Major Observational Findings 2421 Jets

GRBs are most likely not spherical explosions, but collimated relativistic flows (jets). Initially, the jet is ultra-relativistic and the cone (1/r) of emission due to relativistic beaming with Lorentz factor r is smaller than the geometrical opening angle (or collimation angle) of the outflow. The observer in the beam will therefore receive light only from within the relativistic cone, and the dynamical evolution is similar to the case of spherical explosion. As the jet slows down, the relativistic cone will eventually become wider than the collimation angle, and the observer will measure a reduced intensity. This "jet break" is quasi-achromatic and has been seen in many GRB afterglow light curves. For several years it has been considered the telltale of collimated outflows in GRBs.

One direct consequence of synchrotron emission is that the emission from an individual particle is polarized. Because of the probably random nature of the post-shock magnetic fields, the polarization is likely to be largely averaged out, and only a small degree of polarization left. The time at which linear polarization is expected to be detectable is thought to be around the jet-break time. Several (differing) models have been proposed, in which a collimated jet and an off-axis line-of-sight conspire to produce an asymmetry, which leads to net polarization including one or several 90° changes of the polarization angle [32,83]. This behavior could provide independent evidence for the jet structure of the relativistic outflow.

The observed polarization at optical wavelengths is less than 3% [39,76,100] with the exception of one report on 10% polarization [10]. Because of this low-level polarization and the rapid decline of the afterglow brightness during the first day, it has been difficult to observe changes in the polarization as predicted by theory. The by far most extensive polarization light curve with fast variability in polarization degree and angle has been obtained for the afterglow of GRB 030329 [37]. This variability pattern does not follow any of the model predictions and is also not correlated with brightness. The global behavior is consistent with the interpretation that the GRB is produced in arelativistic jet with an initial opening angle of 3°. However, in this GRB afterglow several rebrightenings relative to a power law decline have been found which likely have caused deviations from a simple single-jet model, thus making it difficult to interpret. The low level of polarization implies that the components of the magnetic field parallel and perpendicular to the shock do not differ by more than -10%, and suggests an entangled magnetic field, probably amplified by turbulence behind shocks, rather than a pre-existing field.

The interpretation of light curve breaks due to jets can be taken one step further. Using a sample of GRBs with known estimates of the break time (and thus jet opening angle) and redshift, a surprising clustering of the collimation-corrected energy was found around 1.3 x1051 erg [13,22], suggesting that GRBs are produced by a universal energy reservoir despite their large range in isotropic equivalent energies.

Considering also the additional information from the y-ray spectra of GRBs, a correlation between the isotropic equivalent energy and the peak energy (£peak from Sect. 24.1.1) was found [1]. Correcting for the collimation by a factor of (1 - cos 0)

Energy [erg]

Fig. 24.5 Rest frame peak energy £peak(1 + z) vs. bolometric energy for GRBs with known red-shift. The right (black) part is the relation as reported by [1], while the left (color) part is after correcting for the collimation angle (factor 1 — cos 0). The solid line is the best fit with Epeak - 480 x (£r/1051erg)0J keV (from [31])

Energy [erg]

Fig. 24.5 Rest frame peak energy £peak(1 + z) vs. bolometric energy for GRBs with known red-shift. The right (black) part is the relation as reported by [1], while the left (color) part is after correcting for the collimation angle (factor 1 — cos 0). The solid line is the best fit with Epeak - 480 x (£r/1051erg)0J keV (from [31])

tightens this correlation even more (Fig. 24.5) [31], but also invalidates the standard candle energy of 1.3 x 1051 erg [13,22]. While the underlying physical basis of this correlation is mysterious, its small dispersion has been considered as an indication of the robustness of the afterglow theory on which the estimate of the jet opening angle is based [31].

One problem in the above search for correlations is the assignment of a break in the light curve to the jet break. With denser and earlier sampling becoming increasingly available, GRB afterglow light curves show several breaks at different times. Also, breaks in the radio light curve typically occur substantially later than those in the optical. One prominent example is GRB 030329, where the optical break occurs 12 h after the GRB, but the radio break only 10 days later. The association of the jet break to the optical break would shift GRB 030329 (explicitly labeled in Fig. 24.5) by a factor of 100 away from the best-fit.

Another uncertainty arises from the unknown structure of the jet (Fig. 24.6) for which two alternatives have been proposed [71]: a variable jet opening angle (or uniform) model in which the emissivity is a constant independent of the angle relative to the jet axis, and a universal jet model in which the emissivity is a power-law function of the angle relative to the jet axis. Both models can explain the observed properties of GRBs reasonably well. However, if one tries to account for the properties of X-ray flashes (XRF), X-ray rich GRBs, and GRBs in a unified picture, the extra degree of freedom available in the variable jet opening angle model enables it to explain the observations reasonably well while the power-law universal jet model cannot.

creasing viewing angle 0v. To recover the standard isotropic energy result, Eq(6v) ~ 2 is required. In the variable jet opening-angle model, the isotropic-equivalent energy and luminosity are constant across the jet (from [51])

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