  Elliptic flow of direct photons in relativistic heavy ion collisions is
believed to be dominated by contribution from thermal radiation of quark gluon
plasma up to $p_T$ $\sim 5$ GeV/$c$, although other sources start outshining
the thermal contribution at already smaller values of $p_T$ in the direct
photon spectrum. The elliptic flow of thermal photons from ideal hydrodynamics
considering a smooth initial density distribution under-predicts the PHENIX
direct photon data from 200A GeV Au+Au collisions at RHIC by a large margin in
the range $1 < p_T < 5$ GeV/$c$. However, a significant enhancement of thermal
photon production due to fluctuations in the initial QCD matter density
distributions is expected. We show that such fluctuations result in
substantially larger photon elliptic flow for $p_T > 2.5 $ GeV/$c$ compared to
a smooth initial-state-averaged density profile. The results from
event-by-event hydrodynamics are found to be sensitive to the fluctuation size
parameter. However, the effects of initial state fluctuations are insufficient
to account for the discrepancy to the PHENIX data for direct photon elliptic
flow. Furthermore, the photon $v_2$ is reduced even more when we include the
NLO pQCD prompt photon component. We also calculate the spectra and elliptic
flow of thermal photons for 2.76A TeV Pb+Pb collisions at LHC and for the
0--40% centrality bin. Thermal photons from event-by-event hydrodynamics along
with prompt photons from NLO pQCD calculations explain the ALICE preliminary
direct photon data well in the region $p_T \ge 2.5$ GeV/c. Similar to RHIC, the
elliptic flow results at LHC are again found to be much smaller than the ALICE
preliminary $v_2$ data.
