The anisotropic flow of direct photons produced in relativistic heavy ion collisions is known to be dominated by the thermal radiations. The non-thermal contributions dilute the photon anisotropic flow by adding extra weight factor in the $v_n$ calculation. The discrepancy between experimental photon anisotropic flow data and results from theoretical model calculations is not well understood even after significant developments in the model calculations as well as in the experimental analysis methods.
We show that the ratio of photon $v_n$ can be a potential observable in this regard by minimizing the non-thermal contributions and the ratio along with the individual flow parameters could be valuable to constrain the initial state as well as to understand the photon anisotropic flow from heavy ion collisions better .
The photon $v_2/v_3$ is found to be larger for peripheral collisions than for central collisions and the $p_T$ dependent behavior of the ratio is found to be different from the individual flow parameters. The ratio is found to be sensitive to the initial conditions of the model calculation at different $p_T$ regions compared to the individual anisotropic flow parameters.
The $v_1/v_2$ ( and $v_1/v_3$ ) shows a completely different $p_T$ dependent nature compared to $v_2/v_3$ of photons. An experimental determination of photon $v_1/v_n$ is expected to confirm the range of thermal contribution. In addition, the $v_1/v_n$ is found to be less sensitive to the initial formation time compared to $v_2/v_3$. However, $v_1/v_n$ is expected to be much more sensitive to the final freeze-out temperature as photon $v_1$ does not depend strongly on the value of $T_f$ .
 R. Chatterjee and P. Dasgupta, arXiv: arXiv:2106.15922