Anisotropic flow of thermal photons at energies available at the BNL Relativistic Heavy Ion Collider and at the CERN Large Hadron Collider

We calculate elliptic and triangular flow parameters of thermal photons using an event-by-event hydrodynamic model with fluctuating initial conditions at 200A GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider (RHIC) and at 2.76A TeV Pb+Pb collisions at the Cern Large Hadron Collider (LHC) for three different centrality bins. The photon elliptic flow shows strong centrality dependence where upsilon(2)(pT) increases towards peripheral collisions both at RHIC and at the LHC energies. However, the triangular flow parameter does not show significant dependence on the collision centrality. The elliptic as well as the triangular flow parameters found to underestimate the PHENIX data at RHIC by a large margin for all three centrality bins. We calculate pT spectrum and anisotropic flow of thermal photons from 200A GeV Cu+Cu collisions at RHIC for a 0-20% centrality bin and compare with the results with those from Au+Au collisions. The production of thermal photons is found to decrease significantly for Cu+Cu collisions compared to Au+Au collisions. However, the effect of initial state fluctuation is found to be more pronounced for anisotropic flow, resulting in larger upsilon(2) and upsilon(3) for Cu+Cu collisions. We study the correlation between the anisotropic flow parameters and the corresponding initial spatial anisotropies from their event-by-event distributions at RHIC and at the LHC energies. The linear correlation between upsilon(2) and is an element of(2) is found be stronger compared to the correlation between upsilon(3) and is an element of(3). In addition, the correlation coefficient is found to be larger at LHC than at RHIC.