  Long duration gamma-ray bursts (GRBs), the brightest events since the Big
Bang itself, are believed to originate in an ultra-relativistic jet breaking
out from a massive stellar envelope. Despite decades of study, there is still
no consensus on their emission mechanism. One unresolved question is the origin
of the tight correlation between the spectral peak energy Ep and peak
luminosity Lp discovered in observations. This Yonetoku relation is the
tightest correlation found in the properties of the prompt phase of GRB
emission, providing the best diagnostic for the radiation mechanism. Here we
present 3D hydrodynamical simulations, and post-process radiation transfer
calculations, of photospheric emission from a relativistic jet. Our simulations
reproduce the Yonetoku relation as a natural consequence of viewing angle.
Although jet dynamics depend sensitively on luminosity, the Ep-Lp correlation
holds regardless. This result strongly suggests that photospheric emission is
the dominant component in the prompt phase of GRBs.
