# Pseudorapidity dependent hydrodynamic response in heavy-ion collisions

## TL;DR

This paper introduces a differential hydrodynamic response relation to describe pseudorapidity dependent elliptic flow in heavy-ion collisions, verified through simulations, and reveals insights into medium properties like sound speed and viscosity.

## Contribution

It proposes and verifies a new differential response relation linking initial density fluctuations to elliptic flow, enabling separation of flow correlations and extraction of medium properties.

## Key findings

- Response relation verified with simulations
- Separation of flow and initial eccentricity correlations
- Finite radius of convergence for hydrodynamic expansion

## Abstract

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.