Multi-Model Framework for Reconstructing Gamma-Ray Burst Light Curves

TL;DR

This work tackles the challenge of data gaps in GRB X-ray afterglow light curves by evaluating seven novel reconstruction methods alongside statistical baselines, using a consistent preprocessing and uncertainty framework on 521 Swift GRBs. The study demonstrates that the Quartic Smoothing Spline (QSS) approach delivers the strongest reductions in uncertainties for the plateau parameters $\log T_a$, $\log F_a$, and the post-plateau slope $\alpha$, outperforming other methods and reducing the parameter uncertainties by up to approximately 48%. It also reveals model-specific strengths, such as the lowest outlier rate for $\alpha$ with CNN-BiLSTM and moderate gains for DGP, Isotonic Regression, and TCN, while highlighting the importance of gap-aware reconstruction to prevent systematic shifts. The results bolster confidence in using GRB plateau parameters for cosmological applications, including standard-candle considerations and GRB redshift estimation, and point to future exploration of transformer-based and physics-informed neural approaches to further enhance LC reconstruction and interpretability.

Abstract

Mitigating data gaps in Gamma-ray bursts (GRBs) light curves (LCs) is crucial for cosmological research, enhancing the precision of parameters, assuming perfect satellite conditions for complete LC coverage with no gaps. This analysis improves the applicability of the two-dimensional Dainotti relation, which connects the rest-frame end time of the plateau emission (Ta) and its luminosity (La), derived from the fluxes (Fa). The study expands on a previous 521 GRB sample by incorporating seven models: Deep Gaussian Process (DGP), Temporal Convolutional Network (TCN), Hybrid CNN with Bidirectional Long Short-Term Memory (CNN-BiLSTM), Bayesian Neural Network (BNN), Polynomial Curve Fitting, Isotonic Regression, and Quartic Smoothing Spline (QSS). Results indicate that QSS significantly reduces uncertainty across parameters: 43.5% for log Ta, 43.2% for log Fa, and 48.3% for alpha, outperforming the other models where alpha denotes the slope post-plateau based on Willingale 2007 functional form. The Polynomial Curve Fitting model demonstrates moderate uncertainty reduction across parameters, while CNN-BiLSTM has the lowest outlier rate for alpha at 0.77%. These models broaden the application of machine-learning techniques in GRB LC analysis, enhancing uncertainty estimation and parameter recovery, and complement traditional methods like the Attention U-Net and Multilayer Perceptron (MLP). These advancements highlight the potential of GRBs as cosmological probes, supporting their role in theoretical model discrimination via LC parameters, serving as standard candles, and facilitating GRB redshift predictions through advanced machine-learning approaches.

Figures (14)

• Figure 1: The GRB LCs can be classified into four types based on the afterglow feature: i) Good GRBs (upper left); ii) GRB LCs that have a break in the terminal end (upper right); iii) Flares or Bumps in the afterglow (bottom left); iv) Flares or Bumps that have Double Break at the end of the LC (bottom right).References: [1] 2008ApJS..175..179S; [2] 2018ApJ...866...97B; [3] 2022ApJ...938...41D.
• Figure 2: Deep GP as a Markov chain
• Figure 3: a) Residual block of a Temporal Convolutional Network. (b) Expanded view of a dilated convolution layer
• Figure 4: Workflow of the CNN-BiLSTM model for GRB light-curve reconstruction.
• Figure 5: BNN architecture for GRB light-curve reconstruction