Ranking Prompt--Plateau Correlations in Gamma-Ray Bursts with Symbolic Regression
Abstract
Gamma-ray burst (GRB) correlations probe central engines, relativistic outflows, and radiation processes. The Dainotti relation is an anticorrelation between the X-ray plateau luminosity La and rest-frame plateau duration Tarest. We use symbolic regression to compare it with other low-dimensional correlations in 251 GRBs with Swift-XRT plateau properties and Swift-BAT prompt-emission parameters. We perform a Dainotti-guided search, in which log Tarest is always present, and an unrestricted search over subsets of at most three variables. The guided search recovers the Dainotti dependence; a D'Agostini fit gives log La=(51.92±0.30)−(1.31±0.09)log Tarest, with intrinsic scatter σint=0.82±0.05 dex. In the unrestricted ranking of 377 feature subsets, the classical Dainotti relation remains competitive, within the top ∼25% of the tested search spaces. The highest-ranked screened expression is log La≈0.855log Lpeak−0.782log Tarest, with RMSE ≈0.46 and R2≈0.88. The highest-ranked runs repeatedly reduce to this prompt--plateau structure, without retaining additional spectral, absorption, or afterglow-shape variables. A direct regression gives log La=4.718+0.776log Lpeak−0.805log Tarest, with RP=0.91 for 246 bursts. An errors-in-variables refit gives consistent coefficients. After removing shared luminosity-distance dependence, the relation retains non-negligible explanatory power (R2≈0.62), consistent with a possible intrinsic component. Restricted Monte Carlo null tests give p≈0.01. Plateau luminosity therefore shows a coupled dependence on prompt luminosity and plateau duration.
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BibTeX
@misc{rastegarnia2026ranking,
title = {{Ranking Prompt--Plateau Correlations in Gamma-Ray Bursts with Symbolic Regression}},
author = {Fatemeh Rastegarnia and Rahim Moradi and Brwa Shukur Ismael and Mohsen Asaadi and Yu Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23155},
eprint = {2610.23155},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23155},
note = {CC0},
}
RIS
TY - UNPB
TI - Ranking Prompt--Plateau Correlations in Gamma-Ray Bursts with Symbolic Regression
AU - Fatemeh Rastegarnia
AU - Rahim Moradi
AU - Brwa Shukur Ismael
AU - Mohsen Asaadi
AU - Yu Wang
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23155
UR - https://arxiv.org/abs/2610.23155
AB - Gamma-ray burst (GRB) correlations probe central engines, relativistic outflows, and radiation processes. The Dainotti relation is an anticorrelation between the X-ray plateau luminosity L_a and rest-frame plateau duration T_a^rest. We use symbolic regression to compare it with other low-dimensional correlations in 251 GRBs with Swift-XRT plateau properties and Swift-BAT prompt-emission parameters. We perform a Dainotti-guided search, in which log T_a^rest is always present, and an unrestricted search over subsets of at most three variables. The guided search recovers the Dainotti dependence; a D'Agostini fit gives log L_a=(51.92±0.30)−(1.31±0.09)log T_a^rest, with intrinsic scatter σ_int=0.82±0.05 dex. In the unrestricted ranking of 377 feature subsets, the classical Dainotti relation remains competitive, within the top ∼25% of the tested search spaces. The highest-ranked screened expression is log L_a≈0.855log L_peak−0.782log T_a^rest, with RMSE ≈0.46 and R^2≈0.88. The highest-ranked runs repeatedly reduce to this prompt--plateau structure, without retaining additional spectral, absorption, or afterglow-shape variables. A direct regression gives log L_a=4.718+0.776log L_peak−0.805log T_a^rest, with R_P=0.91 for 246 bursts. An errors-in-variables refit gives consistent coefficients. After removing shared luminosity-distance dependence, the relation retains non-negligible explanatory power (R^2≈0.62), consistent with a possible intrinsic component. Restricted Monte Carlo null tests give p≈0.01. Plateau luminosity therefore shows a coupled dependence on prompt luminosity and plateau duration.
ER -