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The fractal nature in avalanching systems with SOC is investigated here for phenomena in the solar photosphere and transition region. In the standard SOC model, the fractal Hausdorff dimension is expected to cover the range of [1, 2], with a mean of for 2-D observations projected in the plane-of-sky, and the range of [2, 3], with a mean of for real-world 3-D structures. Observations of magnetograms and with IRIS reveal four groups: (i) photospheric granulation with a low fractal dimension of ; (ii) transition region plages with a low fractal dimension of ; (iii) sunspots at transition region heights with an average fractal dimension of ; and (iv) active regions at photospheric heights with an average fractal dimension of . Phenomena with a low fractal dimension indicate sparse curvilinear flows, while high fractal dimensions indicate near space-filling flows. Investigating the SOC parameters, we find a good agreement for the event areas and mean radiated fluxes in events in transition region plages.
The size distribution of waiting times are found to have an exponential distribution in the case of a stationary Poissonian process. In reality, however, the waiting time distributions reveal power law-like distribution functions, which can be modeled in terms of non-stationary Poisson processes by a superposition of Poissonian distribution functions with time-varying event rates. We model the time evolution of such waiting time distributions by polynomial, sinusoidal, and Gaussian functions, which have exact analytical solutions in terms of the incomplete Gamma function, as well as in terms of the Pareto type-II approximation, which has a power law slope of , where represents the linear time evolution, or with representing nonlinear growth rates, which have a power law slope of . Our mathematical modeling confirms the existence of significant deviations from ideal power law size distributions (of waiting times), but no correlation or significant interval–size relationship exists, as would be expected for a simple (linear) energy storage-dissipation model.
The occurrence frequency distributions (size distributions) are the most important diagnostics for self-organized criticality systems. There are at least three formats for size distributions: (i) the differential size distribution function, (ii) the cumulative size distribution function, and (iii) the rank-order plot. Each of the three formats (or methods) has at least three ranges of event sizes: (i) a range with statistically incomplete sampling; (ii) an inertial range or power law fitting range with statistically complete sampling; and (iii) a range bordering finite system sizes. Only the intermediate range with power law behavior should be used to determine the power law slope from fitting the observed size distributions. The establishment of power law functions in a given observed size distribution depends crucially on the choice of the fitting range, which should have a logarithmic range of at least 2–3 decades. Often the fitted distribution functions exhibit significant deviations from an ideal power law and can be fitted better with alternative functions, such as log-normal distributions, Pareto type-II distributions, and Weibull distributions.
Among stellar systems, we find many with applications of SOC, such as stellar flares or pulsar glitches. Stellar flares occur mostly in the wavelength ranges of ultraviolet, soft X-rays and UV, and in visible light. A breakthrough in new stellar data was accomplished with the Kepler spacecraft, which allowed unprecedented detections of exoplanets, while the same light curves could be searched for large stellar flares. Exploiting these promising new datasets, one finds that most stellar flare datasets exhibit dominant size distributions that converges to a power law slope of , regardless of the star type. The size distributions of pulsar glitches are mostly found outside of the valid range of the Standard FD-SOC model and thus require a different model. Power law fits are not always superior to fits with the log-normal function or Weibull function. This discrepancy between observed and modeled power law slopes in stellar SOC systems is mostly due to small-number statistics of the samples, incomplete sampling near the lower threshold, and due to ill-defined power law fitting ranges, which can cause significant deviations from ideal power laws.
From the statistics of solar radio bursts, we learn that we can discriminate between three diagnostic regimes: (i) the incoherent regime where the radio burst flux is essentially proportional to the flare volume (with a power law slope of ), as it occurs for gyroemission, gyroresonance emission, gyrosynchrotron emission; (ii) the coherent regime that implies a nonlinear scaling between the radio flux and the flare volume ; as it occurs for the electron beam instability, the loss-cone instability, or maser emission; and (iii) the exponential regime that does not display a power law function, but rather an exponential cutoff as expected for random noise distributions. Thus, the power law slopes offer a useful diagnostic to verify the flux–volume scaling law and to discriminate between coherent and incoherent radio emission processes, as well as to distinguish between SOC processes and non-SOC processes. An additional diagnostic comes from the inertial range of power law fits: SOC-related power law size distributions should extend over multiple decades, while power law ranges of less than one decade are most likely not related to SOC processes.
Can we claim that the dynamics of the solar wind is consistent with a SOC system? Observationally we find that magnetic field and kinetic energy fluctuations measured in the solar wind exhibit power law distributions, which is consistent with a SOC system. What about the driver, instability, and avalanches expected in a SOC system? The driver mechanism is the acceleration of the solar wind in the solar corona itself, a process that basically follows the hydrodynamic model of Parker (1958), and may be additionally complicated by the presence of nonlinear wave–particle interactions, such as ion-cyclotron resonance. Then, the instability threshold, triggering extreme bursts of magnetic field fluctuations, the avalanches of solar wind SOC events, can be caused by dissipation of Alfven waves, onset of turbulence, or by the ion-cyclotron instability. Thus, in principle the generalized SOC concept can be applied to the solar wind, if there is a system-wide threshold for an instability that causes extreme magnetic field fluctuations.
The size distribution of solar energetic particle (SEP) events, which represent a more energetic subset than flare events, is mostly found to follow power law distribution functions, rather than Poissonian random distribution functions. However, the numerical value of the power law slope is generally flatter than the slopes of the flare size distributions in hard X-rays, soft X-rays, and EUV (Hudson 1978), which can be explained in at least four different ways: (i) normal flares and proton flares are produced by two fundamentally different acceleration mechanisms; (ii) proton flares behave differently than normal flares; (iii) the fractal dimensionality of SEP events is different from normal flares; (iv) proton flares are subject to a selection bias toward the most energetic events and thus are not a representative sample of large flares. Nevertheless, the standard fractal-diffusive SOC model can explain the observed slopes of SEP size distributions, but observations reveal deviations from straight power law functions, or broken power law slopes, and thus are not unique and need to be modeled in more detail.
We focus on the statistics of SOC-related solar flare parameters in soft X-ray wavelengths, including their size and waiting time distributions. An early SOC model assumed a linear increase of the energy storage, but this pioneering model is not consistent with the expected correlation between the waiting time interval and the subsequently dissipated energy. The Neupert effect in solar flares implies a correlation between the hard X-ray fluence and the soft X-ray flux, which predicts identical size distributions for these two parameters. Quantifying of thermal flare energies in soft X-ray emitting plasma needs also to include radiative and conductive losses. The intermittency and bursty variability of the solar dynamo implies a nonstationary SOC driver, which yields a universal value for the power law slope of fluxes, but the power law slopes of waiting times vary with the flare rate. While our focus encompasses primarily SOC models, alternative models in terms of MHD turbulence can explain some characteristics of SOC features also, such as size distribution functions, Fourier spectra, and structure functions.
We present spectroscopic properties of 22 Ly$\alpha$ emitters (LAEs) at $z = 5.5 - 6.6$ with Ly$\alpha$ luminosity $\mathrm{log}( L_{\mathrm{Ly}\alpha} \, [\mathrm{erg} \, \mathrm{s}^{-1}]) = 42.4 - 43.5 $, obtained using VLT/MUSE as part of the Middle Ages Galaxy Properties with Integral Field Spectroscopy (MAGPI) survey. Additionally, we incorporate broad-band photometric data from the Subaru Hyper Suprime-Cam (HSC) Wide layer for 17 LAEs in our sample. The HSC-y band magnitudes show that our LAEs are UV-bright, with rest-frame absolute UV magnitudes $ -19.74 \leq \mathrm{M}_{\mathrm{UV}} \leq -23.27$. We find that the Ly$\alpha$ line width increases with Ly$\alpha$ luminosity, and this trend becomes more prominent at $z \gt 6$ where Ly$\alpha$ lines become significantly broadened ($\gtrsim+260 \, \mathrm{km}\, \mathrm{s}^{-1}$) at luminosities $\mathrm{log}( L_{\mathrm{Ly}\alpha} \, [\mathrm{erg} \, \mathrm{s}^{-1}]) \gt 43 $. This broadening is consistent with previous studies, suggesting that these sources are located inside larger ionised bubbles. We observe a slightly elevated ionising photon production efficiency estimated for LAEs at $z \gt 6$, which indicates that younger galaxies could be producing more ionising photons per UV luminosity. A tentative anti-correlation between ionising photon production efficiency and Ly$\alpha$ rest-frame equivalent width is noticed, which could indicate a time delay between production and escape of ionising photon primarily due to supernovae activity. Furthermore, we find a positive correlation between radius of ionised regions and Ly$\alpha$ line width, which again suggests that large ionised bubbles are created around these LAEs, which are allowing them to self-shield from the scattering effects of the intergalactic medium (IGM). We also detect two very closely separated LAEs at $z = 6.046$ (projected spatial distance between the cores is 15.92 kpc). This is the LAE pair with the smallest separation ever discovered in the reionisation epoch. The size of their respective bubbles suggests that they likely sit inside a common large ionised region. Such a closely separated LAE pair increases the size of ionised bubble, potentially allowing a boosted transmission of Ly$\alpha$ through neutral IGM and also supports an accelerated reionisation scenario.
Neutral and singly ionised states of the magnesium (Mg) are the origin of several spectral lines that are useful for solar diagnostic purposes. An important element in modelling such solar lines is collisional data of the Mg with different perturbers abundant in the Sun, specially with neutral hydrogen. This work aims at providing complete depolarisation and polarisation and population transfer data for Mg II due to collisions with hydrogen atoms. For this purpose, a general formalism is employed to calculate the needed rates of MgII due to collisions with hydrogen atoms. The resulting collisional rates are then employed to investigate the impact of collisions on the polarisation of 25 Mg II lines relevant to solar applications by solving the governing statistical equilibrium equations within multi-level and multi-term atomic models. We find that the polarisation of some Mg II lines starts to be sensitive to collisions for hydrogen density $n_H \!\gtrsim\!$ 10$^{14}$ cm$^{-3}$.
The spin-down law of pulsars is generally perturbed by two types of timing irregularities: glitches and timing noise. Glitches are sudden changes in the rotational frequency of pulsars, while timing noise is a discernible stochastic wandering in the phase, period, or spin-down rate of a pulsar. We present the timing results of a sample of glitching pulsars observed using the Ooty Radio Telescope (ORT) and the upgraded Giant Metrewave Radio Telescope (uGMRT). Our findings include timing noise analysis for 17 pulsars, with seven being reported for the first time. We detected five glitches in four pulsars and a glitch-like event in PSR J1825–0935. The frequency evolution of glitches in pulsars, J0742–2822 and J1740–3015, is presented for the first time. Additionally, we report timing noise results for three glitching pulsars. The timing noise was analysed separately in the pre-glitch and post-glitch regions. We observed an increase in the red noise parameters in the post-glitch regions, where exponential recovery was considered in the noise analysis. Timing noise can introduce ambiguities in the correct evaluation of glitch observations. Hence, it is important to consider timing noise in glitch analysis. We propose an innovative glitch verification approach designed to discern between a glitch and strong timing noise. The novel glitch analysis technique is also demonstrated using the observed data.
Research applications of complex systems and nonlinear physics are rapidly expanding across various scientific disciplines. A common theme among them is the concept of “self-organized criticality systems”, which this volume presents in detail for observed astrophysical phenomena, such as solar flares, coronal mass ejections, solar energetic particles, solar wind, stellar flares, magnetospheric events, planetary systems, galactic and black-hole systems. The author explores fundamental questions: Why do power laws, the hallmarks of self-organized criticality, exist? What power law index is predicted for each astrophysical phenomenon? Which size distributions have universality? What can waiting time distributions tell us about random processes? This is the first monograph that tests comprehensively astrophysical observations of self-organized criticality systems for students, post-docs, and researchers. A highlight is a paradigm shift from microscopic concepts, such as the traditional cellular automaton algorithms, to macroscopic concepts formulated in terms of physical scaling laws.
Existing photometry of the magnetic helium-rich white dwarf Feige 7 is used to derive the parameters $T_\mathrm{eff}=18\,480$ K and log$\;g=8.74$ and a frequency of variability of 10.94192 d$^{-1}$ (period 2.19340 h). New time-series photometry of Feige 7 is presented, covering full cycles of variability in the UBVRI and ugriz filters, which allows the wavelength dependence of the two amplitudes in the double wave light curve to be determined. Amplitudes are virtually constant for wavelengths longer than 5 000 Å, but increase sharply for shorter wavelengths. A simple model consisting of two large cool spots 180$^\circ$ apart on the surface of star provides a reasonable description of the data.
Observations of the 21 cm signal face significant challenges due to bright astrophysical foregrounds that are several orders of magnitude higher than the brightness of the hydrogen line, along with various systematics. Successful 21 cm experiments require accurate calibration and foreground mitigation. Errors introduced during the calibration process such as systematics can disrupt the intrinsic frequency smoothness of the foregrounds, leading to power leakage into the Epoch of Reionisation window. Therefore, it is essential to develop strategies to effectively address these challenges. In this work, we adopt a stringent approach to identify and address suspected systematics, including malfunctioning antennas, frequency channels corrupted by radio frequency interference, and other dominant effects. We implement a statistical framework that utilises various data products from the data processing pipeline to derive specific criteria and filters. These criteria and filters are applied at intermediate stages to mitigate systematic propagation from the early stages of data processing. Our analysis focuses on observations from the Murchison Widefield Array Phase I configuration. Out of the observations processed by the pipeline, our approach selects 18%, totalling 58 h, that exhibit fewer systematic effects. The successful selection of observations with reduced systematic dominance enhances our confidence in achieving 21 cm measurements.
In this paper, we present a semi-empirical calibration between the oxygen abundance and the N2 emission-line ratio for low ionisation nuclear emission regions (LINERs). This relation was derived by comparing the optical spectroscopic data of 118 nuclear spaxels classified as LINERs using three different BPT diagrams from the Mapping Nearby Galaxies survey (MaNGA) and sub-classified as weak (wAGN, 84 objects) and strong (sAGN, 34 objects) active galactic nucleus (AGN) from the WHAN diagnostic diagram and photoionisation model results obtained with the cloudy code assuming gas accretion into a black hole (representing an AGN). We found that our wAGN LINERs exhibit an oxygen abundance in the range of $8.50 \lesssim \mathrm{12+\log(O/H)} \lesssim 8.90 $, with an average value of $\mathrm{12+\log(O/H)}=8.68$, while our sAGN LINERs exhibit an oxygen abundance in the range of $8.51 \lesssim \: \mathrm{12+\log(O/H)} \: \lesssim \: 8.81 $, with an average value of $\mathrm{12+\log(O/H)}=8.65$. Our abundance estimations are in good agreement with those derived for another two different samples one of them with 463 Seyfert 2 objects and the other with 43 LINERs galaxies ionised by post-AGB stars, showing that the assumptions of our models are likely suitable for wAGN and sAGN LINERs. A relation between the equivalent width of the observed H$\alpha$ emission-line and the estimated ionisation parameter provided by models was obtained. Our results also suggest that LINERs does not show a clear correlation between oxygen abundances and the stellar mass of the hosting galaxies.
We investigate the unusual H$\alpha$ features found towards the Scutum Supershell via recent arc-minute and arc-second resolution imaging. These multi-degree features resemble a long central spine ending in a bow-shock morphology. We performed a multi–wavelength study in [S II] optical, radio continuum, infrared continuum, Hi, CO, X-ray, and gamma-ray emissions. Interestingly, we found the Galactic worm GW 16.9−3.8 Hi feature appears within the Scutum Supershell, and likely influences the spine morphology. Furthermore, the rightmost edge of the bow-shock H$\alpha$ emission overlaps with [S II] line emission, 4.85 GHz radio, and both 60 and 100 $\mu$m infrared continuum emissions, suggesting some potential for excitation by shock heating. We estimated the photo-ionisation from O-type and B-type stars in the region (including those from the OB associations Ser OB1B, Ser OB2, and Sct OB3) and found that this mechanism could supply the excitation to account for the observed H$\alpha$ luminosity of the spine and bow-shock of $\sim$1–2 $\times 10^{36}\,\mathrm{erg\,s}^{-1}$ (d/2.5 kpc)$^2$. Recent MHD simulations by Drozdov et al. (2022) demonstrate the potential for supernova events to drive outflow and bow-shock types of features of the same energetic nature and physical scale as the H$\alpha$ emission we observe here. While this clearly requires many supernova events over time, we speculate that one contributing event could have come from the presumably energetic supernova (hypernova) birth of the magnetar tentatively identified in the X-ray binary LS 5039.
Radio-frequency interference detection and flagging is one of the most difficult and urgent problems in 21 cm Epoch of Reionisation research. In this work, we present $\chi^2$ from redundant calibration as a novel method for RFI detection and flagging, demonstrating it to be complementary to current state-of-the-art flagging algorithms. Beginning with a brief overview of redundant calibration and the meaning of the $\chi^2$ metric, we demonstrate a two-step RFI flagging algorithm which uses the values of this metric to detect faint RFI. We find that roughly 27.4% of observations have RFI from digital television channel 7 detected by at least one algorithm of the three tested: 18.0% of observations are flagged by the novel $\chi^2$ algorithm, 16.5% are flagged by SSINS, and 6.8% are flagged by AOFlagger (there is significant overlap in these percentages). Of the 27.4% of observations with detected DTV channel 7 RFI, 37.1% (10.2% of the total observations) are detected by $\chi^2$ alone, and not by either SSINS or AOFlagger, demonstrating a significant population of as-yet undetected RFI. We find that $\chi^2$ is able to detect RFI events which remain undetectable to SSINS and AOFlagger, especially in the domain of long-duration, weak RFI from digital television. We also discuss the shortcomings of this approach and discuss examples of RFI which seems undetectable using $\chi^2$ while being successfully flagged by SSINS and/or AOFlagger.