Initialization of hydrodynamics in relativistic heavy ion collisions with an energy-momentum transport model

A key ingredient of hydrodynamical modeling of relativistic heavy ion collisions is thermal initial conditions, an input that is the consequence of a prethermal dynamics which is not completely understood yet. In the paper we employ a recently developed energy-momentum transport model of the prethermal stage to study influence of the alternative initial states in nucleus-nucleus collisions on flow and energy density distributions of the matter at the starting time of hydrodynamics. In particular, the dependence of the results on isotropic and anisotropic initial states is analyzed. It is found that at the thermalization time the transverse flow is larger and the maximal energy density is higher for the longitudinally squeezed initial momentum distributions. The results are also sensitive to the relaxation time parameter, equation of state at the thermalization time, and transverse profile of initial energy density distribution: Gaussian approximation, Glauber Monte Carlo profiles, etc. Also, test results ensure that the numerical code based on the energy-momentum transport model is capable of providing both averaged and fluctuating initial conditions for the hydrodynamic simulations of relativistic nuclear collisions.

Figure 1

The energy density distribution along axis $x$ ($y=0$) in transverse plane for central rapidity slice at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c for the following conditions of the relaxation evolution: ${\tau }_0=0.1$ fm/c, the Gaussian initial transverse energy density profile, $\lambda =1$, EoS $p=\epsilon /3,{\tau }_{\mathrm{rel}}=0.5$ fm/c, and the target energy-momentum tensor corresponds to ideal hydrodynamics.

Figure 2

The energy density distribution at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c under the same conditions as in Fig. 1, but with large initial anisotropy, $\lambda =0.01$.

Figure 3

The comparison of the results of the relaxation model for energy density distributions at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c for momentum isotropic, $\lambda =1$, and very anisotropic, $\lambda =0.01,\lambda =100$ initial states under the same other conditions as in Fig. 1.

Figure 4

The transverse velocity distribution at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c and $\lambda =1$ under the same conditions as in Fig. 1.

Figure 5

The transverse velocity distribution at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c under the same conditions as in Figs. 1 and 4 but softer EoS: $p=0.15\epsilon$.

Figure 6

The transverse velocity distribution at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c under the same conditions as in Figs. 1 and 4 but harder EoS: $p=0.7\epsilon$.

Figure 7

The transverse velocity distribution at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c under the same conditions as in Figs. 1 and 4, but with large initial anisotropy, $\lambda =0.01$.

Figure 8

The comparison of the results of the relaxation model for transverse velocity distributions at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c for isotropic, $\lambda =1$, and very anisotropic, $\lambda =0.01,\lambda =100$ initial states under the same other conditions as in Fig. 1.

Figure 9

The comparison of the energy density distributions at different ${\tau }_{\mathrm{rel}}=0.2,0.5,0.8$ fm/c under the same other conditions as in Fig. 1.

Figure 10

The comparison of the transverse velocity distributions at different ${\tau }_{\mathrm{rel}}=0.2,0.5,0.8$ fm/c under the same other conditions as in Figs. 1 and 4.

Figure 11

The energy density distribution along axis $x$ ($y=0$) in transverse plane for central rapidity slice at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c for the following conditions of the relaxation evolution: ${\tau }_0=0.1$ fm/c, the Gaussian initial transverse energy density profile, $\lambda =1$, EoS $p=\epsilon /3,{\tau }_{\mathrm{rel}}=0.5$ fm/c, and the target energy-momentum tensor corresponds to viscous hydrodynamics with $\eta /s=0.1$.

Figure 12

The transverse velocity distribution at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c under the same conditions as in Fig. 11.

Figure 13

The initial transverse distribution at $\tau ={\tau }_0=0.1$ fm/c of the energy density along the $x$ axis ($y=0$) for the random single event produced by the GLISSANDO generator within Monte Carlo Glauber model. Smoothed distribution is shown by the dashed line.

Figure 14

The final energy density distribution along axis $x$ ($y=0$) in transverse plane for central rapidity slice at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c for GLISSANDO original and smeared initial energy density profiles shown in Fig. 13. The following conditions of the relaxation evolution are used: ${\tau }_0=0.1$ fm/c, $\lambda =1$, EoS $p=\epsilon /3,{\tau }_{\mathrm{rel}}=0.5$ fm/c, and the target energy-momentum tensor corresponds to viscous hydrodynamics with $\eta /s=0.25$.

Figure 15

The transverse velocity distribution for GLISSANDO original and smeared initial energy density profiles at $\tau ={\tau }_{\mathrm{th}}=1.0$ fm/c under the same conditions as in Fig. 14.