We present an exact solution to the Boltzmann equation which describes a system undergoing boost-invariant longitudinal and azimuthally symmetric radial expansion for arbitrary shear viscosity to entropy density ratio. This new solution is constructe
d by considering the conformal map between Minkowski space and the direct product of three dimensional de Sitter space with a line. The resulting solution respects SO(3)_q x SO(1,1) x Z_2 symmetry. We compare the exact kinetic solution with exact solutions of the corresponding macroscopic equations that were obtained from the kinetic theory in ideal and second-order viscous hydrodynamic approximations. The macroscopic solutions are obtained in de Sitter space and are subject to the same symmetries used to obtain the exact kinetic solution.
Photons are a penetrating probe of the hot medium formed in heavy-ion collisions, but they are emitted from all collision stages. At photon energies below 2-3 GeV, the measured photon spectra are approximately exponential and can be characterized by
their inverse logarithmic slope, often called effective temperature $T_mathrm{eff}$. Modelling the evolution of the radiating medium hydrodynamically, we analyze the factors controlling the value of $T_mathrm{eff}$ and how it is related to the evolving true temperature $T$ of the fireball. We find that at RHIC and LHC energies most photons are emitted from fireball regions with $T{,sim,}T_mathrm{c}$ near the quark-hadron phase transition, but that their effective temperature is significantly enhanced by strong radial flow. Although a very hot, high pressure early collision stage is required for generating this radial flow, we demonstrate that the experimentally measured large effective photon temperatures $T_mathrm{eff}{,>,}T_mathrm{c}$, taken alone, do not prove that any electromagnetic radiation was actually emitted from regions with true temperatures well above $T_mathrm{c}$. We explore tools that can help to provide additional evidence for the relative weight of photon emission from the early quark-gluon and late hadronic phases. We find that the recently measured centrality dependence of the total thermal photon yield requires a larger contribution from late emission than presently encoded in our hydrodynamic model.
