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.

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 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.