  Fermi satellite discovered that cosmological gamma-ray bursts (GRBs) are
accompanied by long GeV flashes. In two GRBs, an optical counterpart of the GeV
flash has been detected. Recent work suggests that the GeV+optical flash is
emitted by the external blast wave from the explosion in a medium loaded with
copious $e^\pm$ pairs. The full light curve of the flash is predicted by a
first-principle radiative transfer simulation and can be tested against
observations. Here we examine a sample of 7 bursts with best GeV+optical data
and test the model. We find that the observed light curves are in agreement
with the theoretical predictions and allow us to measure three parameters for
each burst: the Lorentz factor of the explosion, its isotropic kinetic energy,
and the external density. With one possible exception of GRB 090510 (which is
the only short burst in the sample) the ambient medium is consistent with a
wind from a Wolf-Rayet progenitor. The wind density parameter $A=\rho r^2$
varies in the sample around $10^{11}$g/cm. The initial Lorentz factor of the
blast wave varies from 200 to 540 and correlates with the burst luminosity.
Radiative efficiency of the prompt emission in the sample is between 0.1 and
0.8. For the two bursts with detected optical flash, GRB 120711A and GRB
130427A, we also estimate the magnetization of the external blast wave.
Remarkably, the model reproduces the entire optical light curve of GRB 120711A
(with its sharp peak, fast decay, plateau, and break) as well as the GeV data.
The spectrum of GeV flashes is predicted to extend above 0.1 TeV, where they
can be detected by ground-based Cherenkov telescopes.
