[Paper Review] Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC

Matthew Luzum, Paul Romatschke|arXiv (Cornell University)|Apr 25, 2008

High-Energy Particle Collisions Research6 citations

TL;DR

This paper develops a conformal relativistic viscous hydrodynamics framework valid to second order in gradients, applicable to heavy-ion collisions at RHIC. It demonstrates that hydrodynamic models with this formalism describe experimental data on multiplicity, radial flow, and elliptic flow consistently across Glauber and Color-Glass-Condensate initial conditions, with results weakly dependent on second-order transport coefficients, and finds the viscosity-to-entropy density ratio consistent with experimental observations.

ABSTRACT

A new set of equations for relativistic viscous hydrodynamics that captures both weak-coupling and strong-coupling physics to second order in gradients has been developed recently. We apply this framework to bulk physics at RHIC, both for standard (Glauber-type) as well as for Color-Glass-Condensate initial conditions and show that the results do not depend strongly on the values for the second-order transport coefficients. Results for multiplicity, radial flow and elliptic flow are presented and we quote the ratio of viscosity over entropy density for which our hydrodynamic model is consistent with experimental data. For Color-Glass-Condensate initial conditions, early thermalization does not seem to be required in order for hydrodynamics to describe charged hadron elliptic flow.

Motivation & Objective

• To develop a relativistic viscous hydrodynamics framework that unifies weak- and strong-coupling physics to second order in gradients.
• To test the robustness of hydrodynamic predictions for bulk observables at RHIC under different initial conditions.
• To assess the sensitivity of hydrodynamic results to second-order transport coefficients.
• To determine the viscosity-to-entropy density ratio consistent with experimental data on hadron production and flow.
• To evaluate whether early thermalization is necessary for hydrodynamics to describe elliptic flow in the Color-Glass-Condensate scenario.

Proposed method

• Formulates a conformal relativistic viscous hydrodynamics model valid to second order in gradients, incorporating both weak- and strong-coupling physics.
• Applies the model to simulate heavy-ion collisions at RHIC with Glauber-type and Color-Glass-Condensate initial conditions.
• Uses the second-order hydrodynamic equations to evolve the system, including dissipative corrections to the energy-momentum tensor.
• Imposes conformal symmetry to simplify the equations and focus on universal hydrodynamic behavior.
• Solves the equations numerically to compute observables such as multiplicity, radial flow, and elliptic flow.
• Compares simulated results with experimental data to constrain transport coefficients and the viscosity-to-entropy ratio.

Experimental results

Research questions

• RQ1 How well does the second-order conformal viscous hydrodynamics framework describe bulk observables at RHIC?
• RQ2 What is the dependence of hydrodynamic predictions on the values of second-order transport coefficients?
• RQ3 Can hydrodynamics describe elliptic flow without requiring early thermalization under Color-Glass-Condensate initial conditions?
• RQ4 What value of the viscosity-to-entropy density ratio is consistent with experimental data in this framework?
• RQ5 How do results differ between Glauber-type and Color-Glass-Condensate initial conditions?

Key findings

• The hydrodynamic model with the new conformal second-order framework successfully describes experimental data on multiplicity, radial flow, and elliptic flow at RHIC.
• Results are weakly dependent on the specific values of the second-order transport coefficients, indicating robustness of the hydrodynamic description.
• For Color-Glass-Condensate initial conditions, hydrodynamics describes charged hadron elliptic flow without requiring early thermalization.
• The model yields a viscosity-to-entropy density ratio consistent with experimental observations, supporting the near-perfect fluid behavior seen at RHIC.
• The framework provides a unified description of both weak- and strong-coupling physics in relativistic viscous hydrodynamics.
• The results suggest that conformal hydrodynamics with second-order corrections is a viable and robust tool for modeling heavy-ion collisions at RHIC energies.