Gamma-ray bursts in the comoving frame

Abstract

We estimate the bulk Lorentz factor Γ 0 of 31 GRBs using the measured peak time of their afterglow light curves. We consider two possible scenarios for the estimate of Γ 0 : the case of a homogeneous circumburst medium or a wind density profile. The values of Γ 0 are broadly distributed between few tens and several hundreds with average values ∼138 and ∼66 for the homogeneous and wind density profile, respectively. We find that the isotropic energy and luminosity correlate in a similar way with Γ 0 , i.e. E iso ∝Γ 0 2 and L iso ∝Γ 0 2 , while the peak energy E peak ∝Γ 0 . These correlations are less scattered in the wind density profile than in the homogeneous case. We then study the energetics, luminosities and spectral properties of our bursts in their comoving frame. The distribution of L ′ iso is very narrow with a dispersion of less than a decade in the wind case, clustering around L ′ iso ∼ 5 × 10 48 erg s −1 . Peak photon energies cluster around E ′ peak ∼ 6 keV. The newly found correlations involving Γ 0 offer a general interpretation scheme for the spectral-energy correlation of GRBs. The E peak − E iso and E peak − L iso correlations are due to the different Γ 0 factors and the collimation-corrected correlation, E peak − E γ (obtained by correcting the isotropic quantities for the jet opening angle θ j ), can be explained if θ 2 j Γ 0 = constant. Assuming the E peak − E γ correlation as valid, we find a typical value of θ j Γ 0 ∼ 6-20, in agreement with the predictions of magnetically accelerated jet models.

Ultrahigh-energy cosmic ray production by turbulence in gamma-ray burst jets and cosmogenic neutrinos

“…Owing to the hard spectrum, the spectral peak at ∼ 10 20 eV becomes higher than that for the shock model. To take into account the diversity of Γ, we also adopt an empirical relation between Γ and L γ expressed by Γ = 72.1L 0.49 52 , which was adopted in He et al [21] based on the results of Ghirlanda et al [75]. This relation leads to a slightly softer spectrum, as shown by the model B in Fig.…”

“…Hereafter, we normalize E CR through the total GRB energy in photons as E CR = f CR E γ . An empirical relation obtained by Ghirlanda et al [75] is…”

The extension of variability properties in gamma-ray bursts to blazars

“…Since this method get rid of artificial effect due top the noise floor, hereafter we adopt the MTS measurements reported in and Golkhou et al (2015). The Lorentz factors reported in Sonbas et al (2014) were taken from Lü et al (2012) and Ghirlanda et al (2012). Ghirlanda et al (2012) made use of the Blandford & McKee (1976) self-similar deceleration solution, which led to typically a factor of 2 times smaller Γ than those derived from the conventional method for a same source.…”

“…The Lorentz factors reported in Sonbas et al (2014) were taken from Lü et al (2012) and Ghirlanda et al (2012). Ghirlanda et al (2012) made use of the Blandford & McKee (1976) self-similar deceleration solution, which led to typically a factor of 2 times smaller Γ than those derived from the conventional method for a same source. Since at the peak time, the blast wave is not in the Blandford-McKee self-similar regime, we believe that the conventional method is more reasonable to estimate Γ (see Lü et al 2012, for more discussions).…”

“…The emission of a GRB is believed to originate from an ultrarelativistic jet with a Lorentz factor of a few hundreds. Such a high Lorentz factor is evidenced from the "compactness" argument (e.g., Fenimore et al 1993;Zou et al 2011) or the early afterglow light curves that show the signal of fireball deceleration (e.g., Sari & Piran 1999;Liang et al 2010;Ghirlanda et al 2012). The prompt emission of GRBs in the sub-MeV energy range normally exhibits a non-thermal nature with a smoothly-joint broken power-law shape (i.e.…”