Dissipative effects from transport and viscous hydrodynamics

TL;DR

The study cross-validates Israel-Stewart dissipative hydrodynamics against covariant 2→2 transport theory in a 2+1D boost-invariant, RHIC-like setting with a conformal $\varepsilon = 3p$ equation of state. It demonstrates that IS hydrodynamics can reproduce central-pressure evolution and differential elliptic flow $v_2(p_T)$ from kinetic transport when $\eta/s \sim 1/(4\pi)$ or large cross sections ($\sigma \approx 50$ mb), provided all terms in the IS evolution are retained. Dissipative effects reduce $v_2(p_T)$ by about 30% relative to ideal hydrodynamics, with contributions from both modified hydrodynamic variables and non-equilibrium distortions of the momentum distribution, and the agreement is strongest in the dense core. The results suggest that IS dissipative hydrodynamics is a promising framework for RHIC phenomenology if the QGP shear viscosity is indeed very small, contingent on careful freezeout treatment and momentum-distribution corrections.

Abstract

We compare 2->2 covariant transport theory and causal Israel-Stewart hydrodynamics in 2+1D longitudinally boost invariant geometry with RHIC-like initial conditions and a conformal e = 3p equation of state. The pressure evolution in the center of the collision zone and the final differential elliptic flow v2(pT) from the two theories agree remarkably well for a small shear viscosity to entropy density ratio eta/s ~ 1/(4 pi), and also for a large cross section sigma ~ 50 mb. A key to this agreement is keeping ALL terms in the Israel-Stewart equations of motion. Our results indicate promising prospects for the applicability of Israel-Stewart dissipative hydrodynamics at RHIC, provided the shear viscosity of hot and dense quark-gluon matter is indeed very small for the relevant temperatures T ~ 200-500 MeV.

Figures (2)

• Figure 1: Proper time evolution of the average transverse ($T^{xx}$, solid) and longitudinal pressure ($T^{zz}$, dashed) in covariant transport (symbols) and causal Israel-Stewart hydrodynamics (no symbols) near the center of the collision zone ($r_T < 1$ fm) for RHIC-like initial conditions (see text) and $\eta/s \approx 1/(4\pi$). For clarity, $T^{zz}$ is divided by a factor of 10.
• Figure 2: Left: Elliptic flow as a function of $p_T$ for $Au+Au$ at $\sqrt{s_{NN}} \sim 200$ GeV and $b= 8$ fm from ideal hydrodynamics (dotted) and IS hydrodynamics with Cooper-Frye freezeout ignoring (dashed) or incorporating (solid) dissipative corrections to the local momentum distributions (see text) for $\eta/s \approx 1/(4\pi)$. Right: Comparison of $v_2(p_T)$ from covariant transport (squares) and IS hydrodynamics (lines) for $\eta/s \approx 1/(4\pi)$ (open squares vs dashed), and $\sigma_{gg\to gg} \approx 47$ mb (filled squares vs solid). The ideal hydro reference is also shown (dotted).