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Anisotropic transverse flow and the quark-hadron phase transition

Peter F. Kolb, Josef Sollfrank, Ulrich Heinz

TL;DR

The paper tackles how collision centrality and initial energy density shape transverse flow patterns, especially elliptic flow $v_2$, and how a quark-hadron phase transition might imprint non-monotonic signatures on beam-energy and impact-parameter dependences. It adopts (3+1)-dimensional ideal hydrodynamics, simplified to 2+1D near midrapidity with exact boost invariance, and connects the EOS to observables via freeze-out spectra generated with Cooper-Frye on a fixed decoupling density, solving the evolution with the SHASTA method. By comparing three EOS (hadronic, QGP, and a mixed-phase with Maxwell construction) and spanning beam energies from AGS to beyond the LHC, the study predicts that $v_2$ forms earlier than radial flow and can thus probe high-density EOS, including signatures of a phase transition expected between SPS and RHIC energies. It also proposes central uranium-uranium collisions in a side-on-side configuration as an optimal setup to maximize hydrodynamic applicability and enhance sensitivity to the phase-transition signal in flow observables.

Abstract

We use (3+1)-dimensional hydrodynamics with exact longitudinal boost-invariance to study the influence of collision centrality and initial energy density on the transverse flow pattern and the angular distributions of particles emitted near midrapidity in ultrarelativistic heavy-ion collisions. We concentrate on radial flow and the elliptic flow coefficient v2 as functions of the impact parameter and of the collision energy. We demonstrate that the finally observed elliptic flow is established earlier in the collision than the observed radial flow and thus probes the equation of state at higher energy densities. We point out that a phase transition from hadronic matter to a color-deconfined quark-gluon plasma leads to non-monotonic behaviour in both beam energy and impact parameter dependences which, if observed, can be used to identify such a phase transition. Our calculations span collision energies from the Brookhaven AGS (Alternating Gradient Synchrotron) to beyond the LHC (Large Hadron Collider); the QGP phase transition signature is predicted between the lowest available SPS (CERN Super Proton Synchrotron) and the highest RHIC (Brookhaven Relativistic Heavy Ion Collider) energies. To optimize the chances for applicability of hydrodynamics we suggest to study the excitation function of flow anisotropies in central uranium-uranium collisions in the side-on-side collision geometry.

Anisotropic transverse flow and the quark-hadron phase transition

TL;DR

The paper tackles how collision centrality and initial energy density shape transverse flow patterns, especially elliptic flow , and how a quark-hadron phase transition might imprint non-monotonic signatures on beam-energy and impact-parameter dependences. It adopts (3+1)-dimensional ideal hydrodynamics, simplified to 2+1D near midrapidity with exact boost invariance, and connects the EOS to observables via freeze-out spectra generated with Cooper-Frye on a fixed decoupling density, solving the evolution with the SHASTA method. By comparing three EOS (hadronic, QGP, and a mixed-phase with Maxwell construction) and spanning beam energies from AGS to beyond the LHC, the study predicts that forms earlier than radial flow and can thus probe high-density EOS, including signatures of a phase transition expected between SPS and RHIC energies. It also proposes central uranium-uranium collisions in a side-on-side configuration as an optimal setup to maximize hydrodynamic applicability and enhance sensitivity to the phase-transition signal in flow observables.

Abstract

We use (3+1)-dimensional hydrodynamics with exact longitudinal boost-invariance to study the influence of collision centrality and initial energy density on the transverse flow pattern and the angular distributions of particles emitted near midrapidity in ultrarelativistic heavy-ion collisions. We concentrate on radial flow and the elliptic flow coefficient v2 as functions of the impact parameter and of the collision energy. We demonstrate that the finally observed elliptic flow is established earlier in the collision than the observed radial flow and thus probes the equation of state at higher energy densities. We point out that a phase transition from hadronic matter to a color-deconfined quark-gluon plasma leads to non-monotonic behaviour in both beam energy and impact parameter dependences which, if observed, can be used to identify such a phase transition. Our calculations span collision energies from the Brookhaven AGS (Alternating Gradient Synchrotron) to beyond the LHC (Large Hadron Collider); the QGP phase transition signature is predicted between the lowest available SPS (CERN Super Proton Synchrotron) and the highest RHIC (Brookhaven Relativistic Heavy Ion Collider) energies. To optimize the chances for applicability of hydrodynamics we suggest to study the excitation function of flow anisotropies in central uranium-uranium collisions in the side-on-side collision geometry.

Paper Structure

This paper contains 5 sections, 8 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The hydrodynamic model
  3. The equation of state
  4. Reduction to 2+1 dimensions
  5. Initialization of the fields

Figures (3)

  • Figure 1: The three equations of state discussed in the text, at vanishing net baryon density.
  • Figure 2: The equation of state EOS Q with a quark-hadron phase transition. The pressure is shown as a function of energy and net baryon density, $e$ and $n$. For each value of $n$ there exists a minimum energy density $e_{\rm min}(n)$ with corresponding pressure $p_{\rm min}(e_{\rm min},n)$; below $e_{\rm min}$ the pressure is set to zero by hand.
  • Figure :