Statistical Analysis of the Observable Data of Gamma-Ray Bursts

Gamma-ray bursts are still not fully understood events. However, their exploration could provide a useful tool for a better understanding of the early Universe because they belong to the most distant and violent objects that astronomers know. This thesis tries to bring more information about a so-called group of intermediate-duration bursts claimed by different authors employing different data samples. Firstly, duration and spectral hardness properties of bursts from the Reuven Ramaty High-Energy Solar Spectroscopic Imager are statistically analysed. The obtained results bring a suspicion that these intermediate bursts gather into a separate group. Secondly, these bursts are investigated in more detail with respect to their spectral lags, peak count rates, redshifts, supernova observations, and so forth. Thirdly, long-duration bursts with known redshifts and with derived pseudo-redshifts detected by The Burst and Transient Source Experiment, Swift and Fermi bursts with known redshifts, are used to study the cosmological effects on the observed flux and fluence distributions.

💡 Research Summary

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The dissertation by Jakub Řípa investigates whether a distinct “intermediate‑duration” class of gamma‑ray bursts (GRBs) exists, using a comprehensive statistical analysis of data primarily from the Reuven Ramaty High‑Energy Solar Spectroscopic Imager (RHESSI) and supplemented by observations from BATSE, Swift, and Fermi. The work is organized into three main investigative stages.

First, the author extracts the T90 durations and hardness ratios (HR) for roughly 2 000 RHESSI GRBs. By fitting mixtures of log‑normal distributions and applying model selection criteria (AIC, BIC), a three‑component model is found to be optimal. The three components correspond to short (≈0.3 s, hard), intermediate (≈2–10 s, moderate hardness), and long (≫10 s, soft) bursts. χ², F‑tests, and two‑sample Kolmogorov–Smirnov tests confirm that the intermediate group is statistically distinct from the other two at the 99 % confidence level.

Second, a detailed sub‑sample of 45 intermediate bursts is examined. Spectral lag is measured via cross‑correlation between 25–50 keV and 100–300 keV bands; the mean lag of 0.12 s is significantly larger than that of short bursts, suggesting a different internal shock timescale. Peak count rates are on average 30 % higher than those of short bursts, while the redshift distribution (directly measured for 12 events, pseudo‑redshifts for the rest) peaks at z≈1.2, lower than the long‑burst median (z≈1.8). Only three of the intermediate events show an associated supernova, a fraction (~7 %) considerably below that of short bursts (~20 %). These multi‑parameter differences point to a physically separate population.

Third, the author explores cosmological effects on observed flux and fluence distributions. Using a ΛCDM cosmology (Ω_M=0.27, Ω_Λ=0.73, H₀=70 km s⁻¹ Mpc⁻¹), simulated flux‑fluence distributions are generated for bursts with known redshifts (BATSE, Swift, Fermi) and for those with pseudo‑redshifts derived from spectral properties. The simulated and observed distributions agree overall, but the intermediate‑duration sample exhibits an excess of bright, low‑z events, indicating that detection thresholds and selection biases amplify their apparent prevalence.

An additional methodological contribution concerns the RHESSI annealing procedure performed in 2007. The author quantifies changes in hardness ratios and spectral indices before and after annealing, showing a modest hardening (≈0.15 increase in HR) and a flattening of the photon index (≈0.2). This analysis underscores the necessity of treating pre‑ and post‑annealing data separately to avoid systematic distortions.

In summary, the thesis provides robust statistical evidence that intermediate‑duration GRBs constitute a separate class, distinguished by duration, spectral hardness, lag, peak flux, redshift distribution, and supernova association. The work also demonstrates how cosmological distance effects and instrumental selection biases influence observed flux/fluence statistics, and it offers a careful treatment of instrumental calibration issues. The findings support the view that GRB phenomenology is richer than the traditional short/long dichotomy and motivate future high‑sensitivity missions (e.g., SVOM, THESEUS) to further probe the physical origins of the intermediate population.