oscillations of the loops is in the strong damping regime, so resonant absorption would be the main reason for the damping.

In this study, we propose methods for the automatic detection of photospheric features (bright points and granules) from ultra-violet (UV) radiation, using a feature-based classifier. The methods use quiet-Sun observations at 214 nm and 525 nm images taken by Sunrise on 9 June 2009. The function of region growing and mean shift procedure are applied to segment the bright points (BPs) and granules, respectively. Zernike moments of each region are computed. The Zernike moments of BPs, granules, and other features are distinctive enough to be separated using a support vector machine (SVM) classifier. The size distribution of BPs can be fitted with a power-law slope -1.5. The peak value of granule sizes is found to be about 0.5 arcsec^2. The mean value of the filling factor of BPs is 0.01, and for granules it is 0.51. There is a critical scale for granules so that small granules with sizes smaller than 2.5 arcsec^2 cover a wide range of brightness, while the brightness of large granules approaches unity. The mean value of BP brightness fluctuations is estimated to be 1.2, while for granules it is 0.22. Mean values of the horizontal velocities of an individual BP and an individual BP within the network were found to be 1.6 km/s and 0.9 km/s, respectively. We conclude that the effect of individual BPs in releasing energy to the photosphere and maybe the upper layers is stronger than what the individual BPs release into the network.