Event-by-event Hydrodynamic Simulation Of Relativistic Heavy Ion Collisions

The Relativistic Heavy Ion Collider (RHIC) at the Brookhaven National Lab-oratory and the Larger Hadron Collider (LHC) at the European Organization for Nuclear Research (CERN) are two large high-energy physics facilities where heavy ions are accelerated to relativistic speed and collide with each other. Physicists attempt to produce a form of hot and dense matter called quark gluon plasma (QGP) and study its properties in these nuclear collisions. The QGP was orig-inally expected to be a system of weakly coupled quark and gluon gas due to the asymptotic freedom of Quantum Chromodynamic (QCD). Comparisons be-tween experimental data and relativistic viscous hydrodynamic simulations indi-cate, however, that the QGP formed in heavy-ion collisions at RHIC and LHC behaves like a strongly coupled fluid with extremely small values of shear viscosity to entropy ratio. It is therefore termed as strongly coupled quark gluon plasma (sQGP).In a parton model, relativistic heavy ion collisions can be considered as col-lisions between two beams of quarks and gluons, generally referred to as partons, from inside the nucleons. The collisions between partons can be divided into hard and soft process according to the energy and time scales involved. Hard and incoherent scatterings with large transverse momentum transfer happen at very early time and produce energetic partons or jets in the final state. For collisions with small transverse and longitudinal momentum transfer, the coherence time can become comparable or larger than the nuclear size according to the uncer-tainty principle. The produced soft partons, mainly gluons, become coherent over large longitudinal distance between the leading valence quarks and diquarks of the colliding nucleons. These coherence soft partons can be effectively described as longitudinal color flux tubes which have small transverse momentum and evolve slowly at a time scale that is much longer than that of their color source or va-lence quarks and diquarks. These gluons are so dense and their phase space may overlap to form a condensed matter. Such a picture is also referred to as the Color Glass Condensate (CGC) model of heavy-ion collisions.How these color flux tubes evolve into a dense matter with local equilibrium in less than1fm/c, as indicated by the experimental data, is still not well under-stood. Currently two possible scenarios have been proposed. In the first scenario, color flux tubes break into partons by quantum pair production and the produced partons achieve fast thermalization via2->2elastic and2->3inelastic processes. An alternative scenario is that the non-Abelian plasma instabilities can drive the flux tubes to isotropization with a scattering rate much faster than that given by perturbative parton scattering. The classical Yang-Mills theory, parton cascade and lattice gauge transport all have been used to study the early time evolution in relativistic heavy ion collisions. The subsequent evolution of the quark gluon plasma can be described by ideal or viscous hydrodynamic simulation. At the late stage of the evolution of the expanding system, when the energy density becomes smaller than the critical value for color confinement, hadrons can form via parton combination. Such hadronization can be described through an effective equation of state (EoS) in hydrodynamic simulations. In the later stage of the evolution when the mean free path is too large, system will be far from local thermalization and hydrodynamic description will fail. From this point on, hadron transportation models such as the Ultra Relativistic Quantum Molecular Dynamics (URQMD) model can be be used to describe further evolution of the system.The ideal and viscous hydrodynamic models with smoothed initial condition and hadron cascade in the late stage were widely used to study the momentum spectra and elliptic flow of final particles in relativistic heavy ion collisions. They were used to extract shear viscosity from fitting to experimental data. In these hydrodynamic simulations, one has to provide the initial condition on density and flow velocity distributions. In real relativistic heavy ion collisions, there will also be fluctuations in initial conditions which can be introduced by collision geome-try, nucleon distribution in nucleus, parton distribution in nucleon and quantum fluctuation. These fluctuating initial conditions are critical to describe higher, es-pecially odd order harmonic flows and di-hadron correlation. One therefore has to resort to event-by-event simulation to describe experimental data. Comparisons between experimental data on higher harmonic flows and hydrodynamic simula-tions with the transverse and longitudinal fluctuations in the initial conditions can provide more stringent constraint on extracting transport coefficients.In addition to the soft bulk matter whose evolution can be described by rela-tivistic hydrodynamic model, high energy jets produced in the early time will also interact with partons in the expanding medium, from the pre-equilibrium stage, to the hydrodynamic evolution of QGP and Hadron Resonance Gas (HRS) phases. Such interaction will lead to parton energy loss or jet quenching. Jet Quench-ing can be used as hard probes to stud the properties of the expanding medium since it strongly depends on the local temperature. On the other hand, the bulk medium is also affected by the energy deposited by jet quenching. Energy loss of an energetic jet behaves quite differently in a fluctuating expanding medium than a smoothed background. Therefore, event by event hydrodynamic simulations with fluctuating initial conditions are needed for the study of jet quenching. A full simulation of relativistic heavy ion collisions should include both hard and soft physics in each stage of the evolution. These include the initial production of high energy jets based on pQCD, early time thermalization and late time hy-drodynamic evolution of soft partons, jet quenching and the modification to both hard and soft parton spectra, hadronization from jet fragmentation and parton coalescence and the cascading of hadron resonance gas.This thesis focuses on event-by-event hydrodynamic simulations with fluctu-ating initial conditions. I will start with a review on existing event-by-event hy-drodynamic simulations with different initial conditions, different hydrodynamic algorithms and their results. Then I will describe the3+1D ideal hydrodynamic model that we developed, with the fluctuating initial condition obtained from AMPT(A Multiple Phase Transportation) model and our new projection method for calculation of the freeze out hyper surface. The harden partons from mini-jet and soft partons from string fragmentation all take part in parton cascade dur-ing the pre-equilibrium stage in AMPT. The fluctuating energy density and flow velocity in both transverse and longitudinal direction from AMPT model after a short initial period of time are then used as the initial conditions for event-by-event hydrodynamic simulations. We have studied both AuAu collisions at the RHIC energy of (?)=200GeV/nucleon and PbPb collisions at the LHC energy (?)=2.76TeV/nucleon with our event-by-event3+1D relativistic hydrodynamic simulations. We illustrate the effect of the transverse fluctuation and discovered the effect of the longitudinal fluctuation which suppresses elliptic flow noticeably. We also calculate di-hadron correlation and compare to the experimental data. We also study the effect of flow velocity and longitudinal fluctuations on the di-hadron correlation. By using AMPT initial conditions, our event-by-event3+1D hydrodynamic simulations of central heavy-ion collisions naturally give rise to a long range correlation in rapidity, near-side peak from mini-jets and away side double peaks structure from superposition of all hadronic flows. We will provide a description of the numerical implementation for the3+1D ideal hydrodynamic simulation and present the progresses and some results in solving3+1D viscous hydrodynamics with Relativistic Lattice Boltzmann Method.