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In gold-gold collisions of the Relativistic Heavy Ion Collider a perfect fluid of strongly interacting quark gluon plasma (sQGP) is created. The time evolution of this fluid can be described by hydrodynamical models. After an expansion, hadrons are created during the freeze-out period. Their distribution reveals information about the final state. To investigate the time evolution one needs to analyze penetrating probes: e.g. direct photon observations. In this paper we analyze a 1+3 dimensional solution of relativistic hydrodynamics. We calculate momentum distribution, azimuthal asymmetry and momentum correlations of direct photons. Based on earlier fits to hadronic spectra, we compare photon calculations to measurements to determine the equations of state and the initial temperature of sQGP. We find that the initial temperature in the center of the fireball is 507±12 MeV, while for the sound speed we get cs=0.36±0.02. We also estimate a systematic error of these results. We find that the measured azimuthal asymmetry is also compatible with this model. We also predict a photon source that is significantly larger in the out direction than in the side direction.

Equation of state and initial temperature of quark gluon plasma at RHIC