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Register a new userGamma-Ray Bursts: Temporal Scales and the Bulk Lorentz Factor
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For a sample of Swift and Fermi GRBs, we show that the minimum variability timescale and the spectral lag of the prompt emission is related to the bulk Lorentz factor in a complex manner: For small $Gamma$s, the variability timescale exhibits a shallow (plateau) region. For large $Gamma$s, the variability timescale declines steeply as a function of $Gamma$ ($delta TproptoGamma^{-4.05pm0.64}$). Evidence is also presented for an intriguing correlation between the peak times, t$_p$, of the afterglow emission and the prompt emission variability timescale.
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Knowledge of the bulk Lorentz factor $Gamma_{0}$ of GRBs allows us to compute their comoving frame properties shedding light on their physics. Upon collisions with the circumburst matter, the fireball of a GRB starts to decelerate, producing a peak or a break (depending on the circumburst density profile) in the light curve of the afterglow. Considering all bursts with known redshift and with an early coverage of their emission, we find 67 GRBs with a peak in their optical or GeV light curves at a time $t_{rm p}$. For another 106 GRBs we set an upper limit $t_{rm p}^{rm UL}$. We show that $t_{rm p}$ is due to the dynamics of the fireball deceleration and not to the passage of a characteristic frequency of the synchrotron spectrum across the optical band. Considering the $t_{rm p}$ of 66 long GRBs and the 85 most constraining upper limits, using censored data analysis methods, we reconstruct the most likely distribution of $t_{rm p}$. All $t_{rm p}$ are larger than the time $t_{rm p,g}$ when the prompt emission peaks, and are much larger than the time $t_{rm ph}$ when the fireball becomes transparent. The reconstructed distribution of $Gamma_0$ has median value $sim$300 (150) for a uniform (wind) circumburst density profile. In the comoving frame, long GRBs have typical isotropic energy, luminosity, and peak energy $langle E_{rm iso}rangle=3(8)times 10^{50}$ erg, $langle L_{rm iso}rangle=3(15) times 10^{47}$ erg s$^{-1}$ , and $langle E_{rm peak}rangle =1(2)$ keV in the homogeneous (wind) case. We confirm that the significant correlations between $Gamma$ and the rest frame isotropic energy ($E_{rm iso}$), luminosity ($L_{rm iso}$) and peak energy ($E_{rm peak}$) are not due to selection effects. Assuming a typical opening angle of 5 degrees, we derive the distribution of the jet baryon loading which is centered around a few $10^{-6} {rm M_{odot}}$.
We investigate, independently of specific emission models, the constraints on the value of the bulk Lorentz factor Gamma of a fireball. We assume that the burst emission comes from internal shocks in a region transparent to Thomson scattering and before deceleration due to the swept up external matter is effective. We consider the role of Compton drag in decelerating fast moving shells before they interact with slower ones, thus limiting the possible differences in bulk Lorentz factor of shells. Tighter constraints on the possible range of Gamma are derived by requiring that the internal shocks transform more than a few per cent of the bulk energy into radiation. Efficient bursts may require a hierarchical scenario, where a shell undergoes multiple interactions with other shells. We conclude that fireballs with average Lorentz factors larger than 1000 are unlikely to give rise to the observed bursts.
It is largely recognized that Gamma-Ray Burst (GRB) jets involve ultra-relativistic motion. However, the value of the Lorentz factor Gamma_0 is still not clear and only lower limits are known for most bursts. We suggest here a new method to obtain upper limits on Gamma_0. The early high-energy synchrotron afterglow flux depends strongly on Gamma_0. Upper limits on GeV emission therefore provide uppers limit on Gamma_0. Applying this method to 190 Fermi GRBs that have not been detected by the Fermi-LAT we place upper limits on the high-energy afterglow flux, and in turn on Gamma_0. For bursts at a typical redshift z=2, we find values of the order of 200 (and above) for a homogeneous density medium, and in the range 100-400 for a wind-like medium. These upper limits are consistent with (and are very close to) lower limits and direct estimates inferred using other methods, suggesting that the typical Lorentz factors of GRB jets are of order a few hundred.
The constancy of light speed is a basic assumption in Einsteins special relativity, and consequently the Lorentz invariance is a fundamental symmetry of space-time in modern physics. However, it is speculated that the speed of light becomes energy-dependent due to the Lorentz invariance violation~(LV) in various new physics theories. We analyse the data of the energetic photons from the gamma-ray bursts (GRBs) by the Fermi Gamma-Ray Space Telescope, and find more events to support the energy dependence in the light speed with both linear and quadratic form corrections. We provide two scenarios to understand all the new-released Pass~8 data of bright GRBs by the Fermi-LAT Collaboration, with predictions from such scenarios being testable by future detected GRBs.
The jet opening angle theta_jet and the bulk Lorentz factor Gamma_0 are crucial parameters for the computation of the energetics of Gamma Ray Bursts (GRBs). From the ~30 GRBs with measured theta_jet or Gamma_0 it is known that: (i) the real energetic E_gamma, obtained by correcting the isotropic equivalent energy E_iso for the collimation factor ~theta_jet^2, is clustered around 10^50-10^51 erg and it is correlated with the peak energy E_p of the prompt emission and (ii) the comoving frame E_p and E_gamma are clustered around typical values. Current estimates of Gamma_0 and theta_jet are based on incomplete data samples and their observed distributions could be subject to biases. Through a population synthesis code we investigate whether different assumed intrinsic distributions of Gamma_0 and theta_jet can reproduce a set of observational constraints. Assuming that all bursts have the same E_p and E_gamma in the comoving frame, we find that Gamma_0 and theta_jet cannot be distributed as single power-laws. The best agreement between our simulation and the available data is obtained assuming (a) log-normal distributions for theta_jet and Gamma_0 and (b) an intrinsic relation between the peak values of their distributions, i.e theta_jet^2.5*Gamma_0=const. On average, larger values of Gamma_0 (i.e. the faster bursts) correspond to smaller values of theta_jet (i.e. the narrower). We predict that ~6% of the bursts that point to us should not show any jet break in their afterglow light curve since they have sin(theta_jet)<1/Gamma_0. Finally, we estimate that the local rate of GRBs is ~0.3% of all local SNIb/c and ~4.3% of local hypernovae, i.e. SNIb/c with broad-lines.
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