We use a self-consistent chiral-hydrodynamic formalism which combines the linear $sigma$ model with second-order hydrodynamics in 2+1 dimensions to compute the spectrum of thermal photons produced in Au+Au collisions at $sqrt{s_{NN}}=200$ GeV. The te
mperature-dependent shear viscosity of the model, $eta$, is calculated from the linearized Boltzmann equation. We compare the results obtained in the chiral-hydrodynamic model to those obtained in the second-order theory with a Lattice QCD equation of state and a temperature-independent value of $eta/s$. We find that the thermal photon production is significantly larger in the latter model due to a slower evolution and larger dissipative effects.
We calculate the spectra of produced thermal photons in Au+Au collisions taking into account the nonequilibrium contribution to photon production due to finite shear viscosity. The evolution of the fireball is modeled by second-order as well as by di
vergence-type 2+1 dissipative hydrodynamics, both with an ideal equation of state and with one based on Lattice QCD that includes an analytical crossover. The spectrum calculated in the divergence-type theory is considerably enhanced with respect to the one calculated in the second-order theory, the difference being entirely due to differences in the viscous corrections to photon production. Our results show that the differences in hydrodynamic formalisms are an important source of uncertainty in the extraction of the value of $eta/s$ from measured photon spectra. The uncertainty in the value of $eta/s$ associated with different hydrodynamic models used to compute thermal photon spectra is larger than the one occurring in matching hadron elliptic flow to RHIC data.
