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Register a new userStatistics of X-ray flares of Sagittarius A*: evidence for solar-like self-organized criticality phenomenon
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X-ray flares have routinely been observed from the supermassive black hole, Sagittarius A$^star$ (Sgr A$^star$), at our Galactic center. The nature of these flares remains largely unclear, despite of many theoretical models. In this paper, we study the statistical properties of the Sgr A$^star$ X-ray flares, by fitting the count rate (CR) distribution and the structure function (SF) of the light curve with a Markov Chain Monte Carlo (MCMC) method. With the 3 million second textit{Chandra} observations accumulated in the Sgr A$^star$ X-ray Visionary Project, we construct the theoretical light curves through Monte Carlo simulations. We find that the $2-8$ keV X-ray light curve can be decomposed into a quiescent component with a constant count rate of $sim6times10^{-3}~$count s$^{-1}$ and a flare component with a power-law fluence distribution $dN/dEpropto E^{-alpha_{rm E}}$ with $alpha_{rm E}=1.65pm0.17$. The duration-fluence correlation can also be modelled as a power-law $Tpropto E^{alpha_{rm ET}}$ with $alpha_{rm ET} < 0.55$ ($95%$ confidence). These statistical properties are consistent with the theoretical prediction of the self-organized criticality (SOC) system with the spatial dimension $S = 3$. We suggest that the X-ray flares represent plasmoid ejections driven by magnetic reconnection (similar to solar flares) in the accretion flow onto the black hole.
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The original concept of self-organized criticality (Bak et al.~1987), applied to solar flare statistics (Lu and Hamilton 1991), assumed a slow-driven and stationary flaring rate, which warrants time scale separation (between flare durations and inter-flare waiting times), it reproduces power-law distributions for flare peak fluxes and durations, but predicts an exponential waiting time distribution. In contrast to these classical assumptions we observe: (i) multiple energy dissipation episodes during most flares, (ii) violation of the principle of time scale separation, (iii) a fast-driven and non-stationary flaring rate, (iv) a power law distribution for waiting times $Delta t$, with a slope of $alpha_{Delta t} approx 2.0$, as predicted from the universal reciprocality between mean flaring rates and mean waiting times; and (v) pulses with rise times and decay times of the dissipated magnetic free energy on time scales of $12pm6$ min, up to 13 times in long-duration ($lapprox 4$ hrs) flares. These results are inconsistent with coronal long-term energy storage (Rosner and Vaiana 1978), but require photospheric-chromospheric current injections into the corona.
Power law size distributions are the hallmarks of nonlinear energy dissipation processes governed by self-organized criticality. Here we analyze 75 data sets of stellar flare size distributions, mostly obtained from the {sl Extreme Ultra-Violet Explorer (EUVE)} and the {sl Kepler} mission. We aim to answer the following questions for size distributions of stellar flares: (i) What are the values and uncertainties of power law slopes? (ii) Do power law slopes vary with time ? (iii) Do power law slopes depend on the stellar spectral type? (iv) Are they compatible with solar flares? (v) Are they consistent with self-organized criticality (SOC) models? We find that the observed size distributions of stellar flare fluences (or energies) exhibit power law slopes of $alpha_E=2.09pm0.24$ for optical data sets observed with Kepler. The observed power law slopes do not show much time variability and do not depend on the stellar spectral type (M, K, G, F, A, Giants). In solar flares we find that background subtraction lowers the uncorrected value of $alpha_E=2.20pm0.22$ to $alpha_E=1.57pm0.19$. Furthermore, most of the stellar flares are temporally not resolved in low-cadence (30 min) Kepler data, which causes an additional bias. Taking these two biases into account, the stellar flare data sets are consistent with the theoretical prediction $N(x) propto x^{-alpha_x}$ of self-organized criticality models, i.e., $alpha_E=1.5$. Thus, accurate power law fits require automated detection of the inertial range and background subtraction, which can be modeled with the generalized Pareto distribution, finite-system size effects, and extreme event outliers.
Shortly after the seminal paper {sl Self-Organized Criticality: An explanation of 1/f noise} by Bak, Tang, and Wiesenfeld (1987), the idea has been applied to solar physics, in {sl Avalanches and the Distribution of Solar Flares} by Lu and Hamilton (1991). In the following years, an inspiring cross-fertilization from complexity theory to solar and astrophysics took place, where the SOC concept was initially applied to solar flares, stellar flares, and magnetospheric substorms, and later extended to the radiation belt, the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and boson clouds. The application of SOC concepts has been performed by numerical cellular automaton simulations, by analytical calculations of statistical (powerlaw-like) distributions based on physical scaling laws, and by observational tests of theoretically predicted size distributions and waiting time distributions. Attempts have been undertaken to import physical models into the numerical SOC toy models, such as the discretization of magneto-hydrodynamics (MHD) processes. The novel applications stimulated also vigorous debates about the discrimination between SOC models, SOC-like, and non-SOC processes, such as phase transitions, turbulence, random-walk diffusion, percolation, branching processes, network theory, chaos theory, fractality, multi-scale, and other complexity phenomena. We review SOC studies from the last 25 years and highlight new trends, open questions, and future challenges, as discussed during two recent ISSI workshops on this theme.
The variability in multi-pulse gamma-ray bursts (GRBs) may help to reveal the mechanism of underlying processes from the central engine. To investigate whether the self-organized criticality (SOC) phenomena exist in the prompt phase of GRBs, we statistically study the properties of GRBs with more than 3 pulses in each burst by fitting the distributions of several observed physical variables with a Markov Chain Monte Carlo approach, including the isotropic energy $E_{rm iso}$, the duration time $T$ and the peak count rate $P$ of each pulse. Our sample consists of 454 pulses in 93 GRBs observed by the CGRO/BATSE satellite. The best-fitting values and uncertainties for these power-law indices of the differential frequency distributions are: $alpha^d_{E}=1.54 pm 0.09$, $alpha^d_{T}=1.82_{-0.15}^{+0.14}$ and $alpha^d_{P}=2.09_{-0.19}^{+0.18}$, while the power-law indices in the cumulative frequency distributions are: $alpha^c_{E}=1.44_{-0.10}^{+0.08}$, $alpha^c_{T}=1.75_{-0.13}^{+0.11}$ and $alpha^c_{P}=1.99_{-0.19}^{+0.16}$. We find that these distributions are roughly consistent with the physical framework of a Fractal-Diffusive, Self-Organized Criticality (FD-SOC) system with the spatial dimension $S=3$ and the classical diffusion $beta$=1. Our results support that the jet responsible for the GRBs should be magnetically dominated and magnetic instabilities (e.g., kink model, or tearing-model instability) lead the GRB emission region into the SOC state.
Indian Centre for Space Physics is engaged in pioneering balloon borne experiments with typical payloads less than ~ 3.5kg. Low cost rubber balloons are used to fly them to a height of about 40km. In a double balloon system, the booster balloon lifts the orbiter balloon to its cruising altitude where data is taken for a longer period of time. In this Paper, we present our first scientific report on the variation of Cosmic Rays and muons with altitude and detection of several solar flares in X-rays between 20keV and 100keV. We found the altitude of the Pfotzer maximum at Tropic of Cancer for cosmic rays and muons and catch several solar flares in hard X-rays. We find that the hard X-ray (> 40keV) sky becomes very transparent above Pfotzer maximum. We find the flare spectrum to have a power-law distribution. From these studies, we infer that valuable scientific research could be carried out in near space using low cost balloon borne experiments. Published in Online version of Indian Journal of Physics.
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