Search for Cosmological time dilation from Gamma-Ray Bursts -- A 2021 status update (2108.00395v2)

Abstract: We carry out a search for signatures of cosmological time dilation in the light curves of Gamma Ray Bursts (GRBs), detected by the Neil Gehrels Swift Observatory. For this purpose, we calculate two different durations ($T_{50}$ and $T_{90}$) for a sample of 247 GRBs in the fixed rest frame energy interval of 140-350 keV, similar to Zhang et al. We then carry out a power law-based regression analysis between the durations and redshifts. This search is done using both the unbinned as well as the binned data, where both the weighted mean and the geometric mean was used. For each analysis, we also calculate the intrinsic scatter to determine the tightness of the relation. We find that weighted mean-based binned data for long GRBs and the geometric mean-based binned data is consistent with the cosmological time dilation signature, whereas the analyses using unbinned durations show a very large scatter. We also make our analysis codes and the procedure for obtaining the light curves and estimation of $T_{50}$/$T_{90}$ publicly available.

• The paper employs power‐law regression on 247 GRBs to statistically test for cosmological time dilation in burst durations.
• It contrasts unbinned and binned analyses, with binned methods yielding power‐law indices near unity for long-duration GRBs.
• Results show that despite high intrinsic scatter in individual cases, statistical techniques successfully capture the expected dilation signature.

Cosmological Time Dilation in Gamma-Ray Bursts: A Statistical Analysis

The astrophysical community has long sought to detect and quantify cosmological time dilation—a signature of an expanding universe—within the light curves of Gamma-Ray Bursts (GRBs). This paper, authored by Amitesh Singh and Shantanu Desai, provides a comprehensive update and analysis on this subject using data from the Neil Gehrels Swift Observatory. The primary focus is on assessing the cosmological time dilation in GRB durations, specifically within the rest-frame energy interval of 140-350 keV, by conducting a power-law regression analysis.

Methodology

The researchers analyzed a sample of 247 GRBs with confirmed redshifts, calculating two critical time intervals, $T_{50}$ and $T_{90}$, which denote the durations over which 50% and 90% of the respective GRB's fluence are detected. Importantly, these durations were considered in a fixed rest-frame energy interval to mitigate detector-related biases. A regression analysis was conducted using both unbinned and binned data to discern any correlation between GRB durations and their redshifts, quantified by the power-law model $y = A \cdot x^B$, where $B = 1$ aligns with the expected signature of cosmological time dilation.

Findings

The findings can be distilled into several key points:

1. Unbinned Data Analysis: The intrinsic scatter in the unbinned data was exceedingly large for both $T_{50}$ and $T_{90}$, indicating an undisciplined relationship with redshift. Hence, no definitive signature of cosmological time dilation could be detected from this analysis.
2. Binned Analysis: When the data was binned, different methodologies yielded varying results:
   • For the full sample using weighted means, the power-law index $B$ showed inconsistent results with the expected cosmological value.
   • In contrast, analyses employing geometric mean-based bin averages indicated results more in alignment with cosmological time dilation, especially for long GRBs (defined by $T_{90} > 2 \text{seconds}$), supporting a statistical rather than individual detection of time dilation.
3. Long GRBs Analysis: By isolating long-duration GRBs, the analysis using both weighted and geometric mean binning demonstrated a consistency with the expected time dilation phenomenon, showing reduced scatter and power-law indices $B$ near unity.
4. Rest Frame Durations: Evaluations of rest-frame durations ($T_{50,rest}$ and $T_{90,rest}$) showed no significant evolutionary trends with redshift, suggesting the time dilation observed at higher redshifts in the binned data may primarily reflect statistical effects rather than intrinsic duration increases.

Implications and Future Directions

These findings offer a nuanced perspective. They suggest that cosmological time dilation is detectable in GRBs at a statistical level but remains elusive on a case-by-case basis due to high intrinsic scatter. The insights from this analysis provide a strategic framework for future observational campaigns and theoretical work in GRB physics, particularly in validating the methodologies for capturing the elusive time dilation signature.

Practical advancements may stem from refining instrument sensitivities and leveraging larger data sets, potentially incorporating other observable parameters to enhance the robustness of the time dilation detection. Additionally, future studies might investigate the role of energy spectrum corrections akin to this paper's rest-frame analysis, applying these learnings to other transient astrophysical phenomena like quasars and supernovae.

Conclusion

This paper substantiates a decade-long inquiry into time dilation in GRBs by reaffirming its statistical detection within the scope of rigorous regression analyses. It underscores the essential role of methodological precision and robust statistical tools in unraveling the subtle manifestations of cosmological principles in high-energy astrophysical phenomena.