# Quark Matter 2019 - the XXVIIIth International Conference on Ultra-relativistic Nucleus-Nucleus Collisions

3-9 November 2019
Wanda Reign Wuhan Hotel
Asia/Shanghai timezone

## Longitudinal hydrodynamic response and pseudo-rapidity dependent harmonic flow in relativistic heavy-ion collisions

5 Nov 2019, 09:20
20m
Ball Room 1 (Wanda Reign Wuhan Hotel)

### Ball Room 1

#### Wanda Reign Wuhan Hotel

Oral Presentation Collective dynamics and final state interaction

### Speaker

Li Yan (Fudan University)

### Description

In heavy-ion collisions, it is well-established that geometrical shapes of the initial density distribution in transverse plane are responsible for the observed harmonic flow, through the hydrodynamic response of a set of modes. In particular, elliptic flow $V_2$ is linearly proportional to initial eccentricity $\mathcal{E}_2$.

In this work, we generalize the framework to study hydrodynamic response along the longitudinal direction. We propose a differential hydrodynamic response relation, $V_2(\eta)=\int d\xi G(\eta-\xi) \mathcal{E}_2(\xi)$, to describe the formation of a pseudo-rapidity dependent elliptic flow, in response to a 3D 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 for the Pb-Pb collisions at $\sqrt{s_{NN}}=2.76$ TeV, the differential response relation is verified and expansion coefficients to very high orders are identified in the response function $G(\eta-\xi)$.

Our investigations of the hydrodynamic response function have yielded two important insights: 1. The two-point auto-correlation of elliptic flow in pseudo-rapidity (an observable in heavy-ion experiments), can be separated as medium response and two-point correlation of initial $\mathcal{E}_2$. Especially, shear viscosity of the medium reduces the correlation length systematically. 2. Higher order expansion coefficients increase exponentially, which implies a finite radius of convergence of the gradient expansion in the dispersion relation of hydrodynamics. The radius of convergence in the response function results in a minimal length scale that can be used to estimate the applicability of hydrodynamic modeling of heavy-ion collisions, which provides a possible solution to the question of fluidity in small systems.

### Primary authors

Hui Li (Fudan University) Li Yan (Fudan University)