Anisotropic hydrodynamic modeling of 200 GeV Au-Au collisions

We compare phenomenological results from $(3+1)$-dimensional quasiparticle anisotropic hydrodynamics (aHydroQP) with experimental data collected from RHIC 200 GeV Au-Au collisions. We compare identified particle spectra in different centrality classes, charged particle multiplicity versus pseudorapidity, identified particle multiplicity versus centrality across a wide range of particle species, identified particle elliptic flow versus transverse momentum, and charged particle elliptic flow as a function of transverse momentum and rapidity. We use the same aHydroQP and hadronic production codes that were used previously to describe LHC 2.76 TeV data. The aHydroQP hydrodynamic model includes the effects of both shear and bulk viscosities in addition to an infinite number of transport coefficients computed self-consistently in the relaxation-time approximation. To convert to the final-state hadrons, we use anisotropic Cooper–Frye freeze-out performed on a fixed-energy-density hypersurface and compute the production and feed-down by using a customized version of Therminator 2. We find good agreement with many heavy-ion collision observables using only smooth Glauber initial conditions parametrized by an initial central temperature of $T_0=455$ MeV, a constant shear-viscosity-to-entropy-density ratio $\eta /s=0.179$, and a switching (freeze-out) temperature of $T_{\mathrm{FO}}=130$ MeV.

Figure 1

Quasiparticle model bulk viscosity over entropy density as a function of temperature.

Figure 2

Pion, kaon, and proton spectra compared with experimental observations by the PHENIX collaboration [97]. The panels show the centrality classes (a) 0%–5%, (b) 5%–10%, (c) 10%–15%, (d) 15%–20%, (e) 20%–30%, and (f) 30%–40%.

Figure 3

(left panel) The ratio $\mathrm{\Delta }$ defined in Eq. (20) in the 0%–5% centrality class using the full distribution (solid) and the isotropic distribution (dashed). (right panel) Same in the 20%–30% centrality class. In both panels the solid blue, dashed red, and long-dashed green lines show $\mathrm{\Delta }$ for pions, kaons, and protons, respectively.

Figure 4

Identified particle multiplicities as a function of centrality. From top to bottom, the particles shown are ${\pi }^{+},K^{+},p,\varphi$, and ${\mathrm{\Omega }}^{+}+{\mathrm{\Omega }}^{-}$. The data for ${\pi }^{+},K^{+}$, and $p$ are from the PHENIX collaboration [97]. Data for the $\varphi$ meson production are also from the PHENIX collaboration [98]. The data for ${\mathrm{\Omega }}^{+}+{\mathrm{\Omega }}^{-}$ comes from the STAR collaboration [99]. The aHydroQP theory results are binned by using the centrality bins used by the PHENIX collaboration for ${\pi }^{+},K^{+}$, and $p$.

Figure 5

Theory-to-data ratio for identified particle multiplicity (shown in Fig. 4). For this figure, we rebinned the theory predictions for the $\varphi$ and ${\mathrm{\Omega }}^{+}+{\mathrm{\Omega }}^{-}$ to match the experimental bins.

Figure 6

aHydroQP results for charged particle multiplicity in different centrality classes (solid lines) compared with experimental data from the PHOBOS collaboration [100]. Panel (a) shows centrality classes in the range 0%–25% and panel (b) shows centrality classes in the range 25%–50%.

Figure 7

Elliptic flow for charged particles in four different centrality classes: (a) 0%–10%, (b) 10%–20%, (c) 20%–30%, and (d) 30%–40%. The solid black line is the aHydroQP prediction and the points are observations by the PHENIX collaboration [101]. The experimental errors reported by the PHENIX collaboration are smaller than the point size used. For comparison, the red dashed line shows the result obtained when an isotropic freeze-out prescription with the same effective temperature is used.

Figure 8

aHydroQP results for the identified particle elliptic flow as a function of transverse momentum compared with experimental data from the PHENIX collaboration [103]. The blue solid line, red dashed line, and green dotted lines are the aHydroQP predictions for pions, kaons, and protons, respectively. The blue squares, red triangles, and green circles are experimental observations. The panels (a)–(f) show the centrality classes 0%–10%, 10%–20%, 20%–30%, 30%–40%, 40%–50%, and 50%–60%.

Figure 9

Comparison between our aHydroQP model results for the integrated elliptic flow versus pseudorapidity and experimental data from the PHOBOS collaboration [104, 105]. The aHydroQP results are indicated by a solid red line and the PHOBOS data by black points with error bars. The experimental error bars include both statistical and systematic uncertainties.