Simulating elliptic flow with viscous hydrodynamics (0710.5932v2)

Abstract: In this work we simulate a viscous hydrodynamical model of non-central Au-Au collisions in 2+1 dimensions, assuming longitudinal boost invariance. The model fluid equations were proposed by \"{O}ttinger and Grmela \cite{OG}. Freezeout is signaled when the viscous corrections become large relative to the ideal terms. Then viscous corrections to the transverse momentum and differential elliptic flow spectra are calculated. When viscous corrections to the thermal distribution function are not included, the effects of viscosity on elliptic flow are modest. However, when these corrections are included, the elliptic flow is strongly modified at large $p_T$. We also investigate the stability of the viscous results by comparing the non-ideal components of the stress tensor ($\pi^{ij}$) and their influence on the $v_2$ spectrum to the expectation of the Navier-Stokes equations ($\pi^{ij} = -\eta \llangle \partial_i u_j \rrangle$). We argue that when the stress tensor deviates from the Navier-Stokes form the dissipative corrections to spectra are too large for a hydrodynamic description to be reliable. For typical RHIC initial conditions this happens for $\eta/s \gsim 0.3$.

• The paper demonstrates that incorporating viscous corrections significantly alters elliptic flow at high pT, emphasizing the role of off-equilibrium effects.
• It employs a 2+1 dimensional viscous hydrodynamic model with freezeout conditions that account for dissipative effects in non-central Au-Au collisions.
• The study underscores the need for advanced models when the shear viscosity-to-entropy density ratio exceeds 0.3 to accurately interpret RHIC data.

Simulating Elliptic Flow with Viscous Hydrodynamics: A Technical Overview

In the study of relativistic heavy-ion collisions, understanding the behavior and properties of the quark-gluon plasma (QGP) is of paramount importance. The paper "Simulating elliptic flow with viscous hydrodynamics," authored by K. Dusling and D. Teaney, explores this area by examining how viscous hydrodynamic models can simulate elliptic flow in non-central Au-Au collisions. This work seeks to address both the influence of viscosity on elliptic flow and the limitations of traditional hydrodynamic approaches.

Key Findings and Methodology

The authors employ a 2+1 dimensional viscous hydrodynamic model, assuming longitudinal boost invariance, to simulate non-central Au-Au collisions. Utilizing fluid equations proposed by Öttinger and Grmela, the model incorporates freezeout conditions determined by viscous corrections relative to ideal terms. Key numerical results from this study highlight the sensitivity of the elliptic flow vector $v_2$ at high transverse momentum $p_T$ to viscous corrections in the thermal distribution function.

When viscous corrections are neglected, the impact of viscosity on the elliptic flow is modest. However, incorporating these corrections demonstrates a significant modification of the elliptic flow at large $p_T$, showcasing the dominance of off-equilibrium phenomena in shaping differential flow spectra. It is argued that deviations from the Navier-Stokes stress tensor form, especially when the shear viscosity-to-entropy density ratio $\eta/s$ exceeds a threshold (approximately 0.3), lead to large dissipative corrections, questioning the reliability of hydrodynamic descriptions.

Implications for Heavy-Ion Collision Studies

The nuanced understanding of elliptic flow modifications due to viscosity is crucial for interpreting RHIC (Relativistic Heavy Ion Collider) outcomes. The work suggests that the accurate description of $v_2$ necessitates a careful consideration of dissipative effects, particularly for systems characterized by large viscous corrections. The findings emphasize that hydrodynamic models should integrate realistic transport coefficients and boundary conditions to accurately reflect experimental data.

Furthermore, this research underscores the limitations of first-order viscous hydrodynamics, advancing the proposition that higher-order theories or kinetic descriptions might be required when $\eta/s$ becomes substantial. This indicates a need for more sophisticated models to accurately capture the complete dynamics at large $p_T$.

Theoretical Considerations and Future Directions

Theoretical challenges remain, particularly in estimating $\eta/s$ near the QCD phase transition and understanding its complete influence on collective observables. The comparison of viscous results to kinetic theory calculations is a promising avenue. Future work must explore integrating phase transition dynamics and examining other dissipative mechanisms like bulk viscosity, which may dominate under certain conditions.

Overall, this study represents a significant step toward quantitatively understanding the role of viscosity in elliptic flow, specifically at high transverse momenta. Continued investigation into viscous hydrodynamics, incorporating the interplay between kinetic theory and full hydrodynamic simulations, will be essential for advancing our theoretical and experimental understanding of QGP physics.