Triangular flow of thermal photons from an event-by-event hydrodynamic model for $2.76A$ TeV Pb + Pb collisions at the CERN Large Hadron Collider

We calculate the triangular flow parameter $v_3$ of thermal photons from an event-by-event ideal hydrodynamic model for 0–40% central collisions of Pb nuclei at $\sqrt{s_{NN}}=2.76$ TeV at the CERN Large Hadron Collider. $v_3$ determined with respect to the participant plane (PP) is found to be nonzero and positive, and its $p_T$ dependence is qualitatively similar to the elliptic flow parameter $v_2$(PP) of thermal photons in the range $1\le p_T\le 6\text{GeV}/c$. In the range $p_T\le 3\text{GeV}/c$, $v_3$(PP) is found to be about 50–75% of $v_2$(PP) and for $p_T>3\text{GeV}/c$ the two anisotropy parameters become comparable. The value of $v_3$ is driven by local density fluctuations both directly via the creation of triangular geometry and indirectly via additional flow. As expected, the triangular flow parameter calculated with respect to the reaction plane $v_3$(RP) is found to be close to zero. We show that $v_3$(PP) strongly depends on the spatial size of fluctuations, especially in the higher $p_T(\ge 3\mathrm{GeV}/c)$ region where a larger value of $\sigma$ results in a smaller $v_3\left(\mathrm{PP}\right)$. In addition, $v_3\left(\mathrm{PP}\right)$ is found to increase with the assumed formation time of the thermalized system.

Figure 1

Thermal photon $p_T$ spectra from fluctuating IC (FIC) and smooth IC (SIC) considering complete leading order plasma rates [23] for $2.76A$ TeV Pb + Pb collisions at LHC and for the 0–40% centrality bin. The $p_T$ spectrum using next-to-leading order plasma rates [25] (for SIC only), ALICE direct photon data [28], and prompt photons from next-to-leading order pQCD calculations are also plotted for comparison.

Figure 2

Triangular and elliptic flow of thermal photons with respect to RP and PP for 0–40% central collisions of Pb nuclei at LHC and for $\sigma =0.4$ fm.

Figure 3

Upper panel: Average transverse flow velocities for different events with fixed number of wounded nucleons. Lower panel: $v_3\left(\mathrm{PP}\right)$ for the same events.

Figure 4

Triangular flow of thermal photons for 0–40% central collisions of Pb nuclei at LHC and for size parameter $\sigma =0.4$ and 0.8 fm.

Figure 5

Triangular flow of thermal photons for 0–40% central collisions of Pb nuclei at LHC and for size parameter $\sigma =0.4$ and at ${\tau }_0$ values 0.14 and $0.6\mathrm{fm}/c$.