Spectral Analysis Results of the X-ray Emission of GRB 240825A

Optical Darkness in GRB 240825A afterglow 1 Online Materials The detailed procedures of the spectral fitting are described in Section 2.1 of the main text. The results of the spectral fitting are presented in Tables A1 and A2 of the main text, and are listed here in the same order as presented in the article. (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A1. XRT spectrum extracted from 87-97 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. Panel (a): Spectral fit to the data with PL model and residuals. Panel (b): Corner plot of the posterior distributions of the model parameters. Panel (c): Quantile-Quantile (Q-Q) plot of residuals. Panel (d) Posterior predictive probability integral transformation-empirical cumulative distribution function (PIT-ECDF) check. 2Li et al. (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A2. XRT spectrum extracted from 97-109 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. Optical Darkness in GRB 240825A afterglow 3 (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A3. XRT spectrum extracted from 109-149 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. 4Li et al. (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A4. XRT spectrum extracted from 149-203 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. Optical Darkness in GRB 240825A afterglow 5 (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A5. XRT spectrum extracted from 203-265 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. 6Li et al. (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A6. XRT spectrum extracted from 265-340 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. Optical Darkness in GRB 240825A afterglow 7 (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A7. XRT spectrum extracted from 340-421 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. 8Li et al. (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A8. XRT spectrum extracted from 421-482 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. Optical Darkness in GRB 240825A afterglow 9 (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A9. XRT spectrum extracted from 482-569 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. 16 Li et al. (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A16. XRT spectrum extracted from 8430-14129 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. Optical Darkness in GRB 240825A afterglow 17 (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A17. XRT spectrum extracted from 14129-26067 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. 18 Li et al. (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A18. XRT spectrum extracted from 26067-61951 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. Optical Darkness in GRB 240825A afterglow 19 (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A19. XRT spectrum extracted from 61951-110958 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. 20 Li et al. (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A20. XRT spectrum extracted from 110958-1637153 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. Optical Darkness in GRB 240825A afterglow 21 (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A21. XRT spectrum extracted from 86-1297 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. 22 Li et al. (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A22. XRT spectrum extracted from 4773-89889 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. Optical Darkness in GRB 240825A afterglow 23 (a) XRT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A23. XRT spectrum extracted from 87-832 s post-trigger, fitted with an absorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. 24 Li et al. (a) BAT spectrum, PL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A24. BAT spectrum extracted from 87-832 s post-trigger, fitted with an unabsorbed PL model and shown with posterior diagnostics. This figure follows the format of Figure A1. Optical Darkness in GRB 240825A afterglow 25 (a) Joint spectrum from XRT and BAT, SBPL model, and residuals. (b) Posterior distributions of model parameters. (c) Q-Q plots of residuals. (d) PIT-ECDF diagnostic. Figure A25. BAT and XRT spectra extracted from 87-832 s post-trigger, fitted with an absorbed SBPL model and shown with posterior diagnostics. This figure follows the format of Figure A1.