Rela%vis%c Hydrodynamics in High- Energy Heavy Ion Collisions

Transcription

1 Rela%vis%c Hydrodynamics in High- Energy Heavy Ion Collisions Kobayashi Maskawa Ins/tute Department of Physics, Nagoya University Chiho NONAKA December 13, 2013, Nagoya

2 Rela%vis%c Heavy Ion Collisions RHIC:2000 高 T Heavy Ion Collisions LHC,RHIC Strongly interacting QGP Relativistic hydrodynamics Recombination model Jet quenching Color Glass Condensate Heavy Ion collisions start! Quark- Gluon Plasma sqgp LHC:2010 QCD Cri/cal Point Property of QGP LHC: Energy frontier RHIC: energy scan FAIR, NICA high density 陽子 中間子など Hadron Phase Color Super Conductor C. NONAKA µb

3 Dynamics of Heavy Ion Collisions collisions thermaliza/on hydro hadroniza/on freezeout Observables: a lot of experimental data at RHIC and LHC photons/leptons bulk property Jets heavy quarkonia Phenomenological model Ini%al condi%on? sqgp Hydrodynamic model Freezeout process Experimental data higher harmonics

4 Higher Harmonics Reaction plane z y x more realis/c event by event fluctua/ons y x ellip/c flow higher harmonics

5 Higher RHIC & LHC PHENIX@RHIC, PRL107,252301(2011) ATLAS@LHC, PRC86,014907(2012) P T (GeV) P T (GeV)

6 Ini%al Condi%ons One event Ollitrault

7 Ini%al Condi%ons One event Ollitrault

8 Ini%al Condi%ons One event Ollitrault

9 Numerical Scheme Superposi/on of shock waves Numerical algorithm for hydrodynamic evolu/on shock- wave capturing scheme stable less numerical viscosity

10 Hydrodynamic Expansion Ini%al condi%on sqgp Hydrodynamic model Freezeout process fluctua/ng ini/al condi/ons v n Bulk property transport coefficients.. importance of numerical algorithm!

11 Akamatsu, Inutsuka, CN, Takamoto: arxiv: J. Comp. Phys. (2014) 34 HYDRODYNAMIC MODEL

12 Viscous Hydrodynamic Model Rela/vis/c viscous hydrodynamic equa/on First order in gradient: acausality Second order in gradient: Israel- Stewart, Ofnger and Grmela, AdS/CFT, Grad s 14- momentum expansion, Renomariza/on group Numerical scheme Shock- wave capturing schemes: Riemann problem Godunov scheme: analy/cal solu/on of Riemann problem SHASTA: the first version of Flux Corrected Transport algorithm, Song, Heinz, Pang, Victor Kurganov- Tadmor (KT) scheme, McGill

13 Israel- Stewart Theory Our Approach Takamoto and Inutsuka, arxiv: Akamatsu, Inutsuka, CN, Takamoto, arxiv: (ideal hydro) 1. dissipa/ve fluid dynamics = advec/on + dissipa/on exact solu/on Contact discon/nuity Rarefac/on wave Shock wave Riemann solver: Godunov method Two shock approxima/on Mignone, Plewa and Bodo, Astrophys. J. S160, 199 (2005) Rarefac/on wave shock wave 2. relaxa/on equa/on = advec/on + s/ff equa/on

14 Numerical Scheme Israel- Stewart Theory Takamoto and Inutsuka, arxiv: Dissipa/ve fluid equa/on 2. Relaxa/on equa/on + advec/on s/ff equa/on I: second order terms

15 Comparison Shock Tube Test : Molnar, Niemi, Rischke, Eur.Phys.J.C65,615(2010) T L =0.4 GeV v=0 EoS: ideal gas Analy/cal solu/on Numerical schemes SHASTA, KT, NT Our scheme T R =0.2 GeV v= Nx=100, dx=0.1, dt=0.04

16 Shocktube problem Ideal case shockwave rarefac/on

17 L1 Norm Numerical dissipa/on: devia/on from analy/cal solu/on T L =0.4 GeV v=0 T R =0.2 GeV v= L(p(N cell ),p(anaytic)) = N cell p(n cell ) For analysis of heavy ion collisions N cell =100: dx=0.1 fm p(analytic) Ncell i=1 λ=10 fm

18 Large ΔT difference T L =0.4 GeV, T R =0.172 GeV SHASTA becomes unstable. Our algorithm is stable. T L =0.4 GeV v=0 EoS: ideal gas SHASTA: an/ diffusion term, A ad A ad = 1 : default value, unstable A ad =0.99: stable, more numerical dissipa/on T R =0.172 GeV v= Nx=100, dx=0.1, dt=0.04

19 L1 norm SHASTA with small A ad has large numerical dissipa/on Aad=1 Aad=0.99 T L =400, T R =200 T L =400, T R =172 L(p(N cell ),p(anaytic)) = N cell p(n cell ) p(analytic) Ncell i=1 λ=10 fm

20 Ar%ficial and Physical Viscosi%es Molnar, Niemi, Rischke, Eur.Phys.J.C65,615(2010) An/diffusion terms : ar/ficial viscosity stability

21 Large ΔT difference T L =0.4 GeV, T R =0.172 GeV SHASTA becomes unstable. Our algorithm is stable. T L =0.4 GeV v=0 EoS: ideal gas SHASTA: an/ diffusion term, A ad A ad = 1 : default value A ad =0.99: stable, more numerical dissipa/on Large fluctua/on (ex ini/al condi/ons) T R =0.172 GeV v= Nx=100, dx=0.1, dt=0.04 Our algorithm is stable even with small numerical dissipa/on.

22 DYNAMICAL MODEL

23 Our Dynamical Model collisions thermaliza/on hydro hadroniza/on freezeout Fluctua/ng Ini/al condi/ons Hydrodynamic expansion Freezeout process From Hydro to par/cle Akamatsu, Inutsuka, CN, Takamoto, Final state interac/ons arxiv: J. Comp. Phys. (2014) 34 MC- KLN Nara hop:// hydrodynamic model Cornelius Freezeout hypersurface finder Huovinen, Petersen Oscar sampler Ohio group UrQMD

24 Our Dynamical Model collisions thermaliza/on hydro hadroniza/on freezeout Fluctua/ng Ini/al condi/ons Hydrodynamic expansion Freezeout process From Hydro to par/cle Akamatsu, Inutsuka, CN, Takamoto, Final state interac/ons arxiv: J. Comp. Phys. (2014) 34 MC- KLN Nara hop:// hydrodynamic model Cornelius Freezeout hypersurface finder Huovinen, Petersen Simula/on setups: Free gluon EoS Hydro in 2D boost invariant simula/on UrQMD with y <0.5 Oscar sampler Ohio group UrQMD

25 Ini%al Pressure Distribu%on MC- KLN (centrality 15-20%) Pressure (fm- 4) LHC 10 5 Y(fm) X(fm) C. NONAKA RHIC 5 0 Y(fm) X(fm)

26 Time Evolu%on of v n RHIC v1 v2 v3 v4 v LHC v1 v2 v3 v4 v time (fm) 0 Qualita/vely RHIC ~ LHC v 2 is dominant v 2 > v 3 > v 4 > v time (fm)

27 Hydro + UrQMD Transverse momentum spectrum RHIC P T dn/dp T [GeV -2 ] LHC P T [GeV] P T [GeV] Pt distribu/on at LHC has flaoer slope Larger radial flow at LHC

28 Effect of Hadronic Interac%on Transverse momentum distribu/on RHIC P T [GeV] P T dn/dp T [GeV -2 ] Effect of final state interac/ons is small Slope of proton Pt spectra become flaoer LHC P T [GeV]

29 Higher harmonics from Hydro + UrQMD Effect of hadronic interac/on

30 Summary Importance of numerical scheme in Hydrodynamic Models We develop a state- of- the- art numerical scheme Shock wave capturing scheme: Godunov method Our algorithm Less ar/ficial diffusion: crucial for viscosity analyses Stable for strong shock wave Construc/on of a hybrid model Fluctua/ng ini/al condi/ons + Hydrodynamic evolu/on + Higher Harmonics Time evolu/on, hadron interac/on UrQMD