First Digit Distributions of Gamma-Ray Bursts

The occurrence of the first significant digits from real world sources is usually not equally distributed,but is consistent with a logarithmic distribution instead,known as Benford’s law.In this work,we perform a comprehensive investigation on the first digit distributions of the duration,fluence,and energy flux of gamma-ray bursts (GRBs) for the first time.For a complete GRB sample detected by the Fermi satellite,we find that the first digits of the duration and fluence adhere to Benford’s law.However,the energy flux shows a significant departure from this law,which may be due to the fact that a considerable part of the energy flux measurements is restricted by lack of spectral information.Based on the conventional duration classification scheme,we also check if the durations and fluences of long and short GRBs (with duration T_(90)>2 s and T_(90)≤2 s,respectively) obey Benford’s law.We find that the fluences of both long and short GRBs still agree with the Benford distribution,but their durations do not follow Benford’s law.Our results hint that the long–short GRB classification scheme does not directly represent the intrinsic physical classification scheme.

Time-resolved Spectral Properties of Fermi-GBM Bright Long Gamma-Ray Bursts

The prompt emission mechanism of gamma-ray bursts(GRBs)is still unclear,and the time-resolved spectral analysis of GRBs is a powerful tool for studying their underlying physical processes.We performed a detailed time-resolved spectral analysis of 78 bright long GRB samples detected by Fermi/Gamma-ray Burst Monitor.A total of 1490 spectra were obtained and their properties were studied using a typical Band-shape model.First,the parameter distributions of the time-resolved spectrum are given as follows:the low-energy spectral indexα~-0.72,high-energy spectral indexβ~2.42,the peak energy E_(p)~221.69 keV,and the energy flux F~7.49×10^(-6)erg cm^(-2)s^(-1).More than 80%of the bursts exhibit the hardest low-energy spectral indexα_(max),exceeding the synchrotron limit(-2/3).Second,the evolution patterns of a and E_(p)were statistically analyzed.The results show that for multi-pulse GRBs the intensity-tracking pattern is more common than the hard-to-soft pattern in the evolution of both E_(p)andα.The hard-to-soft pattern is generally shown in single-pulse GRBs or in the initial pulse of multi-pulse GRBs.Finally,we found a significant positive correlation between F and E_(p),with half of the samples exhibiting a positive correlation between F andα.We discussed the spectral evolution of different radiation models.The diversity of spectral evolution patterns indicates that there may be more than one radiation mechanism occurring in the GRB radiation process,including photo spheric radiation and synchrotron radiation.However,it may also involve only one radiation mechanism,but more complicated physical details need to be considered.

Coal bursts that occur during development: A rock mechanics enigma

Coal bursts are typically associated with highly stressed coal.Most bursts occur during retreat mining(longwall mining or pillar recovery) in highly stressed locations like the tailgate corner of the longwall panel.Others are associated with multiple seam interactions.However, a small but significant percentage of coal bursts have occurred during development or in outby locations unaffected by active mining.Most development bursts have been relatively small, but some have been highly destructive.No theory of coal bursts can be complete if it does not account for this type of event.This paper focusses on the development mining coal burst experience in the US, putting it into the context of the entire US coal burst database.The first documented development coal burst occurred almost exactly 100 years ago during slope drivage at the Sunnyside Mine in Utah.Sunnyside subsequently had a long history of bursts, mainly during retreat mining but also during development.Several Colorado mines have also experienced multiple development bursts.Many, but by no means all, of the development bursts in these western US coalfields have been associated with known faults.In the Central Appalachian coalfields, most development bursts have occurred in multiple seam situations.In some of these cases, however, there was no retreat mining in either seam.The paper closes with some lessons from this history, with implications for preventing such events in the future.

Gas-dynamic phenomena caused by rock mass tremors and rock bursts

Similar to coal, rock and gas ejections, rock mass tremors and rock bursts are among the most serious natural hazards accompanying the underground extraction of coal. Gas-dynamic phenomena caused by rock mass tremors and rock bursts observed as transient states of air parameters in mining headings,are usually generated as a result of a change in the geometry of headings and the release of considerable amounts of gases. Particular significance is attributed to transient states caused by disasters, which are often accompanied by rapid incidents, presenting threats to the life and health of the underground crew.In Polish mining there are known examples of transient states of air parameters recorded during gasdynamic phenomena, e.g. tremors and rock bursts. The paper presents the case studies of rapid seismic incidents to show how records in mine monitoring systems broaden the knowledge about the transient states of air parameters in mining headings generated because of them.

Gamma-Ray Bursts in the Swift Era

Since the successful launch of NASA＇s dedicated gamma-ray burst （GRB） mission, Swift, the study of cosmological GRBs has entered a new era. Here I review the rapid observational and theoretical progress in this dynamical research field during the first two-year of the Swift mission, focusing on how observational breakthroughs have revolutionized our understanding of the physical origins of GRBs. Besides summarizing how Swift helps to solve some pre-Swift mysteries, I also list some outstanding problems raised by the Swift observations. An outlook of GRB science in the future, especially in the GLAST era, is briefly discussed.

Protecting miners from coal bursts during development above historic mine workings in Harlan County,KY

In order to reach a large,untapped reserve of high-quality coal,D8 Cloverlick Mine proposed to mine a corridor nearly 600 m deep beneath the Benham Spur of Black Mountain,Kentucky’s highest peak.D8 Cloverlick Mine was extracting the Owl seam,but the corridor’s route lay approximately 20 m above century-old mine workings in the C–(Darby)seam.Adding to the concern,three serious coal bursts had recently occurred in nearby Owl seam workings.Maps of the old workings seemed to indicate that the underlying C–seam had been fully extracted.However,two of the coal bursts had occurred above areas where the C–Seam was also shown as mined out.Mine Safety and Health Administration(MSHA)Technical Support therefore investigated the records of past mining to better understand the old mine maps.Underground conditions observed in current Owl seam workings were also compared with the maps of the old C–seam workings.The study concluded that the presence of hazardous underlying remnants could not be ruled out.To mitigate the burst risk,D8 Cloverlick Mine adopted a strategy of stress probe drilling.A self-propelled coal drill was used to auger 11.5-m-long,small diameter holes in advance of mining.As each hole was drilled,the cuttings were measured to detect the presence of highly stressed coal.Ultimately the crossing was successfully completed without incident.

Convective Bursts Episode of the Rapidly Intensified Typhoon Mujigae(2015)

Convective burst(CB) characteristics at distinct stages of a rapidly intensified Typhoon Mujigae(2015), are investigated based on a 72-h simulation. The spatial features show that almost all CB elements develop in the eyewall. The number of CBs in the inner-core region within a 100 km radius—which account for a large proportion of the total CBs, with a sharp increase about 6 h before the onset of rapid intensification(RI)—provides some indication of the RI of the typhoon. The CBs during pre-RI and RI are examined from dynamic and thermodynamic viewpoints. The combination of lower-level convergent inflow and upper-level divergent outflow pushes a relay-race-like transmission of convective activity, favorable for the development of deep convection. A double warm-core structure is induced by the centripetal outflow sinking and warming associated with CBs, which directly accelerates RI by a sudden decrease in hydrostatic pressure. By utilizing the convection activity degree(CAD) index derived from the local total energy anomaly, a correlation formula between CBs and CAD is deduced.Furthermore, an intense CAD(ICAD) signal threshold(with a value equal to 100) to predict CBs is obtained. It is verified that this ICAD threshold is effective for estimating the occurrence of a CB episode and predicting RI of a typhoon. Therefore,this threshold may be a valuable tool for identifying CB episodes and forecasting rapidly intensified typhoons.

Relationships between Relative Spectral Lags and Relative Widths of Gamma-ray Bursts

The phenomenon of gamma-ray burst （GRB） spectral lags is very common, but a definitive explanation has not yet been given. From a sample of 82 GRB pulses we find that the spectral lags are correlated with the pulse widths, however, there is no correlation between the relative spectral lags and the relative pulse widths. We suspect that the correlations between spectral lags and pulse widths might be caused by the Lorentz factor of the GRBs concerned. Our analysis on the relative quantities suggests that the intrinsic spectral lag might reflect other aspect of pulses than the aspect associated with the dynamical time of shocks or that associated with the time delay due to the curvature effect.

Verification of Short-Term Predictions of Solar Soft X-ray Bursts for the Maximum Phase (2000-2001) of Solar Cycle 23

We present a verification of the short-term predictions of solar X-ray bursts for the maximum phase (2000–2001) of Solar Cycle 23, issued by two prediction centers. The results are that the rate of correct predictions is about equal for RWC-China and WWA; the rate of too high predictions is greater for RWC-China than for WWA, while the rate of too low predictions is smaller for RWC-China than for WWA.

Gamma-Ray Bursts: Afterglows and Central Engines

Gamma-ray bursts (GRBs) are the most intense transient gamma-ray events in the sky; this, together with the strong evidence (the isotropic and inhomogeneous distribution of GRBs detected by BASTE) that they are located at cosmological distances, makes them the most energetic events ever known. For example, the observed radiation energies of some GRBs are equivalent to the total convertion into radiation of the mass energy of more than one solar mass. This is thousand times stronger than the energy of a supernova explosion. Some unconventional energy mechanism and extremely high conversion efficiency for these mysterious events are required. The discovery of host galaxies and association with supernovae at cosmological distances by the recently launched satellite of BeppoSAX and ground based radio and optical telescopes in GRB afterglow provides further support to the cosmological origin of GRBs and put strong constraints on their central engine. It is the aim of this article to review the possible central engines, energy mechanisms, dynamical and spectral evolution of GRBs, especially focusing on the afterglows in multi-wavebands.

Statistical Properties of the Highest Pulses in Gamma-Ray Bursts

We study the statistical properties of the highest pulses within individual gamma-ray bursts (GRBs). A wavelet package analysis technique and a developed pulse-finding algorithm have been applied to identify the highest pulses from burst profiles observed by BATSE on board CGRO from 1991 April 21 to 1999 January 26. The statistical light curves of the highest pulses in four energy channels have been derived by an aligning method, which illustrate the temporal evolution of the pulse emission. Our result that narrower pulses go with higher energies is consistent with previous findings. By normalizing both the pulse durations and counts to unity, 'characteristic' profiles of the highest pulses in the four channels are also derived. The four characteristic profiles are turned out to be almost the same, thus strongly support the previous conclusion that the temporal profiles in different energy channels are self-similar and the previous conjecture on GRB pulses, implying that the emission process is similar at different energies. The cosmological time dilation effect is examined by investigating the relationship between the pulse flux and pulse duration. An anti-correlation between the two was found, which agrees with the expectation of the cosmological time dilation effect. Also, the evolution of the pulse duration with the observational epoch is studied. The result shows that the pulse duration tends to be shorter in later epochs. This trend cannot be explained by the present theoretical models, and may represent a great challenge to current theories.

The Early X-ray Afterglows of Optically Bright and Dark Gamma-Ray Bursts

A systematic study on the early X-ray afterglows of both optically bright and dark gamma-ray bursts （B-GRBs and D-GRBs） observed by Swift is presented. Our sample includes 25 GRBs of which 13 are B-GRBs and 12 are D-GRBs. Our results show that the distributions of the X-ray afterglow fluxes （Fx）, the gamma-ray fluxes （Sγ）, and the ratio （Rγ,x） are similar for the two kinds of GRBs, that any observed differences should be simply statistical fluctuation. These results indicate that the progenitors of the two kinds of GRBs are of the same population with comparable total energies of explosion. The suppression of optical emission in the D-GRBs should result from circumburst but not from their central engine.

Relative Spectral Lag: a New Redshift Indicator of Gamma-ray Bursts

Using 64 ms count data of long gamma-ray bursts （T90 〉 2.6 s）, we analyze the quantity named relative spectral lag （RSL）, T31/FWHM（1）. We investigated in detail all the correlations between the RSL and other parameters for a sample of nine long bursts, using the general cross-correlation technique that includes the lag between two different energy bands. We conclude that the distribution of RSLs is normal and has a mean value of 0.1; that the RSLs are weakly correlated with the FWHM, the asymmetry, peak flux （Fp）, peak energy （Ep） and spectral indexes （α and β）, while they are uncorrelated with τ31, the hardness- ratio （HR31） and the peak time （tm）. Our important discovery is that redshift （z） and peak luminosity （Lp） are strongly correlated with the RSL, which can be measured easily and directly, making the RSL a good redshift and peak luminosity indicator.

Extending the correlation of L_R-L_X to gamma-ray bursts

The well-known correlation between radio luminosity （LR） and X-ray luminosity （Lx）, LR/LX 10^-5, holds for a variety of objects, such as active galactic nuclei, Galactic black holes, solar flares and cool stars. Here we extend the relation to gamma-ray bursts （GRBs） and find that the GRBs also obey a similar LR - LX relation, with a slightly different slope of LR ∝ LX^1.1. This relation implies that the explosions that occur on different scales may have a common underlying origin.

Statistical Properties of X-Ray Bursts from SGR J1935+2154 Detected by Insight-HXMT

As one class of the most important objects in the universe,magnetars can produce a lot of different frequency bursts including X-ray bursts.In Cai et al.,75 X-ray bursts produced by magnetar SGR J1935+2154 during an active period in 2020 are published,including the duration and net photon counts of each burst,and waiting time based on the trigger time difference.In this paper,we utilize the power-law model,dN(x)/dx∝(x+x_0)~((-α)_x),to fit the cumulative distributions of these parameters.It can be found that all the cumulative distributions can be well fitted,which can be interpreted by a self-organizing criticality theory.Furthermore,we check whether this phenomenon still exists in different energy bands and find that there is no obvious evolution.These findings further confirm that the X-ray bursts from magnetars are likely to be generated by some self-organizing critical process,which can be explained by a possible magnetic reconnection scenario in magnetars.

Sequences in the Hardness Ratio-Peak Energy Plane of Gamma-Ray Bursts

The narrowness of the distribution of the peak energy of the νFν spectrum of gamma-ray bursts (GRBs) and the unification of GRB populations are great puzzles yet to be solved. We investigate the two puzzles based on the global spectral behaviors of different GRB populations, the long GRBs, the short GRBs, and the X-ray flashes (XRFs), in the HR?Ep plane (HR the spectral hardness ratio) with BATSE and HETE-2 observations. It is found that the long GRBs and the XRFs observed by HETE-2 seem to follow the same sequence in the HR?Ep plane, with the XRFs at the low end of this sequence. We fit the sequence by a universal Band function, and find that this sequence is mainly defined by the low energy index α, and is insensitive to the high energy index, β. With fixed β = ?5, a best fit is given by α = ?1.00 with χ2min/dof = 2.2. The long and short GRBs observed by BATSE follow significantly different sequences in the HR?Ep plane, with most of the short GRBs having a larger hardness ratio than the long GRBs at a given Ep. For the long GRBs a best-fit yields α = ?0.30 and β = ?2.05. For the short GRBs, a best fit gives α = ?0.60 with χ2min = 1.1 (with β fixed at -2.0 because it is numerically unstable). The α value for the short GRBs is significantly greater than that for the long GRBs. These results indicate that the global spectral behaviors of the long GRB sample and the XRF sample are similar, while that of the short GRBs is different. The short GRBs seem to be a unique subclass of GRBs, and they are not the higher energy extension of the long GRBs.

Constraints on generalized Chaplygin gas model including gamma-ray bursts

Generalized Chaplygin gas （whose equation of state is PGCG = -A/ρGCG^α） was proposed as a candidate for unification of dark energy and dark matter. We investigate constraints on this model with the latest observed data. We test the model with type-Ia supernovae （SNe Ia）, cosmic microwave background （CMB） anisotropy, X-ray gas mass fractions in clusters, and gamma-ray bursts （GRBs）. We calibrate the GRB luminosity relations without assuming any cosmological models using SNe Ia. We show that GRBs can extend the Hubble diagram to higher redshifts （z 〉 6）. The GRB Hubble diagram is well behaved and delineates the shape of the Hubble diagram well. We measure As≡A/ρGCG,0^α＋1 =0.68-0.08^＋0.04（where PGCG,0 is the energy density today） and α=-0.22 -0.13^＋0.15 at the 1σ confidence level using all the datasets. Our results rule out the standard Chaplygin gas model （α = 1） at the 3σ confidence level. The ACDM is allowed at the 2σ confidence level. We find that acceleration could have started at a redshift of z - 0.70. The concordance of the generalized Chaplygin gas model with the age estimate of an old high redshift quasar is found. In addition, we show that GRBs can break the degeneracy between the generalized Chaplygin gas model and the XCDM model.

The isotropic energy function and formation rate of short gamma-ray bursts

Gamma-ray bursts(GRBs)are brief,intense,gamma-ray flashes in the universe,lasting from a few milliseconds to a few thousand seconds.For short gamma-ray bursts(sGRBs)with duration less than 2 seconds,the isotropic energy(E_(iso))function may be more scientifically meaningful and accurately measured than the luminosity(Lp)function.In this work we construct,for the first time,the isotropic energy function of s GRBs and estimate their formation rate.First,we derive the L_(p)-E_(p) correlation using 22 s GRBs with known redshifts and well-measured spectra and estimate the pseduo redshifts of 334 Fermi s GRBs.Then,we adopt the Lynden-Bell c-method to study isotropic energy functions and formation rate of s GRBs without any assumption.A strong evolution of isotropic energy E_(iso)∝(1+z)^(5.79) is found,which is comparable to that between L_(p) and z.After removing effect of the cosmic evolution,the isotropic energy function can be reasonably fitted by a broken power law,which is φ(E_(iso,0))∝E_(iso,0)^(-0.045) for dim sGRBs andφ(E_(iso,0))∝E_(iso,0)^(-1.11) for bright sGRBs,with the break energy 4.92×10^(49)erg.We obtain the local formation rate of s GRBs is about 17.43 events Gpc^(-3)yr^(-1).If assuming a beaming angle is 6° to 26°,the local formation rate including off-axis s GRBs is estimated as ρ_(0,all)=155.79-3202.35 events Gpc^(-3)yr^(-1).

Redshift Independence of the Amati and Yonetoku Relations for Gamma-Ray Bursts

The Amati and Yonetoku relations are two of the main energy and luminosity correlations that currently exist for gamma-ray bursts (GRBs). The Amati relation is a correlation between the intrinsic peak energy, Epeak, in the vFv spectrum of a burst and its equivalent isotropic energy, Eiso. The Yonetoku relation is a correlation between Epeak and the isotropic peak luminosity, Liso. In this paper, we use a recent data sample of 65 GRBs to investigate whether these two relations evolve with redshift, z. The z-correction and the?k-correction are both taken into account. Our method consists of binning the data in redshift, z, then applying (for each bin) a fit of the form:?log(Eiso) = A + Blog(Epeak/Epeak>) for the Amati relation, and of the form:?log(Liso) = A + Blog(Epeak/Epeak>) for the Yonetoku relation, where Epeak> is the mean value of the peak energy for the entire sample. The objective is to see whether the two fitting parameters, A and B, evolve systematically with z. Good least-squares fits were obtained with reasonable values for the linear regression coefficient, r. Our results indicate that the normalization, A, and the slope, B, do not evolve with redshift, and hence the Amati and Yonetoku relations seem to be redshift independent.

Extended Hubble Diagram on the Basis of Gamma Ray Bursts Including the High Redshift Range of z = 0.0331 - 8.1

It is generally accepted that the history of the expansion of the universe can be exactly described by the concordance model, which makes specific predictions about the shape of the Hubble diagram. The redshift-magnitude Hubble diagram in the redshift range z = 0.0104 - 1 seems to confirm this expectation, and it is believed that this conformity is also valid in the high redshift range. However, this belief is not undisputed. Recent work in the high redshift range of up to z = 8.1 has shown that the shape of the Hubble diagram deviates considerably from the predictions made by the Lambda cold dark matter model. These analyses, however, were based on mixed SN1a and gamma ray burst data, and some astronomers argue that this may have biased the results. In this paper, 109 cosmology-independent, calibrated gamma ray burst z/μdata points are used to calculate the Hubble diagram in the range z = 0.034 to z = 8.1. The outcome of this analysis confirms prior results: contrary to expectations, the shape of the Hubble diagram turns out to be exponential, and this is difficult to explain within the framework of the standard model. The cosmological implications of this unexpected result are discussed.