Causal Viscous Hydrodynamics for Central Heavy-Ion Collisions II: Meson Spectra and HBT Radii

TL;DR

The paper addresses extracting the QGP shear viscosity to entropy density ratio $\eta/s$ from RHIC data using causal second-order viscous hydrodynamics. It implements Israel-Stewart-type equations with a relaxation time $\tau_\Pi$ and analyzes central Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV$, computing pion/kaon spectra and HBT radii via Cooper-Frye with viscous corrections and resonance decays. Key findings show that the data can be described for moderate $\eta/s$ (up to about 0.25–0.4 depending on $\tau_\Pi$), and that viscous entropy production accounts for roughly 50–75% of the final meson multiplicity; viscosity also drives $R_{out}/R_{side}$ toward the data, though absolute radii remain undershot, signaling freeze-out modeling improvements are needed. The results imply a non-ideal fluid near the border between weakly and strongly coupled regimes and highlight the importance of future non-central and elliptic-flow studies to tighten bounds on $\eta/s$.

Abstract

Causal viscous hydrodynamic fits to experimental data for pion and kaon transverse momentum spectra from central Au+Au collisions at \sqrt{s_{NN}}=200 GeV are presented. Starting the hydrodynamic evolution at 1 fm/c and using small values for the relaxation time, reasonable fits up to moderate ratios η/s\simeq 0.4 can be obtained. It is found that a percentage of roughly 50 η/s to 75 η/s of the final meson multiplicity is due to viscous entropy production. Finally, it is shown that with increasing viscosity, the ratio of HBT radii R_{out}/R_{side} approaches and eventually matches the experimental data.

Figures (3)

• Figure 1: Viscous hydrodynamic fits of pion spectra to experimental data from PHENIX (circles) and STAR (squares) Adler:2003cbAdams:2003xp, for relaxation time values $\tau_\Pi=\frac{\eta}{s}\frac{6}{T}$ (left) and $\tau_\Pi=\frac{\eta}{s}\frac{1.5}{T}$ (right). Also shown are results for kaons and protons, scaled by $0.1$ and $0.01$, respectively. (The hydrodynamic results and the STAR data include weak decays while the PHENIX data does not). See text for details.
• Figure 2: Pion HBT Radii from hydrodynamics compared to data from the STAR experiment Adams:2004yc. Shown are the ratios $R_{\rm out}/R_{\rm side}$ (left) and $R_{\rm long}/R_{\rm side}$ (right) for ideal and viscous hydrodynamics (with $\tau_\Pi=\frac{\eta}{s}\frac{6}{T}$ except for results indicated by arrows where $\tau_\Pi=\frac{\eta}{s}\frac{1.5}{T}$). See text for details.
• Figure 3: Pion HBT Radii from hydrodynamics compared to data from the STAR experiment Adams:2004yc. Shown are $R_{\rm out}$ (left) and $R_{\rm side}$ (right) for ideal and viscous hydrodynamics (with $\tau_\Pi=\frac{\eta}{s}\frac{6}{T}$ except for results indicated by arrows where $\tau_\Pi=\frac{\eta}{s}\frac{1.5}{T}$). See text for details.