Higher flow harmonics from (3+1)D event-by-event viscous hydrodynamics (1109.6289v2)

Abstract: We present event-by-event viscous hydrodynamic calculations of the anisotropic flow coefficients v_2 to v_5 for heavy-ion collisions at the Relativistic Heavy-Ion Collider (RHIC). We study the dependence of different flow harmonics on shear viscosity and the morphology of the initial state. v_3 and higher flow harmonics exhibit a particularly strong dependence on both the initial granularity and shear viscosity. We argue that a combined analysis of all available flow harmonics will allow to determine eta/s of the quark gluon plasma precisely. Presented results strongly hint at a value (eta/s)_QGP < 2/4pi at RHIC. Furthermore, we demonstrate the effect of shear viscosity on pseudo-rapidity spectra and the mean transverse momentum as a function of rapidity.

Anisotropic Flow Coefficients in Heavy-Ion Collisions: A Study Using (3+1)D Event-by-Event Viscous Hydrodynamics

In the paper "Higher flow harmonics from (3+1)D event-by-event viscous hydrodynamics," the authors Schenke, Jeon, and Gale undertake a detailed study of anisotropic flow coefficients, specifically $v_2$ to $v_5$, within heavy-ion collisions at the Relativistic Heavy-Ion Collider (RHIC). Using a (3+1)-dimensional event-by-event viscous hydrodynamic model, they analyze the impact of shear viscosity and initial state morphology on these flow harmonics, with implications for determining the shear viscosity to entropy density ratio, $\eta/s$, of the quark-gluon plasma (QGP).

Hydrodynamic Modeling Framework

The methodology employed relies on second-order relativistic viscous hydrodynamics in the Israel-Stewart framework. The authors present equations of conservation for energy, momentum, and baryon number, extending the description to include dissipative effects. The rigorous numerical implementation uses a coordinate system advantageous for analyzing systems with rapid longitudinal expansion, utilizing hyperbolic conservation equations solved through the Kurganov-Tadmor scheme and Heun's method.

Analysis and Key Findings

The analysis reveals a pronounced sensitivity of higher flow harmonics $v_3$ to $v_5$ to the system's shear viscosity and the granularity of the initial state, determined through the Monte-Carlo Glauber model. The results imply that finer initial state structures lead to a hardening of the spectra and amplify odd flow harmonics generated by fluctuations. Notably, an increase in initial state granularity results in a substantial enhancement of higher $v_n$, whereas the shear viscosity predominantly suppresses these coefficients. The simulations indicate a substantial sensitivity, with $v_5$ reflecting an 80% suppression in viscous simulations compared to ideal ones. These effects compound the ability to constrain the value of $\eta/s$, with suggestions of a possible value lower than $2/4\pi$, given current results.

Further insights are drawn on the influence of shear viscosity across long-range rapidity, impacting pseudo-rapidity spectra and mean transverse momentum deviations, where the longitudinal coupling significantly redistributes momentum. The authors also address the algorithms stabilizing computations under conditions of high flow velocity, contributing to the robustness of the simulation results.

Implications and Future Directions

Practically, this research underscores the utility of probing higher flow harmonics to refine the estimates of transport coefficients of the QGP. The weak dependence of $v_2$ on viscosity compared to higher $v_n$ highlights the latter's potential in offering more granular control and understanding of the heavy-ion collision dynamics. The findings serve as a precursor to systematic extraction of $\eta/s$, integrating robust quantitative analysis of initial state models with sophisticated fluctuation descriptions.

Theoretically, event-by-event hydrodynamic simulations bridge fundamental understanding of initial state influence on flow observables with emergent phenomena in QGP dynamics. Future advancements could explore alternative initial state models like the Color Glass Condensate and incorporate full (3+1)-dimensional fluctuations. Moreover, extending these studies to LHC energies will further corroborate with experimental data and enhance predictive capabilities across different heavy-ion collision environments.

In summary, Schenke, Jeon, and Gale provide insightful contributions, advancing understanding of anisotropic flow in the QGP and highlighting complex interactions between initial state conditions and dissipative properties—a pivotal step in precision modeling of heavy-ion physics.