  We use joint observations by the Neil Gehrels Swift X-ray Telescope (XRT) and
the Fermi Large Area Telescope (LAT) of gamma-ray burst (GRB) afterglows to
investigate the nature of the long-lived high-energy emission observed by Fermi
LAT. Joint broadband spectral modeling of XRT and LAT data reveal that LAT
nondetections of bright X-ray afterglows are consistent with a cooling break in
the inferred electron synchrotron spectrum below the LAT and/or XRT energy
ranges. Such a break is sufficient to suppress the high-energy emission so as
to be below the LAT detection threshold. By contrast, LAT-detected bursts are
best fit by a synchrotron spectrum with a cooling break that lies either
between or above the XRT and LAT energy ranges. We speculate that the primary
difference between GRBs with LAT afterglow detections and the non-detected
population may be in the type of circumstellar environment in which these
bursts occur, with late-time LAT detections preferentially selecting GRBs that
occur in low wind-like circumburst density profiles. Furthermore, we find no
evidence of high-energy emission in the LAT-detected population significantly
in excess of the flux expected from the electron synchrotron spectrum fit to
the observed X-ray emission. The lack of excess emission at high energies could
be due to a shocked external medium in which the energy density in the magnetic
field is stronger than or comparable to that of the relativistic electrons
behind the shock, precluding the production of a dominant synchrotron
self-Compton (SSC) component in the LAT energy range. Alternatively, the peak
of the SSC emission could be beyond the 0.1-100 GeV energy range considered for
this analysis.
