Calibrating Gamma-Ray Bursts by Using a Gaussian Process with Type Ia Supernovae
Nan Liang, Zihao Li, Xiaoyao Xie, Puxun Wu
Abstract
Abstract In this paper, we calibrate the Amati relation (the E p – E iso correlation) of gamma-ray bursts (GRBs) in a cosmology-independent way. By using a Gaussian process to reconstruct the smoothed luminosity distance from the Pantheon type Ia supernovae sample, we utilize the reconstructed results to calibrate the E p – E iso correlation with the Markov Chain Monte Carlo method and construct a Hubble diagram with the A220 GRB data, in which there are A118 GRB data with the higher qualities appropriate for cosmological purposes. With 98 GRBs at 1.4 < z ≤ 8.2 in the A118 sample and the observed Hubble data, we obtain Ω m = <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>0.346</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.069</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.048</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , h = <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>0.677</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.029</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.029</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> for the flat ΛCDM model, and Ω m = <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>0.314</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.055</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.072</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , h = <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msubsup> <mml:mrow> <mml:mn>0.705</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.069</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.055</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> , w = <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo>−</mml:mo> <mml:msubsup> <mml:mrow> <mml:mn>1.23</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.64</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.33</mml:mn> </mml:mrow> </mml:msubsup> </mml:math> for the flat w CDM model, which are consistent with those from fitting the coefficients of the Amati relation and the cosmological parameters simultaneously.