  We calculate the spectra of high energy photons emitted in relativistic Au+Au
collisions for various centralities and compare to data recently collected at
the Relativistic Heavy Ion Collider by the PHENIX collaboration. Our results
for photons from primary hard scatterings and photons from interactions of jets
with the medium are consistent with the measurements of neutral pion and direct
photon production in p+p collisions and give a good description of direct
photon spectra measured in Au+Au collisions. The contribution of photons from
jet-to-photon conversion in the medium can be as large as the photon yield from
hard scatterings in the momentum range p_T = 2...6 GeV/c. We show that this
novel mechanism is not ruled out by any existing data.
