Context. Two classes of gamma-ray bursts (GRBs), short and long, have been determined without any doubts, and are usually prescribed to different physical scenarios. A third class, intermediate in T 90 durations has been reported in the datasets of BATSE, Swift, RHESSI, and possibly BeppoSAX. The latest release of >1500 GRBs observed by Fermi gives an opportunity to further investigate the duration distribution. Aims. The aim of this paper is to investigate whether a third class is present in the log T 90 distribution, or whether it is described by a bimodal distribution. Methods. A standard χ 2 fitting of a mixture of Gaussians was applied to 25 histograms with different binnings. Results. Different binnings give various values of the fitting parameters, as well as the shape of the fitted curve. Among five statistically significant fits, none is trimodal. Conclusions. Locations of the Gaussian components are in agreement with previous works. However, a trimodal distribution, understood in the sense of having three distinct peaks, is not found for any binning. It is concluded that the duration distribution in the Fermi data is well described by a mixture of three log-normal distributions, but it is intrinsically bimodal, hence no third class is present in the T 90 data of Fermi. It is suggested that the log-normal fit may not be an adequate model.

The long range dependence of the fractional Brownian motion (fBm), fractional Gaussian noise (fGn), and differentiated fGn (DfGn) is described by the Hurst exponent H. Considering the realisations of these three processes as time series, they might be described by their statistical features, such as half of the ratio of the mean square successive difference to the variance, A, and the number of turning points, T . This paper investigates the relationships between A and H, and between T and H. It is found numerically that the formulae A(H) = ae bH in case of fBm, and A(H) = a + bH c for fGn and DfGn, describe well the A(H) relationship. When T (H) is considered, no simple formula is found, and it is empirically found that among polynomials, the fourth and second order description applies best. The most relevant finding is that when plotted in the space of (A, T ), the three process types form separate branches. Hence, it is examined whether A and T may serve as Hurst exponent indicators. Some real world data (stock market indices, sunspot numbers, chaotic time series) are analyzed for this purpose, and it is found that the H's estimated using the H(A) relations (expressed as inverted A(H) functions) are consistent with the H's extracted with the well known wavelet approach. This allows to efficiently estimate the Hurst exponent based on fast and easy to compute A and T , given that the process type: fBm, fGn or DfGn, is correctly classified beforehand. Finally, it is suggested that the A(H) relation for fGn and DfGn might be an exact (shifted) 3/2 power-law.

It was recently shown that the T 90 −H 32 distributions of gamma-ray bursts from CGRO/BATSE and Fermi/GBM are well described by a mixture of only two skewed components, making the presumed third, intermediate class unnecesary. The Swift/BAT, Konus-Wind, RHESSI and Suzaku/WAM data sets are found to be consistent with a two-class description as well.

Two classes of GRBs have been identified thus far without doubt and are prescribed to different physical scenarios-NS-NS or NS-BH mergers, and collapse of massive stars, for short and long GRBs, respectively. The existence of two distinct populations was inferred through a bimodal distribution of the observed durations T 90 , and the commonly applied 2 s limit between short and long GRBs was obtained by fitting a parabola between the two peaks in binned data from BATSE 1B. Herein, by means of a maximum likelihood (ML) method a mixture of two Gaussians is fitted to the datasets from BATSE, Swift, BeppoSAX, and Fermi in search for a local minimum that might serve as a new, more proper, limit for the two GRB classes. It is found that Swift and BeppoSAX distributions are unimodal, hence no local minimum is present, Fermi is consistent with the conventional limit, whereas BATSE gives the limit significantly longer (equal to 3.38 ± 0.27 s) than 2 s. These new values change the fractions of short and long GRBs in the samples examined, and imply that the observed T 90 durations are detector dependent, hence no universal limiting value may be applied to all satellites due to their different instrument specifications. Because of this, and due to the strong overlap of the two-Gaussian components, the straightforward association of short GRBs to mergers and long ones to collapsars is ambiguous.

We present the results of the Fermi-Large Area Telescope 10 yr long light curve (LC) modeling of selected blazars: six flat-spectrum radio quasars (FSRQs) and five BL Lacertae (BL Lacs), examined in 7, 10, and 14 day binning. The LCs and power spectral densities (PSDs) were investigated with various methods: Fourier transform, Lomb–Scargle periodogram (LSP), wavelet scalogram, autoregressive moving average (ARMA) process, continuous-time ARMA (CARMA), Hurst exponent (H), and the plane. First, with extensive simulations we showed that parametric modeling returns unreliable parameters, with a high dispersion for different realizations of the same stochastic model. Hence, any such analysis should be supported with Monte Carlo simulations. For our blazar sample, we find that the power-law indices β calculated from the Fourier and LSP modeling mostly fall in the range 1 ≲ β ≲ 2. Using the wavelet scalograms, we confirm a quasi-periodic oscillation (QPO) in PKS 2155−304 at a 3σ significance level, but do not detect any QPOs in other objects. The ARMA fits reached higher orders for 7 day binned LCs and lower orders for 10 and 14 day binned LCs for the majority of blazars, suggesting there might exist a characteristic timescale for the perturbations in the jet and/or accretion disk to die out. ARMA and CARMA modeling revealed breaks in their PSDs at timescales of a few hundred days. The estimation of H was performed with several methods. We find that most blazars exhibit H > 0.5, indicating long-term memory. Finally, the FSRQ and BL Lac subclasses are clearly separated in the plane.

Two classes of GRBs have been confidently identified thus far and are prescribed to different physical scenarios -NS-NS or NS-BH mergers, and collapse of massive stars, for short and long GRBs, respectively. A third, intermediate in duration class, was suggested to be present in previous catalogs, such as BATSE and Swift, based on statistical tests regarding a mixture of two or three log-normal distributions of T 90 . However, this might possibly not be an adequate model. This paper investigates whether the distributions of log T 90 from BATSE, Swift, and Fermi are described better by a mixture of skewed distributions rather than standard Gaussians. Mixtures of standard normal, skew-normal, sinh-arcsinh and alpha-skew-normal distributions are fitted using a maximum likelihood method. The preferred model is chosen based on the Akaike information criterion. It is found that mixtures of two skew-normal or two sinharcsinh distributions are more likely to describe the observed duration distribution of Fermi than a mixture of three standard Gaussians, and that mixtures of two sinharcsinh or two skew-normal distributions are models competing with the conventional three-Gaussian in the case of BATSE and Swift. Based on statistical reasoning, and it is shown that other phenomenological models may describe the observed Fermi, BATSE, and Swift duration distributions at least as well as a mixture of standard normal distributions, and the existence of a third (intermediate) class of GRBs in Fermi data is rejected.

Two classes of gamma-ray bursts (GRBs), short and long, have been determined without any doubts, and are usually ascribed to different progenitors, yet these classes overlap for a variety of descriptive parameters. A subsample of 46 long and 22 short Fermi GRBs with estimated Hurst Exponents (HEs), complemented by minimum variability time-scales (MVTS) and durations (T 90 ) is used to perform a supervised Machine Learning (ML) and Monte Carlo (MC) simulation using a Support Vector Machine (SVM) algorithm. It is found that while T 90 itself performs very well in distinguishing short and long GRBs, the overall success ratio is higher when the training set is complemented by MVTS and HE. These results may allow to introduce a new (non-linear) parameter that might provide less ambiguous classification of GRBs.

The mechanism responsible for the prompt emission of gamma-ray bursts (GRBs) is still a debated issue. The prompt phase-related GRB correlations can allow discriminating among the most plausible theoretical models explaining this emission. We present an overview of the observational two-parameter correlations, their physical interpretations, and their use as redshift estimators and possibly as cosmological tools. The nowadays challenge is to make GRBs, the farthest stellar-scaled objects observed (up to redshift = 9.4), standard candles through well established and robust correlations. However, GRBs spanning several orders of magnitude in their energetics are far from being standard candles. We describe the advances in the prompt correlation research in the past decades, with particular focus paid to the discoveries in the last 20 years.