Higher order flow coefficients -- A Messenger of QCD medium formed in heavy-ion collisions at the Large Hadron Collider

Anisotropic flow and fluctuations are sensitive observables of the initial state effects in heavy ion collisions and are characterized by the medium properties and final state interactions. Using event-shape observables, one can constrain the probability distributions of anisotropic flow coefficients, thus reducing the linear and nonlinear contributions in the measured higher-order harmonics. In this paper, we use transverse spherocity as an event shape observable to study the flow coefficients and elliptic flow fluctuations. Transverse spherocity is found to have a strong correlation with elliptic flow and its fluctuations. We exploit this feature of transverse spherocity to remove the contribution to elliptic flow from higher-order harmonics. The study is performed in Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV using a multi-phase transport model. The multi-particle Q-cumulant method estimates the anisotropic flow coefficients, which reduces the non-flow contributions. We observe a stronger system response to the flow coefficients for the events with smaller values of elliptic flow.