Average Power-Density Spectrum of short and long Fermi-GBM Gamma-Ray Bursts

Abstract

Gamma-ray bursts (GRBs) are the most powerful electromagnetic outbursts in the Universe and emit a vast amount of their energy in the form of gamma rays. Their duration is extremely short on cosmic timescales, but they show a wealth of time variability in their light curves. Properties of this variability may carry information about the processes the gamma rays emerge from, which are still poorly understood. This research investigates the redshift-corrected gamma-ray light curves of 159 long GRBs, observed with the Gamma-Ray Burst Monitor on the Fermi Gamma-Ray Space Telescope between 2008 and 2023. We calculate the average power-density spectrum (PDS) of different groups of GRBs that are distinguished based on fluence, peak rate, duration, redshift, and the different GRB phases. Almost all redshift-corrected spectra reveal a power-law behavior with high-frequency power-law indices distributed around $\sim -1.9 \pm 0.2$. The precursor phase and redshift-corrected short bursts exhibit a shallower power law with index $\sim -1.30 \pm 0.04$, potentially due to the limited statistics that these samples represent. Only in some cases, the high-frequency index is still consistent with the $-5/3$ (Kolmogorov) slope, found by earlier studies and linked to the appearance of fully developed turbulence.

Figures (14)

• Figure 1: Observed $T_{90}$ distribution (left), redshift distribution (center) and fluence distribution (right) of the 204 selected GRBs, distinguishing between short (blue) and long (red) GRBs.
• Figure 2: Observed $T$ distribution of the 204 selected GRBs, where $T$ is defined as the duration of the total signal region, identified by the phase identification used in this analysis.
• Figure 3: Left: The phase-identification procedure identifies the signal regions in the light curve, in this case a precursor and prompt phase. A Tukey window function with $\alpha = 0.25$ selects only the relevant emission zone in the light curve, based on these signal regions. The duration of the total emission region is called $T$. Right: The PDS analysis is performed on the relevant signal region and, subsequently, on a noise region of the same length.
• Figure 4: Best-fit parameters $\chi^2/n_{d.o.f.}$, $\beta_{LF}$, $\beta_{HF}$, $f_b$, $F_0$ of the average PDS for different groups of GRBs (with $N$ GRBs). If not mentioned differently, the spectra are fitted with a broken power law (BPL). If the spectrum is fitted with a single power law (SPL), the exponent enters in the $\beta_{HF}$ column, and the multiplication factor in the $F_0$ column. Abbreviations: SPL, single power law; OF, observer frame; RF, redshift-corrected frame.
• Figure 5: The average PDS of long and short bursts (purple) is a combination of the characteristics of the PDS of short GRBs (red) and long GRBs (yellow). As both are significantly different, they are analyzed separately.