In gold-gold collisions of the Relativistic Heavy Ion Collider (RHIC) a
perfect fluid of quarks, sometimes called the strongly interacting quark gluon
plasma (sQGP) is created for an extremely short time. The time evolution of
this fluid can be described by hydrodynamical models. After expansion and
cooling, the freeze-out happens and hadrons are created. Their distribution
reveals information about the final state of the fluid. To investigate the time
evolution one needs to analyze penetrating probes, such as direct photon
observables. Transverse momentum distributions of low energy direct photons
were mesured in 2010 by PHENIX, while azimuthal asymmetry in 2011. These
measurements can be compared to hydrodynamics to determine the equation of
state and the initial temperature of sQGP. In this paper we analyze an 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 equation 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 a speed of sound of 0.36+-0.02.
We also estimate a systematic error of these results. We find that the measured
azimuthal asymmetry is also not incompatible with this model, and predict a
photon source that is significantly larger in the out direction than in the
side direction.Comment: 12 pages, 4 figures. This work was supported by the OTKA grant
NK-73143 and NK-101438 and M. Csanad's Bolyai scholarshi
