An analytic derivation of the empirical correlations of gamma-ray bursts

Abstract

Empirical correlations between various key parameters have been extensively explored ever since the discovery of gamma-ray bursts (GRBs) and have been widely used as standard candles to probe the Universe. The Amati relation and the Yonetoku relation are two good examples that enjoyed special attention. The former reflects the connection between the peak photon energy (Ep) and the isotropic $\gamma$-ray energy release (Eiso), while the latter links Ep with the isotropic peak luminosity (Lp), both in the form of a power-law function. Most GRBs are found to follow these correlations well, but a theoretical interpretation is still lacking. Some obvious outliers may be off-axis GRBs and may follow correlations that are different from those at the on-axis. Here we present a simple analytical derivation for the Amati relation and the Yonetoku relation in the framework of the standard fireball model, the correctness of which is then confirmed by numerical simulations. The off-axis Amati relation and Yonetoku relation are also derived. They differ markedly from the corresponding on-axis relation. Our results reveal the intrinsic physics behind the radiation processes of GRBs, and they highlight the importance of the viewing angle in the empirical correlations of GRBs.

12 pages, 7 figures, 2 tables. A&A accepted

References in corpus (21)

• The Internal-Collision-Induced Magnetic Reconnection and Turbulence (ICMART) Model of Gamma-Ray Bursts
• Discerning the physical origins of cosmological Gamma-ray bursts based on multiple observational criteria: the cases of z=6.7 GRB 080913, z=8.3 GRB 090423, and some short/hard GRBs
• Detection of a Thermal Spectral Component in the Prompt Emission of GRB 100724B
• GRB110721A: An extreme peak energy and signatures of the photosphere
• Temporal Evolution Of Thermal Emission From Relativistically Expanding Plasma
• Cosmology with gamma-ray bursts: I. The Hubble diagram through the calibrated $E_{\mathrm{p},\mathrm{i}}$ - $E_{\mathrm{iso}}$ correlation
• The Ep,i - Eiso correlation: type I gamma-ray bursts and the new classification method
• Bulk Lorentz factors of Gamma-Ray Bursts
• Lessons from the short GRB170817A - the First Gravitational Wave Detection of a Binary Neutron Star Merger
• The X-ray fundamental plane of the Platinum Sample, the Kilonovae and the SNe Ib/c associated with GRBs
• Low-energy Spectra of Gamma-ray Bursts from Cooling Electrons
• Measuring cosmological parameters with a luminosity-time correlation of gamma-ray bursts
• X-ray Plateaus in Gamma-Ray Burst Afterglows and Their Application in Cosmology
• $E_{\mathrm{iso}}$-$E_{\mathrm{p}}$ correlation of gamma ray bursts: calibration and cosmological applications
• Pseudo Redshifts of Gamma-Ray Bursts Derived from the L-T-E Correlation
• Testing High-latitude Curvature Effect of Gamma-Ray Bursts with {\it Fermi} Data: Evidence of Bulk Acceleration in Prompt Emission
• Is the Birth of PSR J0538+2817 Accompanied by a Gamma-ray Burst?
• On Spectral Peak Energy of Swift Gamma-Ray Bursts
• Characteristics of Long Gamma-Ray bursts in the Comoving Frame
• The $E_{\mathrm{p}}$ - $E_{\mathrm{iso}}$ relation and the internal shock model
• Inferring the emission regions for different kinds of gamma-ray bursts

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