Population III GRB Afterglows: Constraints on Stellar Masses and
  External Medium Densities
  Population III stars are theoretically expected to be prominent around
redshifts z ~ 20, consisting of mainly very massive stars with M_* >~ 10
M_sun$, but there is no direct observational evidence for these objects. They
may produce collapsar gamma-ray bursts (GRBs), with jets driven by
magnetohydrodynamic processes, whose total isotropic-equivalent energy could be
as high as E_iso >~ 10^{57} erg over a cosmological-rest-frame duration of t_d
>~ 10^4 s, depending on the progenitor mass. Here we calculate the afterglow
spectra of such Pop. III GRBs based on the standard external shock model, and
show that they will be detectable with the Swift BAT/XRT and Fermi LAT
instruments. We find that in some cases a spectral break due to
electron-positron pair creation will be observable in the LAT energy range,
which can put constraints on the ambient density of the pre-collapse Pop. III
star. Thus, high redshift GRB afterglow observations could be unique and
powerful probes of the properties of Pop. III stars and their environments. We
examine the trigger threshold of the BAT instrument in detail, focusing on the
image trigger system, and show that the prompt emission of Pop. III GRBs could
also be detected by BAT. Finally we briefly show that the late-time radio
afterglows of Pop. III GRBs for typical parameters, despite the large
distances, can be very bright: ~ 140 mJy at 1 GHz, which may lead to a
constraint on the Pop. III GRB rate from the current radio survey data, and
~2.4 mJy at 70 MHz, which implies that Pop. III GRB radio afterglows could be
interesting background source candidates for 21 cm absorption line detections.
