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We calculate the triangular flow parameter $v_3$ of thermal photons from anevent-by-event ideal hydrodynamic model for $0--40\%$ central collisions of Pbnuclei at $\sqrt{s_{NN}}$=2.76 TeV at LHC. $v_3$ determined with respect to theparticipant plane (PP) is found to be non-zero, positive and its $p_T$dependence is qualitatively similar to the elliptic flow parameter $v_2$(PP) ofthermal photons in the range $1 \le p_T \le 6$ GeV/$c$. In the range $p_T \,\le $ 3 GeV/$c$, $v_3$(PP) is found to be about $50--75\%$ of $v_2$(PP) and for$p_T \, >$ 3 GeV/$c$ the two anisotropy parameters become comparable. The localfluctuations in the initial density distribution as well as the initial globalgeometry of the produced matter in the event-by-event hydrodynamic frameworkare responsible for this substantial value of $v_3({\rm PP})$. However, asexpected, the triangular flow parameter calculated with respect to the reactionplane $v_3$(RP) is found to be close to zero. We show that $v_3$(PP) stronglydepends on the value of the fluctuation size scale $\sigma$ especially in thehigher $p_T \, (\ge 3 {\rm GeV}/c)$ region where a larger value of $\sigma$results in a smaller $v_3({\rm PP})$. In addition, the $v_3{\rm (PP)}$ is foundto increase with the assumed formation time of the thermalized system.

Triangular flow of thermal photons from an event-by-event hydrodynamic model for 2.76A TeV Pb+Pb collisions at LHC