Characterizing the Gamma-Ray Variability of the Brightest Flat Spectrum
  Radio Quasars Observed with the Fermi LAT
  Almost 10 yr of $\gamma$-ray observations with the Fermi Large Area Telescope
(LAT) have revealed extreme $\gamma$-ray outbursts from flat spectrum radio
quasars (FSRQs), temporarily making these objects the brightest $\gamma$-ray
emitters in the sky. Yet, the location and mechanisms of the $\gamma$-ray
emission remain elusive. We characterize long-term $\gamma$-ray variability and
the brightest $\gamma$-ray flares of six FSRQs. Consecutively zooming in on the
brightest flares, which we identify in an objective way through Bayesian blocks
and a hill-climbing algorithm, we find variability on subhour time scales and
as short as minutes for two sources in our sample (3C279, CTA102) and weak
evidence for variability at time scales less than the Fermi satellite's orbit
of 95 minutes for PKS1510-089 and 3C454.3. This suggests extremely compact
emission regions in the jet. We do not find any signs for $\gamma$-ray
absorption in the broad-line region (BLR), which indicates that $\gamma$-rays
are produced at distances greater than hundreds of gravitational radii from the
central black hole. This is further supported by a cross-correlation analysis
between $\gamma$-ray and radio/millimeter light curves, which is consistent
with $\gamma$-ray production at the same location as the millimeter core for
3C273, CTA102, and 3C454.3. The inferred locations of the $\gamma$-ray
production zones are still consistent with the observed decay times of the
brightest flares if the decay is caused by external Compton scattering with BLR
photons. However, the minute-scale variability is challenging to explain in
such scenarios.
