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In high-energy heavy-ion collisions a nearly perfect fluid, the so-calledstrongly coupled quark gluon plasma forms. After the short period ofthermalisation, the evolution of this medium can be described by the laws ofrelativistic hydrodynamics. The time evolution of the quark gluon plasma can beunderstood through direct photon spectra measurements, which are sensitive tothe entire period between the thermalisation and the freeze-out of the medium.I present a new analytic formula that describes the thermal photon radiationand it is derived from an exact and finite solution of relativistichydrodynamics with accelerating velocity field. Then I compare my calculationsto the most recent nonprompt spectrum of direct photons for $Au+Au$ at$\sqrt{s_{NN}}=$200 GeV collisions. I have found a convincing agreement betweenthe model and the data, which allows to give an estimate of the initialtemperature in the center of the fireball. My results predict hydrodynamicscaling behaviour for the thermal photon spectra of high-energy heavy-ioncollisions.

Describing the Thermal Radiation in $Au+Au$ Collisions at $\sqrt{s_{NN}}=$200 GeV by an Analytic Solution of Relativistic Hydrodynamics