Centrality and initial formation time dependence of the emission of thermal photons from fluctuating initial conditions at RHIC and LHC

Event-by-event fluctuating initial conditions (IC) in the ideal hydrodynamic calculation are known to enhance the production of thermal photons significantly compared to a smooth initial state averaged profile in the range $p_T >$ 1 GeV/$c$ for 200A GeV Au+Au collisions at RHIC and 2.76A TeV Pb+Pb collisions at LHC. The 'hotspots' or the over-dense regions in the fluctuating IC produce more high $p_T$ photons compared to the smooth IC due to the strong temperature dependent emission of the thermal radiation. This enhancement is expected to be more pronounced for peripheral collisions, for lower beam energies, and for larger values of plasma formation time. A suitably normalized ratio of central to peripheral yield of thermal photons ($R_{cp}^\gamma$) is a potential probe to study the density fluctuations and their size in the initial conditions.