Causal viscous hydrodynamics in 2+1 dimensions for relativistic heavy-ion collisions (0712.3715v2)

Abstract: We explore the effects of shear viscosity on the hydrodynamic evolution and final hadron spectra of Cu+Cu collisions at ultrarelativistic collision energies, using the newly developed (2+1)-dimensional viscous hydrodynamic code VISH2+1. Based on the causal Israel-Stewart formalism, this code describes the transverse evolution of longitudinally boost-invariant systems without azimuthal symmetry around the beam direction. Shear viscosity is shown to decelerate the longitudinal and accelerate the transverse hydrodynamic expansion. For fixed initial conditions, this leads to a longer quark-gluon plasma (QGP) lifetime, larger radial flow in the final state, and flatter transverse momentum spectra for the emitted hadrons compared to ideal fluid dynamic simulations. We find that the elliptic flow coefficient v_2 is particularly sensitive to shear viscosity: even the lowest value allowed by the AdS/CFT conjecture, eta/s=1/4pi, suppresses v_2 enough to have significant consequences for the phenomenology of heavy-ion collisions at the Relativistic Heavy Ion Collider. A comparison between our numerical results and earlier analytic estimates of viscous effects within a blast-wave model parametrization of the expanding fireball at freeze-out reveals that the full dynamical theory leads to much tighter constraints for the specific shear viscosity eta/s, thereby supporting the notion that the quark-gluon plasma created at RHIC exhibits almost ``perfect fluidity''.

• The paper demonstrates that incorporating shear viscosity within the Israel-Stewart framework extends the QGP lifetime and enhances radial flow.
• The VISH2+1 code accurately predicts transverse momentum spectra and sensitive elliptic flow (v2) behavior compared to ideal fluid models.
• The findings highlight the necessity of viscous corrections in modeling heavy-ion collisions, encouraging a re-evaluation of experimental interpretations.

Overview of Causal Viscous Hydrodynamics in Relativistic Heavy-Ion Collisions

This paper by Huichao Song and Ulrich Heinz investigates the impact of shear viscosity on the dynamics of ultrarelativistic heavy-ion collisions using a 2+1 dimensional viscous hydrodynamics code named VISH2+1. The study integrates the Israel-Stewart causal viscous hydrodynamics to analyze the Cu+Cu collision systems, focusing on how shear viscosity affects the hydrodynamic evolution and final state hadron spectra.

The VISH2+1 code adopts the boost-invariant longitudinal evolution framework and accounts for systems lacking azimuthal symmetry, potentially enhancing the preciseness of hydrodynamic simulations previously characterized by ideal fluid dynamics. It efficiently predicts the effects of the quark-gluon plasma (QGP) lifetime, radial flow, and transverse momentum spectra by incorporating causal viscous dynamics.

Key Findings

The authors demonstrate that shear viscosity plays a crucial role in decelerating longitudinal expansion while accelerating transverse dynamics. Key numerical results indicate that for fixed initial conditions, the presence of viscosity leads to an extended QGP lifetime, amplified radial flow, and relatively flat transverse momentum spectra, compared to an ideal fluid case. Notably, the elliptic flow coefficient $v_2$, a crucial observable for understanding the anisotropic flow in non-central collisions, exhibits a significant sensitivity to shear viscosity, highlighting the importance of including viscous corrections in theoretical models, even when employing values near the lower limit predicted by the AdS/CFT correspondence, $\eta/s \approx 1/4\pi$.

A noteworthy comparison made between numerical solutions and prior analytic estimates within a blast-wave model shows that dynamic models, like VISH2+1, offer more robust constraints on the specific shear viscosity, advocating that the QGP at RHIC demonstrates nearly "perfect fluidity." This signifies the advanced constraints and evaluation capabilities that viscous hydrodynamics provide when applied accurately in such scenarios.

Implications and Future Directions

The study exemplifies the importance of incorporating viscous terms in hydrodynamic models to capture realistic QGP dynamics. The reduction of $v_2$ due to viscosity emphasizes a need to revisit previous conclusions drawn from ideal models for elliptic flow. Addressing the dynamics of QGP precisely can expose significant insights into the nature of the strong interaction under extreme conditions.

Theoretical implications point toward improved modeling strategies for representing the early stages of heavy-ion collisions and the transitions involved. Practically, the results could signify a re-evaluation of experimental data interpretation, requiring models that account for such dissipative effects for more realistic correlations with experimental observables.

Future developments in AI and high-performance computing can enhance the accuracy and efficiency of simulations like VISH2+1. Leveraging emerging computational techniques to solve complex physical systems can extend this research, exploring hitherto inaccessible dimensions and scaling the analysis for larger systems and different energies, potentially unlocking further insights into the QGP's properties and behaviors. Additionally, augmenting computational methodologies with AI-driven optimizations or machine learning could provide deeper predictive insights and help refine theoretical models.

In conclusion, VISH2+1's ability to integrate causal viscous hydrodynamics provides substantial improvements over previous ideal fluid models, bringing the theoretical simulations closer to physical realism, thereby broadening our understanding of the quark-gluon plasma and its unique behavior under extreme conditions. This paper marks a significant step towards precise modeling and represents a pivot towards incorporating detailed microscopic interactions in macroscopic dynamic simulations of heavy-ion collisions.