New Exact Solutions of Relativistic Hydrodynamics for Longitudinally Expanding Fireballs

Tamás Csörgő,Máté Csanád,Zefang Jiang,Gábor Kasza

doi:10.3390/universe4060069

Abstract

We present new, exact, finite solutions of relativistic hydrodynamics for longitudinally expanding fireballs for arbitrary constant value of the speed of sound. These new solutions generalize earlier, longitudinally finite, exact solutions, from an unrealistic to a reasonable equation of state, characterized by a temperature independent (average) value of the speed of sound. Observables such as the rapidity density and the pseudorapidity density are evaluated analytically, resulting in simple and easy to fit formulae that can be matched to the high energy proton–proton and heavy ion collision data at RHIC and LHC. In the longitudinally boost-invariant limit, these new solutions approach the Hwa–Bjorken solution and the corresponding rapidity distributions approach a rapidity plateaux.

Highlights

Some of the most renowned theoretical papers in high energy heavy ion physics deal with exact solutions of perfect fluid hydrodynamics for a 1 + 1 dimensional, longitudinally expanding fireball.In high energy collisions involving strong interactions, statistical particle production rates were noted by Fermi already in 1950 [1]
New exact solutions including a realistic, lattice QCD based equation of state and the effects of angular momentum [34] were found to describe well the mass systematics of single particle spectra from a strongly interacting quark-gluon plasma being converted to a multi-component hadron gas [32]
It was found that the BJP solution describes the longitudinal evolution in relativistic heavy ion collisions both at Relativistic Heavy Ion Collider (RHIC) and at Large Hadron Collider (LHC), when a leading particle effect is included, for a realistic, constant value of the speed of sound, including the centrality dependence in Cu + Cu and Au + Au collisions at s NN = 200 GeV and in Pb + Pb collisions at s NN = 2.76 TeV [54]

Summary

Introduction

Some of the most renowned theoretical papers in high energy heavy ion physics deal with exact solutions of perfect fluid hydrodynamics for a 1 + 1 dimensional, longitudinally expanding fireball.In high energy collisions involving strong interactions, statistical particle production rates were noted by Fermi already in 1950 [1]. Landau’s prediction about the perfect fluid behaviour in high energy heavy ion collisions was, at that time quite unexpectedly, fully confirmed by the discoveries after the first four years of data-taking at Brookhaven National Laboratory’s Relativistic Heavy Ion Collider (RHIC) where the picture of a nearly perfect strongly interacting fluid emerged from the first years of observations of the four RHIC collaborations, BRAHMS [5], PHENIX [6], PHOBOS [7], and STAR [8]. When the experiment called “A Large Ion Collider Experiment” (ALICE) Collaboration reported the first elliptic flow measurement at the Large Hadron Collider (LHC) in Pb + Pb collisions at √. S NN = 2.76 TeV [9], they noted the similarity of the transverse momentum dependence of the elliptic flow to earlier, lower energy data at RHIC and noted its consistency with predictions of hydrodynamic models, confirming the creation of a nearly perfect fluid of strongly interacting. More detailed measurements by ALICE, and the experiments called “A Toroidal LHC ApparatuS” or ATLAS and “Compact Muon Solenoid”

Results

Discussion

Conclusion