2005/12/31 by Enwei Liang, En‐Wei Liang, Bing Zhang · 5 citations
Physics and Astronomy · #Astro and Planetary Science #Gamma-ray bursts and supernovae #Pulsars and Gravitational Waves Research #astro-ph
paper · pdf · doi:10.1111/j.1745-3933.2006.00169.x
published as Mon.Not.Roy.Astron.Soc.Lett.369:L37-L41,2006 · 5 pages in compact MNARS format, 4 figures, version accepted for publication in MNRAS Letters
arxiv created 2006/03/26 · openalex publication_date 2006/05/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract Several gamma-ray burst (GRB) luminosity indicators have been proposed which can be generally written in the form of , where c is the coefficient, xi is the ith observable, and ai is its corresponding power-law index. Unlike in Type Ia supernovae, calibration of GRB luminosity indicators using a low-redshift sample is difficult. This is because the GRB rate drops rapidly at low redshifts, and some nearby GRBs may be different from their cosmological brethren. Calibrating the standard candles using GRBs in a narrow redshift range (Δz) near a fiducial redshift has been proposed recently. Here we elaborate such a possibility and propose to calibrate ai based on the Bayesian theory and to marginalize the c value over a reasonable range of cosmological parameters. We take our newly discovered multivariable GRB luminosity indicator, Eiso = cEa1pta2b, as an example and test the validity of this approach through simulations, where Eiso is the isotropic energy of prompt gamma-rays, Ep is the spectral break energy, and tb is the temporal break time of the optical afterglow light curve. We show that while c strongly depends on the cosmological parameters, neither a1 nor a2 does as long as Δz is small enough. The selection of Δz for a particular GRB sample could be judged according to the size and the observational uncertainty of the sample. There is no preferable redshift to perform the calibration of the indices ai, while a lower redshift is preferable for c-marginalization. The best strategy would be to collect GRBs within a narrow redshift bin around a fiducial intermediate redshift (e.g. zc ∼ 1 or zc ∼ 2), as the observed GRB redshift distribution is found to peak around this range. Our simulation suggests that with the current observational precisions of measuring Eiso, Ep and tb, 25 GRBs within a redshift bin of Δz ∼ 0.30 would give fine calibration to the Liang–Zhang luminosity indicator.