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Register a new userConstraints on the bulk Lorentz factor in the internal shock scenario for gamma-ray bursts
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Added by
Gabriele Ghisellini
Publication date
1999
fields
Physics
and research's language is
English
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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.
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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.
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 $10^{-6} {rm M_{odot}}$.
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 prompt emission of gamma-ray bursts probably comes from a highly relativistic wind which converts part of its kinetic energy into radiation via the formation of shocks within the wind itself. Such internal shocks can occur if the wind is generated with a highly non uniform distribution of the Lorentz factor. We estimate the expected photospheric emission of such a wind when it becomes transparent. We compare this thermal emission (temporal profile + spectrum) to the non-thermal emission produced by the internal shocks. In most cases, we predict a rather bright thermal emission that should already have been detected. This favors acceleration mechanisms for the wind where the initial energy input is under magnetic rather than thermal form. Such scenarios can produce thermal X-ray precursors comparable to those observed by GINGA and WATCH/GRANAT.
The prompt GRB emission is thought to arise from electrons accelerated in internal shocks propagating within a highly relativistic outflow. The launch of Fermi offers the prospect of observations with unprecedented sensitivity in high-energy (>100 MeV) gamma-rays. The aim is to explore the predictions for HE emission from internal shocks, taking into account both dynamical and radiative aspects, and to deduce how HE observations constrain the properties of the relativistic outflow. The emission is modeled by combining a time-dependent radiative code with a dynamical code giving the evolution of the physical conditions in the shocked regions.Synthetic lightcurves and spectra are compared to observations. The HE emission deviates significantly from analytical estimates, which tend to overpredict the IC component, when the time dependence and full cross-sections are included. The exploration of the parameter space favors the case where the dominant process in the BATSE range is synchrotron emission. The HE component becomes stronger for weaker magnetic fields. The HE lightcurve can display a prolonged pulse duration due to IC emission, or even a delayed peak compared to the BATSE range.Alternatively, having dominant IC emission in the BATSE range requires most electrons to be accelerated into a steep power-law distribution and implies strong 2nd order IC scattering. In this case, the BATSE and HE lightcurves are very similar. The combined dynamical and radiative approach allows a firm appraisal of GRB HE prompt emission. A diagnostic procedure is presented to identify from observations the dominant emission process and derive constrains on the bulk Lorentz factor, particle density and magnetic field of the outflow.
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