  We extract synthetic photon spectra from first-principles particle-in-cell
simulations of relativistic shocks propagating in unmagnetized pair plasmas.
The two basic ingredients for the radiation, namely accelerated particles and
magnetic fields, are produced self-consistently as part of the shock evolution.
We use the method of Hededal & Nordlund (2005) and compute the photon spectrum
via Fourier transform of the electric far-field from a large number of
particles, sampled directly from the simulation. We find that the spectrum from
relativistic collisionless shocks is entirely consistent with synchrotron
radiation in the magnetic fields generated by Weibel instability. We can
recover the so-called "jitter'' regime only if we artificially reduce the
strength of the electromagnetic fields, such that the wiggler parameter K = qB
lambda/mc^2 becomes much smaller than unity ("B" and "lambda" are the strength
and scale of the magnetic turbulence, respectively). These findings may place
constraints on the origin of non-thermal emission in astrophysics, especially
for the interpretation of the hard (harder than synchrotron) low-frequency
spectrum of Gamma-Ray Bursts.
