⚛️ phenomenology

Generalized Linear Models of T $_{90}$ -T $_{50}$ relation to classify GRBs

This study utilizes Generalized Linear Models to analyze the $T_{90}$ - $T_{50}$ relation in Fermi GBM and BATSE catalogs, revealing multiple linear features that suggest the existence of more than the traditional two classes of Gamma-ray bursts.

Original authors: Sourav Dutta, Sunanda, Reetanjali Moharana, Manish Kumar

Published 2026-09-01

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Sourav Dutta, Sunanda, Reetanjali Moharana, Manish Kumar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast, silent expanse of the universe, there are moments of violence so intense they outshine entire galaxies for a fleeting second. These are gamma-ray bursts, the most energetic explosions known to science. They flash across the sky in a blink, lasting anywhere from a fraction of a second to several minutes. For decades, astronomers have tried to make sense of these cosmic flashes, sorting them into categories much like a librarian organizing books. The most common way to sort them has been by how long they last. By measuring the time it takes for a burst to deliver 90 percent of its total energy, scientists have traditionally divided these events into two distinct groups: short bursts that vanish in less than two seconds, and long bursts that linger for much longer. This simple split has seemed to explain the data, suggesting that short bursts come from the collision of tiny, dense stars, while long bursts are the death throes of massive, collapsing stars. However, the universe is rarely as tidy as our first guesses, and for years, researchers have wondered if there might be a third, hidden category lurking in the data, or if the two groups we see are actually just the most visible parts of a more complex family.

A team of physicists at the Indian Institute of Technology Jodhpur decided to look deeper than just the length of the flash. They realized that if you measure not just the total duration of a burst, but also the time it takes to deliver half of its energy, these two measurements should be related. If a burst is long, it is generally expected to take a long time to reach its halfway point as well. Instead of just counting how many bursts fall into "short" or "long" bins, the researchers treated the relationship between these two time measurements as a line. They gathered a massive collection of data from two major satellite missions, one that has been watching the sky since 1991 and another that has been recording events since 2008. By plotting the time to reach half-energy against the time to reach 90-percent energy for thousands of bursts, they used a sophisticated statistical tool to see if the points on the graph formed a single straight line or if they clustered into several different lines.

The results of this investigation challenge the simple two-class view. When the researchers analyzed the data from the older satellite mission, the statistical model suggested the possibility of four linear features, directing towards the possibility of more than two GRB classes. When they applied the same method to the newer, larger dataset, the model identified five linear features, also directing towards the possibility of more than two GRB classes. This implies that the gamma-ray bursts are not just a mix of two types, but likely consist of at least four or five different sub-groups, each following its own specific rule for how its duration and intensity evolve. The study also looked at the "hardness" of the bursts, which is a measure of how energetic the light is compared to lower-energy light, finding that this too might separate the bursts into multiple groups rather than just two.

While the traditional method of looking at a histogram of burst lengths still shows a clear split between short and long events, this new approach reveals a more intricate structure underneath. The researchers found that some bursts increase their duration much more slowly than others, creating distinct groups that were previously hidden when looking at time alone. The evidence suggests that the universe may be producing several different kinds of these explosions, perhaps originating from different types of stellar collisions or collapse scenarios that we have not yet fully distinguished. The study does not claim to have solved the mystery of every gamma-ray burst, but it provides strong statistical evidence that the family of these cosmic events is larger and more diverse than the simple "short and long" classification has led us to believe. By mapping these relationships, the team has opened a new door for understanding the true variety of the most powerful explosions in the cosmos.

Technical Summary: Generalized Linear Models of T90-T50 Relation to Classify GRBs

Problem Statement
Gamma-ray bursts (GRBs) are traditionally classified into two distinct populations: Short GRBs (SGRBs) and Long GRBs (LGRBs), based on the bimodal distribution of their duration parameter, $T_{90}$ (the time to collect 90% of the fluence). While this binary classification is well-established and linked to different astrophysical origins (compact star mergers for SGRBs and supernovae for LGRBs), the existence of a third class or sub-classes has been a subject of debate. Previous studies utilizing univariate and bivariate analyses with Gaussian distributions have occasionally suggested a third class, but these findings remain contested. Furthermore, standard classification often relies on single-parameter histograms, which may overlook linear dependencies between multiple observed parameters such as duration ( $T_{50}$ , $T_{90}$ ) and spectral hardness ratio (HR).

Methodology
The authors analyze two major GRB catalogs: the Fermi GBM catalog (3,440 events, 2008–2023) and the BATSE 4B catalog (1,637 events, 1991–1996). The study employs two primary machine learning and statistical approaches:

Gaussian Mixture Model (GMM): Used first to verify the bimodality of $T_{90}$ and $T_{50}$ distributions. The optimal number of components ( $k$ ) is determined using the Bayesian Information Criterion (BIC). The model assumes the data is a weighted sum of $k$ Gaussian distributions.
Generalized Linear Models (GLM): To investigate linear dependencies between parameters, the authors apply the GLM algorithm (specifically the flexmix package in R). This method treats the data as a finite mixture of regression models. The authors analyze three parameter spaces:
- $T_{90}$ vs. $T_{50}$
- $T_{90}$ vs. HR
- $T_{50}$ vs. HR
  The number of distinct linear features (classes) is determined by minimizing the BIC. To account for randomness in class assignment, the BIC minimization was performed $10^5$ times for each parameter space.

Key Results

Univariate Analysis (GMM): Both the Fermi GBM and BATSE 4B datasets confirm the existence of two distinct populations in the $T_{90}$ and $T_{50}$ distributions.
- Fermi GBM: SGRBs ( $\mu \approx 0.965$ s) and LGRBs ( $\mu \approx 28.47$ s).
- BATSE 4B: SGRBs ( $\mu \approx 0.57$ s) and LGRBs ( $\mu \approx 32.15$ s).
  The BIC analysis strongly favors a two-component model for these single-parameter distributions.
Multivariate Linear Analysis (GLM): The analysis of linear correlations reveals a more complex structure than the univariate histograms suggest:
- $T_{90}$ vs. $T_{50}$ (Fermi GBM): While the overall correlation coefficient is high ( $\rho = 0.96$ ), the GLM analysis identifies five distinct linear features (classes). The BIC difference ( $\Delta_4 = 10.8$ ) provides strong evidence for a five-component model. The fitted slopes for these five classes vary (0.95, 1.2, 1.18, 0.99, and 0.82).
- $T_{90}$ vs. $T_{50}$ (BATSE 4B): The GLM analysis identifies four distinct linear features ( $\Delta_3 = 3.97$ ).
- Hardness Ratio Correlations: The results for $T_{90}$ -HR and $T_{50}$ -HR are less definitive regarding multiple classes. The Fermi GBM data suggests the possibility of more than three linear fits for $T_{90}$ -HR and four for $T_{50}$ -HR, whereas the BATSE 4B data suggests a bilinear dependency for both.

Significance and Claims
The paper claims that while the traditional bimodal classification of GRBs holds true when examining single parameters ( $T_{90}$ or $T_{50}$ ) in isolation, the relationship between these parameters is more nuanced. By applying Generalized Linear Models to the $T_{90}$ - $T_{50}$ plane, the study identifies five linear features in the Fermi GBM catalog and four in the BATSE catalog.

The authors conclude that these linear features direct toward the possibility of more than two GRB classes. Specifically, the GLM technique allows for the grouping of GRB events that exhibit a slower increase in $T_{50}$ relative to $T_{90}$ , a distinction that standard histogram-based classification methods fail to capture. The study suggests that investigating linear dependencies between parameters is a robust method for establishing the existence of sub-classes or additional GRB populations beyond the standard short/long dichotomy.

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