# Characteristics of Long Gamma-Ray bursts in the Comoving Frame

## TL;DR

This study analyzes the intrinsic properties and correlations of long gamma-ray bursts in the comoving frame, revealing narrow distributions and confirming that observed spectral-energy relations are influenced by Doppler effects.

## Contribution

It provides the first comprehensive analysis of long GRBs in the comoving frame, demonstrating intrinsic parameter distributions and the impact of Doppler effects on observed correlations.

## Key findings

- Distributions of duration, peak energy, isotropic energy, and luminosity are narrow in the comoving frame.
- Confirmed key spectral-energy correlations and their persistence in the comoving frame.
- Peak energies are independent of durations, with a weak anticorrelation between peak energy and Lorentz factor.

## Abstract

We compile a sample of 93 long gamma-ray bursts (GRBs) from Fermi satellite and 131 from Konus-Wind, which have measured redshifts and well determined spectra, and estimate their pseudo Lorentz factors (${\Gamma_0}$) using the tight ${L_{{\rm{iso}}}}$-${E_{\rm p}}$-${\Gamma_0}$ correlation. The statistical properties and pair correlations of temporal and spectral parameters are studied in the observer frame, rest frame and comoving frame, respectively. We find that the distributions of the duration, peak energy, isotropic energy and luminosity in the different frames are basically lognormal, and their distributions in the comoving frame are narrow, clustering around $T'_{\rm 90}\sim 4000$ s, $E'_{\rm p,c}\sim 0.7$ keV, $E'_{\rm iso,c} \sim 8\times10^{49}$ erg and $L'_{\rm iso,c}\sim 2.5\times10^{46}$ erg s$^{-1}$, where the redshift evolution effect has been taken into account. We also find that the values of ${\Gamma_0}$ are broadly distributed between few tens and several hundreds with median values $\sim 270$. We further analyze the pair correlations of all the quantities, and well confirm ${E_{{\rm{iso}}}}$-${E_{\rm p}}$, ${L_{{\rm{iso}}}}$-${E_{\rm p}}$, ${L_{{\rm{iso}}}}$-${\Gamma_0}$ and $E_{\rm{iso}}$-${\Gamma_0}$ relations, and find that the corresponding relations in the comoving frame do still exist, but have large dispersions. This suggests not only the well-known spectrum-energy relations are intrinsic correlations, but also the observed correlations are governed by the Doppler effect. In addition, the peak energies of long GRBs are independent of durations both in the rest frame and in the comoving frame. And there is a weak anticorrelation between the peak energy and Lorentz factor.