scholarly journals Statistical properties of magnetar bursts and FRB 121102

2019 ◽  
Vol 491 (1) ◽  
pp. 1498-1505 ◽  
Author(s):  
Yingjie Cheng ◽  
G Q Zhang ◽  
F Y Wang
Keyword(s):  
Power Law ◽  
Time Distribution ◽  
Statistical Properties ◽  
Occurrence Rate ◽  
Waiting Time Distribution ◽  
X Ray ◽  
Central Engine ◽  
Fast Radio Burst ◽  
Soft Gamma Repeater ◽  
Critical Process

ABSTRACT In this paper, we present statistics of soft gamma repeater (SGR) bursts from SGR J1550−5418, SGR 1806−20, and SGR 1900+14 by adding new bursts from Kırmızıbayrak et al. detected with the Rossi X-ray Timing Explorer. We find that the fluence distributions of magnetar bursts are well described by power-law functions with indices 1.84, 1.68, and 1.65 for SGR J1550−5418, SGR 1806−20, and SGR 1900+14, respectively. The duration distributions of magnetar bursts also show power-law forms. Meanwhile, the waiting time distribution can be described by a non-stationary Poisson process with an exponentially growing occurrence rate. These distributive features indicate that magnetar bursts can be regarded as a self-organizing critical process. We also compare these distributions with the repeating fast radio burst (FRB) 121102. The statistical properties of repeating FRB 121102 are similar with magnetar bursts, combining with the large required magnetic field (B ≥ 1014 G) of neutron star for FRB 121102, which indicates that the central engine of FRB 121102 may be a magnetar.

The Waiting‐Time Distribution of Solar Flare Hard X‐Ray Bursts

1998 ◽  
Vol 509 (1) ◽  
pp. 448-455 ◽  
Author(s):  
M. S. Wheatland ◽  
P. A. Sturrock ◽  
J. M. McTiernan
Keyword(s):  
Solar Flare ◽  
Waiting Time ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
X Ray

scholarly journals Scale-invariance in the repeating fast radio burst 121102

2019 ◽  
Author(s):  
Hai-Nan Lin ◽  
Yu Sang
Keyword(s):  
Total Energy ◽  
Flux Density ◽  
Radio Burst ◽  
Probability Density Functions ◽  
Statistical Properties ◽  
Density Functions ◽  
Scale Invariant ◽  
Invariant Structure ◽  
Fast Radio Burst ◽  
Soft Gamma Repeater

Abstract The statistical properties of the repeating fast radio burst FRB 121102 are investigated. We find that the cumulative distributions of fluence, flux density, total energy and waiting time can be well fitted by the bent power law. In addition, the probability density functions of fluctuations of fluence, flux density and total energy well follow the Tsallis q-Gaussian distribution. The q values keep steady around q ∼ 2 for different scale intervals, indicating a scale-invariant structure of the bursts. The statistical properties of FRB 121102 are very similar to that of the soft gamma repeater SGR J1550-5418. The underlying physical implications need to be further investigated.

scholarly journals Iron Line Emission from NGC1068

1989 ◽  
Vol 134 ◽  
pp. 167-172
Author(s):  
Katsuji Koyama
Keyword(s):  
Energy Range ◽  
Power Law ◽  
Equivalent Width ◽  
Line Emission ◽  
X Rays ◽  
Iron Line ◽  
X Ray ◽  
Central Engine ◽  
Photon Index ◽  
The Continuum

X-ray emission in the 2–10 keV energy range was observed with the Ginga satellite from the Seyfert 2 galaxy NGC1068. The continuum spectrum can be described by a power-law of photon index about 1.5. An intense iron line at 6.5 keV with an equivalent width of 1.3 keV was clearly noticed. The X-ray flux was about 6 × 10 −12 erg/sec/cm2 or 3 × 1041 erg/sec, assuming a distance of 22 Mpc. The observed spectrum is consistent with the scattering and reprocessing of X-rays by the gas surrounding the central engine. With this picture we estimate that the X-ray flux of the central engine is about 1043 - 1044 erg/sec, a typical value for a Seyfert 1 galaxy.

scholarly journals Hard X-ray properties of NuSTAR blazars

2018 ◽  
Vol 619 ◽  
pp. A93 ◽  
Author(s):  
Gopal Bhatta ◽  
Maksym Mohorian ◽  
Illya Bilinsky
Keyword(s):  
Power Law ◽  
Primary Objective ◽  
Emission Region ◽  
X Ray ◽  
Bl Lacertae ◽  
Central Engine ◽  
Spectrum Radio ◽  
Cross Correlation Analysis ◽  
The Magnetic Field ◽  
Radio Quasar

Context. Investigation of the hard X-ray emission properties of blazars is key to the understanding of the central engine of the sources and associated jet process. In particular, simultaneous spectral and timing analyses of the intraday hard X-ray observations provide us a means to peer into the compact innermost blazar regions that are not accessible to our current instruments. Aims. The primary objective of the work is to associate the observed hard X-ray variability properties in blazars with their flux and spectral states, thereby, based on the correlation among these states, extract the details about the emission regions and processes occurring near the central engine. Methods. We carried out timing, spectral, and cross-correlation analysis of 31 NuSTAR observations of 13 blazars. We investigated the spectral shapes of the sources using single power-law, broken power-law, and log-parabola models. We also studied the co-relation between the soft and hard emission using z-transformed discrete correlation function. In addition, we attempted to constrain the smallest emission regions using minimum variability timescales derived from the light curves. Results. We found that, for most of the sources, the hard X-ray emission can be well represented by the log-parabola model and that the spectral slopes for different blazar subclasses are consistent with the so-called blazar sequence. We also report the steepest spectra (Γ ∼ 3) in the BL Lacertae PKS 2155–304 and the hardest spectra (Γ ∼ 1.4) in the flat-spectrum radio quasar PKS 2149–306. In addition, we noted a close connection between the flux and spectral slope within the source subclass in the sense that high flux and/or flux states tend to be harder in spectra. In BL Lacertae objects, assuming particle acceleration by diffusive shocks and synchrotron cooling as the dominant processes governing the observed flux variability, we constrain the magnetic field of the emission region to be a few Gauss; whereas in flat-spectrum radio quasars, using external Compton models, we estimate the energy of the lower end of the injected electrons to be a few Lorentz factors.

scholarly journals Statistical Analysis of Acoustic Emission in Uniaxial Compression of Tectonic and Non-Tectonic Coal

2020 ◽  
Vol 10 (10) ◽  
pp. 3555 ◽  
Author(s):  
Rong Liu ◽  
Yi He ◽  
Yunfeng Zhao ◽  
Xiang Jiang ◽  
Song Ren
Keyword(s):  
Acoustic Emission ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Uniaxial Compression ◽  
Power Law ◽  
Waiting Time ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
Tectonic Coal

Tectonic coal has become an important research topic for preventing coal mine disasters and for exploring and developing coal-bed methane resources. To investigate the mechanical and acoustic properties of tectonic coal, we conducted a uniaxial compression test for tectonic and non-tectonic coal, and acoustic emission (AE) signals have been simultaneous captured in the compression process. The AE energy and waiting time of events have been studied statistically. The results show that the probability density function of AE energy follows the power law distribution well, and indicates that the AE of non-tectonic coal is mainly generated from the fracture source, while the probability density function distribution of tectonic coal is the mixing result of fracture and friction effects. Only the waiting time distribution of non-tectonic coal follows the typical brittle fracture’s double power law behavior. The waiting time distribution of tectonic coal shows the single power law with a smaller exponent value, which is associated with the granular microstructure of tectonic coal. The distribution of aftershock and Båth’s law are not sensitive to microstructure, and are identical for non-tectonic and tectonic coal. At last, the correlation dimension results for the spatial distribution of AE hypocenters indicated that the rough continuous decrease in multifractal dimension might be a precursor to devastating destruction.

scholarly journals Tempered fractional order compartment models and applications in biology

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yejuan Wang ◽  
Lijuan Zhang ◽  
Yuan Yuan
Keyword(s):  
Power Law ◽  
Waiting Time ◽  
Time Distribution ◽  
Dynamical Behavior ◽  
Real Data ◽  
Compartment Model ◽  
Waiting Time Distribution ◽  
Compartment Models ◽  
Power Law Function ◽  
First Moment

<p style='text-indent:20px;'>Compartment models with classical derivatives have diverse applications and attracted a lot of interest among scientists. To model the dynamical behavior of the particles that existed in the system for a long period of time with little chance to be removed, a power-law waiting time technique was introduced in the most recent work of Angstmann et al. [<xref ref-type="bibr" rid="b2">2</xref>]. The divergent first moment makes the power-law waiting time distribution less physical because of the finite lifespan of the particles. In this work, we take the tempered power-law function as the waiting time distribution, which has finite first moment while keeping the power-law properties. From the underlying physical stochastic process with the exponentially truncated power-law waiting time distribution, we build the tempered fractional compartment model. As an application, the tempered fractional SEIR epidemic model is proposed to simulate the real data of confirmed cases of pandemic AH1N1/09 influenza from Bogotá D.C. (Colombia). Some analysis and numerical simulations are carried out around the equilibrium behavior.</p>

scholarly journals Non-Thermal Emission from Radio-Loud AGN Jets: Radio vs. X-rays

Galaxies ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 6
Author(s):  
Elena Fedorova ◽  
Bohdan Hnatyk ◽  
Antonino Del Popolo ◽  
Anatoliy Vasylenko ◽  
Vadym Voitsekhovskyi
Keyword(s):  
Active Galactic Nuclei ◽  
Power Law ◽  
Thermal Emission ◽  
Galactic Nuclei ◽  
X Rays ◽  
X Ray ◽  
Compact Source ◽  
Central Engine ◽  
Sky Survey ◽  
Inverse Compton

We consider the sample of 55 blazars and Seyferts cross-correlated from the Planck all-sky survey based on the Early Release Compact Source Catalog (ERCSC) and Swift BAT 105-Month Hard X-ray Survey. The radio Planck spectra vs. X-ray Swift/XRT+BAT spectra of the active galactic nuclei (AGN) sample were fitted with the simple and broken power law (for the X-ray spectra taking into account also the Galactic neutral absorption) to test the dependencies between the photon indices of synchrotron emission (in radio range) and synchrotron self-Compton (SSC) or inverse-Compton emission (in X-rays). We show that for the major part of the AGN in our sample there is a correspondence between synchrotron and SSC photon indices (one of two for broken power-law model) compatible within the error levels. For such objects, this can give a good perspective for the task of distinguishing between the jet base counterpart from that one emitted in the disk-corona AGN “central engine”.

scholarly journals Repeating behaviour of FRB 121102: periodicity, waiting times, and energy distribution

2020 ◽  
Vol 500 (1) ◽  
pp. 448-463 ◽  
Author(s):  
M Cruces ◽  
L G Spitler ◽  
P Scholz ◽  
R Lynch ◽  
A Seymour ◽  
...  
Keyword(s):  
Energy Distribution ◽  
Power Law ◽  
Waiting Times ◽  
Cumulative Energy ◽  
Single Observation ◽  
Arrival Times ◽  
X Ray ◽  
Fast Radio Burst ◽  
Arecibo Observatory ◽  
Green Bank Telescope

ABSTRACT Detections from the repeating fast radio burst FRB 121102 are clustered in time, noticeable even in the earliest repeat bursts. Recently, it was argued that the source activity is periodic, suggesting that the clustering reflected a not-yet-identified periodicity. We performed an extensive multiwavelength campaign with the Effelsberg telescope, the Green Bank telescope, and the Arecibo Observatory to shadow the Gran Telescope Canaria (optical), NuSTAR (X-ray) and INTEGRAL (γ-ray). We detected 36 bursts with Effelsberg, one with a pulse width of 39 ms, the widest burst ever detected from FRB 121102. With one burst detected during simultaneous NuSTAR observations, we place a 5σ upper limit of 5 × 1047 erg on the 3–79 keV energy of an X-ray burst counterpart. We tested the periodicity hypothesis using 165 h of Effelsberg observations and find a periodicity of 161 ± 5 d. We predict the source to be active from 2020 July 9 to October 14 and subsequently from 2020 December 17 to 2021 March 24. We compare the wait times between consecutive bursts within a single observation to Weibull and Poisson distributions. We conclude that the strong clustering was indeed a consequence of a periodic activity and show that if the few events with millisecond separation are excluded, the arrival times are Poisson distributed. We model the bursts’ cumulative energy distribution with energies from ∼1038–1039 erg and find that it is well described by a power law with slope of γ = −1.1 ± 0.2. We propose that a single power law might be a poor descriptor of the data over many orders of magnitude.

Space and Time Distribution of Hard X-Ray Emission in a Loop at the Beginning of a Flare

1994 ◽  
Vol 144 ◽  
pp. 275-277
Author(s):  
M. Karlický ◽  
J. C. Hénoux
Keyword(s):  
Time Distribution ◽  
Electron Bombardment ◽  
Spatial Evolution ◽  
Superthermal Electrons ◽  
Flare Loop ◽  
X Ray ◽  
Superthermal Electron ◽  
Flare Loops ◽  
Chromospheric Evaporation ◽  
Temporal And Spatial

AbstractUsing a new ID hybrid model of the electron bombardment in flare loops, we study not only the evolution of densities, plasma velocities and temperatures in the loop, but also the temporal and spatial evolution of hard X-ray emission. In the present paper a continuous bombardment by electrons isotropically accelerated at the top of flare loop with a power-law injection distribution function is considered. The computations include the effects of the return-current that reduces significantly the depth of the chromospheric layer which is evaporated. The present modelling is made with superthermal electron parameters corresponding to the classical resistivity regime for an input energy flux of superthermal electrons of 109erg cm−2s−1. It was found that due to the electron bombardment the two chromospheric evaporation waves are generated at both feet of the loop and they propagate up to the top, where they collide and cause temporary density and hard X-ray enhancements.

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