Fully Dynamical Simulation of Central Nuclear Collisions

We present a fully dynamical simulation of central nuclear collisions around midrapidity at LHC energies. Unlike previous treatments, we simulate all phases of the collision, including the equilibration of the system. For the simulation, we use numerical relativity solutions to anti–de Sitter space/conformal field theory for the preequilibrium stage, viscous hydrodynamics for the plasma equilibrium stage, and kinetic theory for the low-density hadronic stage. Our preequilibrium stage provides initial conditions for hydrodynamics, resulting in sizable radial flow. The resulting light particle spectra reproduce the measurements from the ALICE experiment at all transverse momenta.

Figure 1

Assuming Eq. (2) applied, a “pseudo” temperature [defined by using Eq. (2) with $ϵ=ϵ(T_{\mathrm{pseudo}})$] and radial velocity $v_{\rho }$ are extracted for a representative simulation. The plot illustrates four physical tools used: (i) early time expansion, (ii) numerical AdS evolution, (iii) viscous hydrodynamics until $T=0.17\mathrm{GeV}$, (iv) kinetic theory after conversion into particles (indicated by arrows). The (white) region close to $\tau \sim 0.2\mathrm{fm}/c$, $\rho \sim 5\mathrm{fm}$ indicates a far-from-equilibrium domain where a local rest frame cannot be found.

Figure 2

Time evolution of the energy density at the center of the fireball for different values of the regulator $\sigma$, different AdS/CFT starting times ${\tau }_{\mathrm{init}}$, and different AdS/hydro switching times ${\tau }_{\mathrm{hydro}}$. Shown are the analytic early time result (dotted lines), the numerical AdS/CFT evolution (full lines), the numerical hydro evolution (dashed lines), and the conversion point to the hadron cascade. For $\tau \lesssim 0.35\mathrm{fm}/c$, no sensible matching from AdS/CFT to a hydrodynamic evolution is possible (“no hydro matching”), cf. Fig. 4.

Figure 3

Radial velocity profile at $\tau =1\mathrm{fm}/c$ for different AdS/CFT starting times ${\tau }_{\mathrm{init}}$, different AdS/hydro switching times ${\tau }_{\mathrm{hydro}}>0.35$, and different values for the regulator $\sigma$ (in a.u.). One observes that when normalized to the same final multiplicity, all these choices lead to similar velocity profiles.

Figure 4

Time evolution of the pressure anisotropy $P_L/P_T$ at the center of the fireball for single values of $\sigma$, ${\tau }_{\mathrm{init}}$ but multiple AdS/hydro switching times ${\tau }_{\mathrm{hydro}}$. For $\tau \lesssim 0.35\mathrm{fm}/c$, the pressure anisotropy is wildly varying, prohibiting a sensible matching to hydrodynamics. At later times, matching to hydrodynamics can be performed (indicated by triangles down) and leads to approximately universal late-time evolution until freeze-out to the hadron cascade (indicated by square).

Figure 5

Final $dN/dY$ and pion $⟨p_T⟩$ as a function of the hydro switching time ${\tau }_{\mathrm{hydro}}$ for a single value of $\sigma$, ${\tau }_{\mathrm{init}}$ ($\mathrm{AdS}+\mathrm{hydro}+\mathrm{\text{cascade}}$) compared to experimental data (“ALICE”). AdS results seem to be independent of ${\tau }_{\mathrm{hydro}}$ provided that ${\tau }_{\mathrm{hydro}}>0.5\mathrm{fm}/c$. By contrast, results for FS models with ${\tau }_{\mathrm{init}}=0.05\mathrm{fm}/c$ exhibit strong ${\tau }_{\mathrm{hydro}}$ dependence. Error bars correspond to accumulated numerical error.

Figure 6

Pion and kaon momentum spectra for 0%–5% most central $\mathrm{Pb}+\mathrm{Pb}$ collisions at $\sqrt{s}=2.76\mathrm{TeV}$. Experimental measurements (ALICE, Ref. 22) are compared to our $\mathrm{AdS}+\mathrm{hydro}+\mathrm{\text{cascade}}$ model (lines correspond to different choices of ${ϵ}_0$, $\sigma$), the ZF and FS model initialized from Eq. (1) followed by hydro at ${\tau }_{\mathrm{hydro}}=1\mathrm{fm}/c$.