  Gamma-ray bursts are the most energetic electromagnetic sources in the
Universe. Their prompt gamma-ray radiation corresponds to an energy release of
1E42-1E47J. Fifty years after their discovery and several dedicated space-based
instruments, the physical origin of this emission is still unknown. Synchrotron
emission has been one of the early contenders but was criticized because
spectral fits of empirical models (such as a smoothly-connected broken power
law or a cut-off power law) suggest too hard a slope of the low-energy power
law, violating the so-called synchrotron line-of-death. We perform
time-resolved gamma-ray spectroscopy of single-peaked GRBs as measured with
Fermi/GBM. We demonstrate that idealized synchrotron emission, when properly
incorporating time-dependent cooling of the electrons, is capable of fitting
~95% of all these GBM spectra. The comparison with spectral fit results based
on previous empirical models demonstrates that the past exclusion of
synchrotron radiation as an emission mechanism derived via the line-of-death
was misleading. Our analysis probes the physics of these ultra-relativistic
outflows and the related microphysical processes, and for the first time
provides estimates of magnetic field strength and Lorentz factors of the
emitting region directly from spectral fits. Our modeling of the Fermi/GBM
observations provides evidence that GRBs are produced by moderately magnetized
jets in which relativistic mini-jets emit optically-thin synchrotron radiation
at large emission radii.
