Elliptic and triangular flow in event-by-event (3+1)D viscous hydrodynamics (1009.3244v2)

Abstract: We present results for the elliptic and triangular flow coefficients in Au+Au collisions at root-s=200 AGeV using event-by-event (3+1)D viscous hydrodynamic simulations. We study the effect of initial state fluctuations and finite viscosities on the flow coefficients v_2 and v_3 as functions of transverse momentum and pseudo-rapidity. Fluctuations are essential to reproduce the measured centrality dependence of elliptic flow. We argue that simultaneous measurements of v_2 and v_3 can determine eta/s more precisely.

• The paper demonstrates that initial state fluctuations in the hydrodynamic model significantly enhance elliptic flow in central collisions and induce triangular flow in peripheral events.
• The paper employs a (3+1)D viscous hydrodynamic framework with Israel-Stewart corrections and a Glauber Monte Carlo initialization to simulate heavy-ion collisions accurately.
• The paper finds that increasing shear viscosity systematically reduces both v2 and v3 coefficients, aligning simulation results with experimental transverse momentum and rapidity dependencies.

Elliptic and Triangular Flow in Event-by-Event (3+1)D Viscous Hydrodynamics

The paper authored by B. Schenke, S. Jeon, and C. Gale offers a comprehensive paper on elliptic ($v_2$) and triangular ($v_3$) flow coefficients in heavy-ion collisions using a (3+1)D viscous hydrodynamic simulation. Specifically, it explores Au+Au collisions at $\sqrt{s}=200A\,{\rm GeV}$, integrating event-by-event fluctuations while also incorporating finite shearing viscosities to assess their impact on transverse momentum and pseudo-rapidity dependencies.

Key Methodologies and Theoretical Framework

The paper employs a relativistic hydrodynamic model, enhanced with viscous terms derived from the Israel-Stewart formalism to circumvent issues posed by the Navier-Stokes equations, such as unphysical superluminal signals. The stress-energy tensor is adapted to include viscous corrections, deploying the Kurganov-Tadmor (KT) scheme alongside Heun's method to solve the resulting equations.

For initialization, the paper uses a Glauber Monte-Carlo model to configure energy densities, accounting for initial state fluctuations. This model distributes energy densities in proportion to wounded nucleons, incorporating flux-tube structures that are corroborated by long-range rapidity correlation measurements. A Woods-Saxon parametrization is applied to describe the nucleon distribution, ensuring compatibility with observed multiplicity distributions.

The authors perform a Cooper-Frye freeze-out to compute final particle distributions, incorporating resonance decay contributions to evaluate transverse momentum ($p_T$) and rapidity. They demonstrate the computation of event-plane-aligned flow coefficients, which differ from those averaged over reaction planes but align more accurately with experimental data across centrality classes.

Numerical Results and Analysis

Simulation results reveal that initial state fluctuations enhance the elliptic flow in central collisions due to larger anisotropies relative to the event-plane. Conversely, for less central collisions, odd flow coefficients like the triangular flow $v_3$ emerge primarily due to these fluctuations. Moreover, increasing the shear viscosity $\eta/s$ systematically reduces both $v_2$ and $v_3$, with notable reductions observed at larger $|\eta_p|$ values.

For charged hadrons, empirical data aligns with the transverse momentum dependency for $v_2$, particularly when a value of $\eta/s=0.08$ is employed, which corresponds with the theoretical bounds suggested by AdS/CFT. Notably, the simulations indicate viscosity's significant damping effect on $v_2(\eta_p)$, which yet exceeds empirical data away from mid-rapidity.

Implications and Future Directions

This work provides pivotal insights into the role of initial state fluctuations and viscosity in heavy-ion collision dynamics, advancing the precision of hydrodynamic models. The findings suggest that combining analyses of elliptic and triangular flow coefficients can refine shear viscosity determinations, potentially enhancing predictive capabilities in QCD matter studies.

The implications of this research extend to improving the understanding of the quark-gluon plasma's properties and informing the development of more accurate theoretical models. Future endeavors may focus on refining initial condition models and investigating other collision systems or energies, further bolstering the synergy between theoretical simulations and experimental investigations.