Quark-gluon plasma formation time and direct photons from heavy ion collisions

We investigated the information carried by the data on direct photons, i.e., the transverse momentum spectrum and the elliptic flow v₂ from Pb + Pb collisions at √sNN=2.76 TeV measured at the Large Hadron Collider and from Au + Au collisions at √sNN=200 GeV measured at the Relativistic Heavy Ion Collider, in the framework of ($3+1$)--dimensional ideal hydrodynamical models constrained with hadronic data. We found that these direct photon data may serve as a useful clock at the early stage of heavy ion collisions. The time scales for reaching thermal and chemical equilibrium, extracted from those data, are about 1/3 and 1.5 fm/c, respectively. Thus the large elliptic flow of direct photons is explainable. High-order harmonics, i.e., v₃, v₄, and v₅, of direct photons from Pb + Pb collisions at 2.76 TeV are also predicted, as a further test to compete with those who claim new sources of photons to account for the large elliptic flow of direct photons.