Benchmark of initial state models for heavy-ion collisions at $\sqrt{s_{NN}}=27$ and 62 GeV

Description of relativistic heavy-ion collisions at the energies of the BNL Relativistic Heavy Ion Collider (RHIC) Beam Energy Scan program with fluid dynamic approach poses several challenges, one of which being a complex geometry and a longer duration of the prehydrodynamic stage. Therefore, existing fluid dynamic models for heavy-ion collisions at the RHIC Beam Energy Scan energies rely on rather complex initial states, such as urqmd cascade or multifluid dynamics. In this study, we show that functionally simpler, nondynamical initial states can be employed for the fluid-dynamical simulations of Au-Au collisions at $\sqrt{s_{{}_{NN}}}=27$ and 62.4 GeV. We adapt the initial states based on the Monte Carlo Glauber model (glissando 2) and $\sqrt{T_A{T}_B}$ ansatz based on reduced thickness (${\mathrm{t}}_{\mathrm{r}}$ ento $p=0$), extended into the longitudinal direction and finite baryon density. We find that both initial states, when coupled to a three-dimensional event-by-event viscous fluid dynamic $+$ cascade model, result in an overall fair reproduction of basic experimental data: pseudorapidity distributions, transverse momentum spectra, and elliptic flow, at both collision energies. This is rather surprising given that the $\sqrt{T_A{T}_B}$ ansatz is functionally similar to the EKRT and IP-Glasma models, which are successful at much larger energies and rely on a partonic picture of the initial state.

Figure 1

Pseudorapidity density of charged hadrons in Au-Au collisions at $\sqrt{s_{{}_{NN}}}=27$ and 62.4 GeV from the vhlle $+$ urqmd simulations with glissandro and urqmd initial states. Given that no experimental data points are available for $\sqrt{s_{{}_{NN}}}=27$ GeV, the data points from Ref. [24] are plotted for neighboring energy $\sqrt{s_{{}_{NN}}}=19.6$ GeV.

Figure 2

Rapidity distribution of net protons at $\sqrt{s_{{}_{NN}}}=62.4$ GeV (top panel) and $\sqrt{s_{{}_{NN}}}=27$ GeV (bottom panel) from the vhlle$+$ urqmd simulations with the urqmd, glissandro, and $t_r$ento initial states. The experimental data points for 0%–5% central Au-Au collisions are taken from BRAHMS [25], whereas the model calculations correspond to 5%–10% centrality. The experimental data points for $\sqrt{s_{{}_{NN}}}=17.2$ GeV are taken from NA49 [26].

Figure 3

Transverse momentum spectra of positively charged pions, kaons, and protons at $\sqrt{s_{{}_{NN}}}=27$ GeV from the vhlle$+$urqmd simulations with urqmd, glissandro and $t_r$ento initial states. The experimental data points for 20%–30% central Au-Au collisions are taken from Ref. [27].

Figure 4

Same as Fig. 3 but for $\sqrt{s_{{}_{NN}}}=62.4$ GeV. The experimental data points for 20%–30% central Au-Au collisions are taken from Ref. [28].

Figure 5

Mean transverse momentum of positively charged pions, kaons, and protons as a function of centrality at $\sqrt{s_{{}_{NN}}}=27$ GeV from the vhlle $+$ urqmd simulations with urqmd, glissandro, and $t_r$ento initial states. The experimental data points for 20%–30% central Au-Au collisions are taken from Ref. [27].

Figure 6

Same as Fig. 5 but for $\sqrt{s_{{}_{NN}}}=62.4$ GeV. The experimental data points for 20%–30% central Au-Au collisions are taken from Ref. [28].

Figure 7

Elliptic and triangular flows of all charged hadrons as a function of transverse momentum $p_T$, for 20%–30% Au-Au collisions at $\sqrt{s_{{}_{NN}}}=27$ GeV, from the calculations using urqmd, glissandro, and $t_r$ento initial states. The experimental data points are taken from Ref. [23].

Figure 8

Same as Fig. 7 but for $\sqrt{s_{{}_{NN}}}=62$ GeV Au-Au collisions.

Figure 9

Elliptic and triangular flows of all charged hadrons as a function of centrality for $\sqrt{s_{{}_{NN}}}=27$ GeV Au-Au collisions, from the calculations using urqmd, glissandro, and $t_r$ento initial states. The experimental data points are taken from Ref. [23].

Figure 10

Same as Fig. 9 but for $\sqrt{s_{{}_{NN}}}=62$ GeV Au-Au collisions. The experimental data points are taken from Ref. [29].

Figure 11

Elliptic flow of all charged hadrons as a function of centrality for $\sqrt{s_{{}_{NN}}}=27$ GeV Au-Au collisions, computed with the event plane method. The curves represent model calculations using the urqmd, glissandro, and $t_r$ento initial states. The experimental data points are taken from Ref. [23].

Figure 12

Average eccentricities of the initial-state energy density as a function of centrality percentile for $\sqrt{s_{{}_{NN}}}=27$ GeV Au-Au collisions. The eccentricities are computed in the urqmd, glissandro, and $t_r$ento ($p=0$) initial states.

Figure 13

Elliptic flow of all charged hadrons as a function of centrality for $\sqrt{s_{{}_{NN}}}=27$ GeV Au-Au collisions, computed with event plane method. The curves represent model calculations using the urqmd initial state with and without transverse flow at the fluidization, and the $t_r$ento initial state with and without shear viscosity at the fluid stage. The experimental data points are taken from Ref. [23].

Figure 14

Mean transverse momentum of positively charged pions, kaons, and protons as a function of centrality for $\sqrt{s_{{}_{NN}}}=27$ GeV Au-Au collisions. The curves represent model calculations using the urqmd initial state with and without transverse flow at the fluidization, and the $t_r$ento initial state with and without shear viscosity at the fluid stage. The experimental data points are taken from Ref. [27].