tokens: ( 2010 ). They have also shown that when these are combined with lower limits required to avoid the compactness problem, values of Γ 0 are in the range 10 2 –10 3 . Concerning direct estimates (rather than limits) of Γ 0 , a spectral break in the prompt component has been observed only in a few cases (Ackermann et al. 2011 ; Tang et al. 2015 ). Most of the available estimates of the value of Γ 0 have been inferred from the detection of an early peak in the afterglow lightcurve. Ghirlanda et al. ( 2012 ) collected all GRBs with known redshift and with an early peak in the optical lightcurve, and inferred Γ 0 under the assumption that the peak corresponds to the blast wave deceleration time. The Γ 0 values have been derived both for a constant and wind-like medium, and are shown in Fig. 4 as star symbols (the green colour refers to optical lightcurves, while the yellow colour refers to a similar analysis applied to GeV lightcurves of LAT GRBs with temporally extended GeV emission). The most stringent limits derived in this work lie above most of the values inferred from GRBs with an optical peak. This implies that the non-detection of synchrotron afterglow radiation is consistent with the simplest model, and there is no evidence that mechanisms producing a suppression of the GeV flux (see Section 2.2 ) are at work. The possibility of testing the relevance of these processes is however limited by the instrument sensitivity. We can conclude that present instrument capabilities are not pointing to the need for a relevant suppression of the high-energy afterglow synchrotron flux. On the other hand, the upper limits lie not far from (and sometimes below) the estimated values of Γ 0 . This suggests that the LAT should be able to detect the synchrotron afterglow component for those GRBs with the largest bulk Lorentz factors and largest energetics. A fraction of the LAT-detected GRBs are indeed characterized by the presence of an emission above 100 MeV lasting much longer than the prompt radiation, whose flux decays in time as a PL (Ackermann et al. 2013 ). These are the brightest GBM GRBs, and a large Lorentz factor Γ 0 > 500 has been inferred for them. An association with synchrotron afterglow radiation has been claimed to be consistent also with their spectral and temporal properties (Kumar Barniol Duran 2009 , 2010 ; De Pasquale et al. 2010 ; Ghirlanda, Ghisellini Nava 2010 ; Ghisellini et al. 2010 ; Lemoine, Li Wang 2013 ; Nava et al. 2014 ; Beniamini et al. 2015 ), although photons with particularly large energies (>10 GeV) detected at late times (>10 2 s) are in excess of the synchrotron limit and require a different explanation (Piran Nakar 2010 ; Wang, Liu Lemoine 2013 ; Ackermann et al. 2014 ). Finally, we comment on the dependence of these results on the unknown parameters ε e and η γ , with reference to a homogeneous density medium (similar considerations hold also for a wind-shaped density medium). In the first regime, where observations
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