2. ELECTROMAGNETIC OBSERVATIONS

2.4    MULTI-WAVELENGTH AFTERGLOWS

2.4.4    EARLY AFTERGLOW IN THE CONTEXT OF THE FIREBALL & CANNONBALL MODELS

       In the fireball model, the interaction of external shocks with the surrounding matter produces multi-wavelength afterglow emissions (Costa et al. 1997). The early light curve of the OT associated with GRB030329 is illustrated in figure 2.4.4.1. Spectral breaks are apparent at 0.25 and 0.5 days. The breaks are understood to occur due the deceleration of the relativistic wind due to interaction with ambient matter. It is important to note that even in the case of isotropic emission, the source appears constrained to a cone in the observer's frame due to relativistic aberration. As the wind evolves, the bulk Lorentz factor grows linearly with radius until it saturates at a peak value during the prompt emission phase. During the prompt phase, G ~ 300, and hence a narrow cone of half opening angle q ~ G^-1 is observed in our frame. At this point, anisotropic and spherically symmetric isotropic emission are indistinguishable since both are constrained, i.e. "beamed" to within a conical section of half angle q. However, the signature of a true astrophysical jet reveals itself as a characteristic break in the afterglow emission, coinciding with the reduction of the bulk Lorentz factor to order unity. At this point, the ejecta are no longer constrained or forward beamed in the direction of emission and begin to expand side ways, causing the appearance of a break in the light curve as observed in our frame. Simulations of the propagation and eruption of relativistic jets from stellar progenitors of GRBs have been performed in 2 and 3 dimensions and yield that the a highly relativistic jet erupts from the core with a half angle of 3 to 5 degrees and Lorentz factors ≥ 100 (Zhang et al. 2004).

FIGURE 2.4.4.1: An early light curve for the OT associated with GRB030329 (Lipkin et al. 2004).

        In the context of the cannonball (CB) model, studies of GRB030329 have provided compelling observational reasons that question its viability. Consider that the cannonball model predicts that an Earth-sized plasmoid a.k.a. "cannonball" is ejected out of the GRB jet. This is the "smoking gun" feature of the cannonball model and it was predicted in the literature (Dado et al. 2003, Dado et al. 2003b). This was not seen in the afterglow observations of GRB030329. High-resolution (~1 pc) observations made by Dale Frail of the National Radio Astronomy Observatory (NRAO), Shri Kulkarni of Caltech as well as others using instruments such as the Very Long Baseline Array (VLBA) have shown that the predicted signature of such a phenomenon was not observed. If it existed, instruments such as the NRAO and VLBA would have seen it. Since it was not observed, we have very damaging evidence against the CB model since its predictions were falsified by observation.

    Consider (Taylor et al. 2004), where they confront the afterglow observations of GRB030329 with both the CB and fireball models. It is demonstrated that the measured superluminal motion in GRB030329 is at a distance an order of magnitude smaller than the original prediction of the CB model and a factor of 5 smaller than a revised CB model estimate. In addition to the inconsistency between the proper motion limits and the predictions of the CB model, there is a conspicuous absence of rapid fluctuations in the radio light curves of GRB030329. Strong and persistent intensity variations in centimeter radio light curves are expected for all GRBs in the CB model. However, these are not expected in relativistic blast wave models such as the fireball model. In fact Taylor et al. 2004 and, in greater detail, Oren et al 2004 conclude that the
afterglow observations of GRB030329 are in perfect agreement with the fireball model and are inconsistent with the CB model. However see Dado et al. 2004b for a different view.

    According to the CB model, the plasmoid that emits the radiation retains a very high Lorentz factor (~1000) for a very long time, and, by about 1 day (in observer's frame) after the GRB, it has traveled at least 1 kpc, in a direction almost straight towards us. This means that by the time we usually take a GRB spectrum, the plasmoid should be in front of the (host) galaxy from which it originated (typical galactic disk dust layers are ~ 100 pc thick). However, barring only 1 exception in over 30 cases, absorption lines are always observed from gas in the disk of the host galaxy. Therefore, the prediction of the cannonball model as to how far the cannonballs travel is very wrong. The CB model also exhibits a fundamental inability to account for some of the basic observations (such as the quenching of the radio scintillation) that the fireball model naturally predicts. For example, we observe that the radio scintillation slowly die away over the first month, which in the standard fireball model is explained by the emitting region becoming too big to scintillate. The CB model prediction is that the cannonballs stop expanding when they reach about 1E14 cm in size, which is 2 to 3 orders of magnitude smaller than what is needed to stop the scintillation. Therefore, the cannonball model prediction for the size of the emitting region is very wrong. For these reasons, many feel that the cannonball model is no longer viable since it makes predictions that are observationally falsified.