Pseudorapidity dependent hydrodynamic response in heavy-ion collisions

We propose a differential hydrodynamic response relation, $V_2(\zeta)=\int d\xi G(\zeta-\xi) \mathcal{E}_2(\xi)$, to describe the formation of a pseudorapidity dependent elliptic flow in heavy-ion collisions, in response to a fluctuating three-dimensional initial density profile. By analyzing the medium expansion using event-by-event simulations of 3+1D MUSIC, with initial conditions generated via the AMPT model, the differential response relation is verified. Given the response relation, we are able to separate the two-point correlation of elliptic flow in pseudorapidity into fluid response and two-point correlation of initial eccentricity. The fluid response contains information of the speed of sound and shear viscosity of the medium. From the pseudorapidity dependent response relation, a finite radius of convergence of hydrodynamic gradient expansion is obtained with respect to realistic fluids in heavy-ion collisions.