Insights on the Gamma-Ray Bursts variability in their cosmological rest frame

Technical Summary: Insights on the Gamma-Ray Bursts variability in their cosmological rest frame

Problem Statement
Gamma-ray bursts (GRBs) exhibit extreme temporal variability, ranging from single pulses to complex sequences of superimposed pulses. While the fireball model attributes this variability to central engine activity or magnetic reconnection, the specific composition of GRB jets (Poynting flux vs. baryonic matter) remains unclear, as these scenarios predict different variability signatures. A critical open question is the identification of the Minimum Variability Timescale (MVT), defined as the shortest timescale over which a significant variation in the GRB profile is observed. Determining the MVT is essential for constraining the dimensions and activity of the central engine and distinguishing between theoretical models. Previous studies have investigated MVT down to hundreds of microseconds, but a comprehensive analysis of thousands of GRBs in their cosmological rest frame, specifically correlating MVT with spectral parameters like isotropic energy ($E_{iso}$) and peak energy ($E_p$), is required to refine these constraints.

Methodology
The authors analyzed a sample of 3,155 GRBs detected by the Fermi Gamma-ray Burst Monitor (GBM) between July 2008 and October 2021. After filtering for data completeness, 3,062 GRBs were retained (511 short, 2,551 long). A subset of 150 GRBs with measured redshifts (129 long, 21 short) was selected for analysis in the cosmological rest frame.

The data processing pipeline involved:

1. Data Retrieval: Accessing Time-Triggered Event (TTE) unbinned data files for triggered detectors.
2. Background Subtraction: Using the gbm.background routine to fit and subtract background counts from intervals 20–5 seconds pre-burst and 75–150 seconds post-burst.
3. MVT Calculation: Two methods based on the Haar discrete wavelet transform were employed to determine the MVT:
   • Method 1: Identifies the MVT as the timescale where the structure function ($\sigma_{X,\Delta t}$) deviates from a linear rising phase (determined via $\chi^2$ test).
   • Method 2: Defines MVT as the intersection between a linear fit of the rising phase and a fit of the subsequent flatter region (based on Golkhou et al. 2015).
4. Rest Frame Correction: For the redshifted sample, observed MVTs ($\Delta t_{min}$) were converted to the cosmological rest frame ($\Delta t_{min,z}$) by dividing by $(1+z)$.
5. Correlation Analysis: The study examined correlations between $\Delta t_{min,z}$ and spectral parameters ($E_{iso}$, $E_p$) across different energy bands (Soft: 20–100 keV; Hard: 100–1000 keV). The Amati relation was utilized to compare $\Delta t_{min,z}$, $E_{iso}$, and $E_p$ simultaneously.

Key Results

• MVT Values: In the observer frame, the median MVT for long GRBs was 738 ms (Method 1) and 583 ms (Method 2); for short GRBs, it was 77.6 ms and 53 ms, respectively. In the cosmological rest frame, these values decreased to 236 ms (long) and 37.3 ms (short).
• Energy Dependence: A "narrowness-hardness" relation was confirmed in the rest frame: MVTs calculated in the hard energy band (100–1000 keV) were consistently shorter than those in the soft band (20–100 keV), indicating that temporal profiles sharpen at higher energies.
• Time Dilation: Binning long GRBs by redshift groups revealed a trend compatible with cosmological time dilation ($\Delta t_{min} \propto 1+z$), although the statistical significance was limited by the 2$\sigma$ confidence interval.
• Anti-correlation with Isotropic Energy: A significant anti-correlation was found between $\Delta t_{min,z}$ and $E_{iso}$ for long GRBs ($r = -0.59$), indicating that bursts with higher isotropic energies exhibit faster variability. This relation held even when controlling for fluence. Notably, some high-redshift GRBs classified as "short" by observer-frame duration ($T_{90}$) but possessing "long" spectral characteristics behaved like long GRBs in this relation, challenging the traditional duration-based classification.
• Peak Energy Relation: $\Delta t_{min,z}$ was found to be anti-correlated with peak energy ($E_{p,z}$). For short GRBs, the relation followed $\Delta t_{min,z} \propto E_{p,z}^{-0.98}$; for long GRBs, $\Delta t_{min,z} \propto E_{p,z}^{-0.62}$.
• Total Variability: The study calculated a total variability parameter ($V$) and found no clear correlation between $V$ and MVT, though a slight anti-correlation between $V$ and $E_{iso}$ was observed.
• Simulation: A simulated GRB containing a microsecond-scale pulse demonstrated that the analysis tools are capable of identifying variabilities as short as 3–5 $\mu$s, provided the signal-to-noise ratio is sufficient.

Significance and Claims
The paper claims to provide a robust statistical characterization of GRB variability in the cosmological rest frame using a large sample size. The primary contributions are:

1. Confirmation of Physical Trends: The study validates the energy-dependent sharpening of GRB pulses and the time dilation effect on variability timescales using a larger sample than previous works.
2. Central Engine Constraints: The observed anti-correlation between MVT and $E_{iso}$ (and $E_p$) suggests a physical link between the burst's total energy output and the timescale of the central engine's activity. The authors suggest that if the internal shock model holds, the MVT traces the distance between the central engine and the $\gamma$-ray production site.
3. Classification Challenges: The results highlight inconsistencies in the traditional short/long GRB division based solely on $T_{90}$. High-redshift bursts with short durations but long-like spectral properties (and MVT-$E_{iso}$ relations) suggest that alternative classification criteria, such as the Amati relation or spectral hardness, may be more physically motivated.
4. Future Readiness: The work demonstrates that current analysis techniques are capable of resolving microsecond variability, setting the stage for future missions (e.g., HERMES Pathfinder) with improved timing resolution to probe the sub-millisecond regime and potentially distinguish between magnetic reconnection and internal shock models.

The authors remain modest regarding the definitive nature of these findings, noting that the statistical power for short GRBs is currently limited and that the exact physical origin of the MVT-$E_{iso}$ relation requires further theoretical investigation. They emphasize that the existence of microsecond variability remains to be confirmed by next-generation instrumentation.