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.

arXiv comment9 pages, 7 figures, ApJ in press

References in corpus (51)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• emcee: The MCMC Hammer
• Planck 2015 results. XIII. Cosmological parameters
• Improved cosmological constraints from a joint analysis of the SDSS-II and SNLS supernova samples
• The Hubble Space Telescope Cluster Supernova Survey: V. Improving the Dark Energy Constraints Above z>1 and Building an Early-Type-Hosted Supernova Sample
• Gamma-Ray Bursts and the Fireball Model
• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• Intrinsic spectra and energetics of BeppoSAX Gamma-Ray Bursts with known redshifts
• Gamma-Ray Bursts
• The Physics of Gamma-Ray Bursts and Relativistic Jets
• Theories of Gamma-Ray Bursts
• GRB Formation Rates inferred from the Spectral Peak Energy - Luminosity Relation
• The collimation--corrected GRB energies correlate with the peak energy of their $\nu F_{\nu }$ spectrum
• A glimpse of the end of the dark ages: the gamma-ray burst of 23 April 2009 at redshift 8.3
• Connection Between Energy-dependent Lags And Peak Luminosity In Gamma-ray Bursts
• GRB 090423 at a redshift of z~8.1
• A Photometric Redshift of z ~ 9.4 for GRB 090429B
• The Hubble Diagram to Redshift >6 from 69 Gamma-Ray Bursts
• Model-Independent Multi-Variable Gamma-Ray Burst Luminosity Indicator and Its Possible Cosmological Implications
• Detection of a Thermal Spectral Component in the Prompt Emission of GRB 100724B
• Constraining ${\Omega }_M$ and Dark Energy with Gamma-Ray Bursts
• Gamma Ray Bursts: new rulers to measure the Universe
• A Cosmology-Independent Calibration of Gamma-Ray Burst Luminosity Relations and the Hubble Diagram
• Evidence for a Photospheric Component in the Prompt Emission of the Short GRB120323A and its Effects on the GRB Hardness-Luminosity Relation
• Gamma Ray Bursts as standard candles to constrain the cosmological parameters
• Observational Constraints on Cosmological Models with the Updated Long Gamma-Ray Bursts
• Gamma-Ray Burst Hubble Diagram to z=4.5
• Gamma-ray Burst Cosmology
• Measuring dark energy with the $E_{\mathrm{iso}}-E_{\mathrm{p}}$ correlation of gamma-ray bursts using model-independent methods
• Slope evolution of GRB correlations and 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
• The updated luminosity correlations of gamma-ray bursts and cosmological implications
• Fits, and especially linear fits, with errors on both axes, extra variance of the data points and other complications
• Testing GRBs as Standard Candles
• Cosmological Models and Gamma-Ray Bursts Calibrated by Using Pade Method
• A new method optimized to use Gamma Ray Bursts as cosmic rulers
• Overcoming the Circular Problem for γ-ray Bursts in Cosmological Global Fitting Analysis
• Reconstructing the Cosmic Expansion History up to Redshift z=6.29 with the Calibrated Gamma-Ray Bursts
• GRB 131014A: a Laboratory to Study the Thermal-Like and Non-Thermal Emissions in Gamma-Ray Bursts, and the new L${}_{\mathrm{i}}^{\mathrm{nTh}}$-E${}_{\mathrm{peak},\mathrm{i}}^{\mathrm{nTh},\mathrm{rest}}$ relation
• 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?
• Exploring the Systematic Uncertainties of Type Ia Supernovae as Cosmological Probes
• A Unified Model for GRB Prompt Emission from Optical to $\gamma$-Rays: Exploring GRBs as Standard Candles
• Exploring the evolution of color-luminosity parameter $\beta$ and its effects on parameter estimation
• Are long gamma-ray bursts standard candles?
• CGRO/BATSE Data Support the New Paradigm for GRB Prompt Emission and the New L${}_i^{nTh}$-E${}_{peak,i}^{nTh,rest}$ relation
• Effect of GRB spectra on the empirical luminosity correlations and the GRB Hubble diagram
• Unbiased constraints on the clumpiness of universe from standard candles
• The highest redshift gamma-ray bursts

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• 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?
• Reconciling low and high redshift GRB luminosity correlations
• Constraints on Cosmological Models with Gamma-Ray Bursts in Cosmology-Independent Way
• Constraining Coupling Constants' Variation with Supernovae, Quasars, and GRBs
• Confirmed width-Eiso and width-Liso relations in GRB: comparison with the Amati and Yonetoku relations