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

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