Evolutions and Calibrations of Long Gamma-Ray Bursts Luminosity Correlations Revisited

Abstract

Luminosity correlations of long Gamma-ray bursts (GRB) are extensively proposed as an effective complementarity to trace the Hubble diagram of Universe at high redshifts, which is of great importance to explore properties of dark energy. Recently, several empirical luminosity correlations have been statistically proposed from GRB observations. However, to treat GRB as the distance indicator, there are two key issues: the redshift evolution of luminosity correlations and their calibrations. In this paper, we choose the Amati relation, the correlation between the peak spectra energy and the equivalent isotropic energy of GRBs ($E_{\mathrm{p}}-E_{\mathrm{iso}}$), as an example, and find that the current GRB dataset implies that there could be a evolution of the luminosity correlation with respect to the redshift. Therefore, we propose an extended Amati relation with two extra redshift-dependent terms to correct the redshift evolution of GRB relation. Secondly, we carefully check the reliability of the calibration method using the low-redshift GRB data. Importantly, we find that the low-redshift calibration method does not take whole correlations between ${\Omega }_{\mathrm{m}}$ and coefficients into account. Neglecting these correlation information can break the degeneracies and obtain the biased constraint on ${\Omega }_{\mathrm{m}}$ which is very sensitive to values of parameters for the calibration. A small shift of parameters of "calibrated" relation could significantly change the final constraint on ${\Omega }_{\mathrm{m}}$ in the low-redshift calibration method. Finally, we simulate several GRB samples with different statistical errors and find that, in order to correctly recover the fiducial value of ${\Omega }_{\mathrm{m}}$ using the low-redshift calibration method, we need a large number of GRB samples with high precisions.

9 pages, 7 figures, ApJ in press

References in corpus (12)

• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• The Physics of Gamma-Ray Bursts and Relativistic Jets
• The Hubble Diagram to Redshift >6 from 69 Gamma-Ray Bursts
• Detection of a Thermal Spectral Component in the Prompt Emission of GRB 100724B
• A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram
• Gamma-ray Burst Cosmology
• Towards a Better Understanding of the GRB Phenomenon: a New Model for GRB Prompt Emission and its effects on the New Non-Thermal L${}_{\mathrm{i}}^{\mathrm{NT}}$-E${}_{\mathrm{peak},\mathrm{i}}^{\mathrm{rest},\mathrm{NT}}$ relation
• An unexpectedly low-redshift excess of Swift gamma-ray burst rate
• Reconstructing the Cosmic Expansion History up to Redshift z=6.29 with the Calibrated Gamma-Ray Bursts
• The Hubble diagram extended to z>>1: the gamma-ray properties of GRBs confirm the Lambda-CDM model
• Variation of the Amati Relation with the Cosmological Redshift: a Selection Effect or an Evolution Effect?
• Unbiased constraints on the clumpiness of universe from standard candles

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• Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae
• Gamma ray burst constraints on cosmological models from the improved Amati correlation
• The improved Amati correlations from Gaussian copula
• Redshift evolution of the Amati relation: calibrated results from the Hubble diagram of quasars at high redshifts
• High Redshift Long Gamma-Ray Bursts Hubble Diagram as a Test of Basic Cosmological Relations
• Gamma Rays Bursts: A Viable Cosmological Probe?
• Constraining Coupling Constants' Variation with Supernovae, Quasars, and GRBs
• Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way
• Confirmed width-Eiso and width-Liso relations in GRB: comparison with the Amati and Yonetoku relations