Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 1 Rashmi Raniwala Department of Physics University of Rajasthan Jaipur HYDRO & FREEZEOUT FROM STAR DATA For STAR collaboration

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 2 Time Initial conditions Initial hard interactions Dense Partonic Matter Hydro description Hadronization and chemical freeze-out Kinetic freeze-out Some experimental handles on Bulk Properties at various stages: ● Anisotropic flow : develops in early expansion stage (EoS,  ) ● Hadron Yield ratios : are fixed at Chemical Freezeout (T chemical,  B,  S ) ● Identified particle p T spectra reflect the random and collective motion at kinetic freezeout: (T f,    EVOLUTION OF A HEAVY ION COLLISION AT RHIC Bulk of this produced matter is soft

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 3 PLAN OF THE TALK STAR results on: ● Freezeout parameters from identified particle spectra ● Freezeout parameters from integrated particle ratios ● Elliptic flow

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 4 STAR : A SUITE OF DETECTORS Barrel EM Calorimeter FTPCs Time Projection Chamber Silicon Tracker SVT & SSD Endcap Calorimeter Magnet Coils TPC Endcap & MWPC Central Trigger Barrel & TOF Beam Beam Counters 4.2 meters Not Shown: pVPDs, ZDCs, and FPDs A TPC lies at the heart of STAR PMD

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 5 SOME EXPERIMENTAL ASPECTS TO DETERMINE THE SPECTRA A bulk of the identified particle information comes from TPC. ● Particle identification accomplished through ● dE/dx at low p T (π ±, K ±, p and p-bar) ● Decay topology with invariant mass reconstruction (K s 0, Λ, Λ-bar, Ξ, Ξ-bar, Ω + Ω-bar) ● Combinatorial invariant mass reconstruction (φ, K*) ● Corrections applied for tracking inefficiency, detector acceptance, hadronic interactions and particle decays. These corrections obtained from embedding MC tracks. ● Spectra integrated over all phase space to obtain total particle yields

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 6 SPECTRA OF IDENTIFIED PARTICLES IN AuAu AT 200GEV ● p T spectra of identified particles in AuAu 200GeV at various centralities. ● These spectra are flatter than the spectra at SPS and also for pp collisions. ● Mass dependent hardening of the spectra : collective radial motion STAR data : N.P.A 757(2005) 102 PHENIX data: P.R.C 69(2004) Inspired by the thermal equilibrium scenario of hydrodynamics, a Blast-wave model is fit to Spectra of all hadrons simultaneously to give a common radial flow velocity  T & freeze-out temperature T f The multi-strange hadrons do not fit to the common values of T f and  T : Different production mechanism? Decouple at a different time ?

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 7 FREEZE-OUT PARAMETERS (E.Schnedermann et al, PRC48 (1993) 2462) whereand Blast-wave model: , K, p  T= 90MeV,   T=160MeV,  STAR Preliminary

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 8 SYSTEMATICS OF KINETIC FREEZEOUT PARAMETERS: CENTRALITY AND SYSTEM SIZE DEPENDENCE STAR Preliminary Freeze-out parameters T f and β T are extracted for each centrality ● for different colliding systems ● for different colliding energies Fall on a narrow band with overlapping values STAR Preliminary STAR has fit the spectra of π ±,K ±, p,pbar for AuAu and CuCu collisions at 62.4 GeV and 200 GeV to Blast-Wave model 10% central, 200 GeV STAR Preliminary

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 9 As a function of dN ch /dη : T f decreases &  T increases Peripheral collisions are slower and hotter & central collisions are faster and cooler Freezeout parameters for different systems and different energy scale with dN ch /dη Consistent with hydrodynamic expectations: fireball in peripheral collision is short lived -> radial flow does not build up so particles decouple earlier at a higher temperature STAR Preliminary SYSTEMATICS OF KINETIC FREEZE-OUT VALUES STAR Preliminary

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 10 HADRON YIELDS AT STAR Hadron Yield Ratios are fit to statistical model to derive the properties of a macroscopic system at chemical freezeout Statistical model characterizes this stage by 4 parameters : T chemical, μ B, μ S,  S  S approaching 1 in central collisions : strangeness saturation T chemical is constant for all dN ch /d  : universal chemical freeze-out (T kinetic for multistrange hadrons ~ T chemical : freezeout soon after hadronization STAR Preliminary Universal temperature

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 11 ● Hadron ratios fit to statistical model show that the strangeness is saturated at chemical freezeout ● T chemical is independent of system size and energy for AuAu and CuCu at 200 and 62.4 GeV and is close to the critical temperature predicted by Lattice QCD. The universality of T chemical indicates a “critical energy density” at which hadrons are formed ● T chemical > T kinetic : T kinetic decreases with increasing dN ch /d  With increasing centrality the system expands more rapidly after chemical freezeout. ● A larger and denser system is therefore faster and colder at kinetic freeze-out CONCLUSIONS FROM SPECTRA AND HADRONIC YIELDS

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 12 Anisotropic overlap geometry of collision -> causes anisotropic pressure gradients -> momentum anisotropy Reaction zone expands faster in the reaction plane -> decrease spatial eccentricity (self quenching) Elliptic flow develops before spatial eccentricity vanishes. So elliptic flow is sensitive to early stages of evolution P.F.Kolb & U.Heinz Nucl.Phys.A 71(2003) 653c WHY IS ANISOTROPIC FLOW IMPORTANT?

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 13 First Elliptic Flow Results at RHIC Centrality Dependence of elliptic flow results: hydrodynamic predictions agree for more central collisions and show deviations for peripheral collisions. In addition to initial state anisotropy, magnitude of v 2 controlled by : ● Time of thermalization ● Amount of re-scattering ● Softness of the equation of state Large values of v 2 at RHIC indicate early thermalization time (t ~ 1fm/c): presence of a strongly interacting medium AuAu √s NN = 130GeV STAR Coll. PRL 86(2001) 402

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 14 FLOW FOR IDENTIFIED PARTICLES: TRANSVERSE MOM. DEPENDENCE v 2 increases with p T as predicted by hydrodynamical model. Mass ordering of v 2 for identified particles as expected from hydro. Data for ,K,p,  is plotted for 200GeV along with ideal hydro predictions: match within 30% Hydrodynamics fails to predict the v 2 behaviour above p T >1.5GeV: v 2 saturates at two different values for mesons and baryons.

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 15 v 2 OF IDENTIFIED PARTICLES AT INTERMEDIATE TRANSVERSE MOM. The mass ordering and the saturation values of v 2 for mesons and baryons seems to obey an interesting scaling. Here we show v 2 scaled by number of constituent quarks, n q, as a function of p T also scaled by n q Results for different particles fall on a single curve: indicating that the flow originates at the partonic level, and that hadrons are seemingly formed by a coalescence of partons.

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 16 All centralities: mass ordering at low p T  m T -m scaling at low m T -m. All centralities: baryon v 2 > meson v 2 at intermediate p T or m T -m. STAR Preliminary Transverse kinetic energy: m T – m =  (p T ) 2 + m 2 - m Transverse momentum Hydro: P. Huovinen, private communications, GeV Au+Au CENTRALITY DEPENDENCE OF v 2 FOR STRANGE IDENTIFIED PARTICLES

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 17 ECCENTRICITY SCALING(?) STAR Preliminary v 2 /n q is scaled by  part to remove initial geometric effects Larger v2/  part indicates stronger flow in more central collisions. We do not observe the  part scaling claimed by PHENIX Divided v 2 by ch instead of  part, it appears that the scaling works better PHENIX: Phys. Rev. Lett 98, (2007) Phys. Lett. B 503, 58 (2001) 200 GeV Au+Au (c)

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 18 STAR Preliminary Charge particle data: STAR, Phys. Rev. C 72, , v 2 /  part versus N part  data: increasing trend indicates stronger flow in more central collisions.  hydro: little sensitivity to the collision centrality as expected in equilibrium scenario. v 2 /  part for a given centrality  data for diff. hadrons: not clear due to large errors  hydro: a clear hadron mass dependence Above N part ~ 170, integrated v 2 consistent with hydro prediction local thermalization? 200 GeV Au+Au pp p T -INTEGRATED v 2 /ε part

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 19 SYSTEM SIZE DEPENDENCE OF ELLIPTIC FLOW STAR Preliminary A given colliding system ; clear scaling with n q. System size dependence: - No  part scaling claimed by PHENIX - v 2 seems to fall at lower p T in Cu+Cu than in Au+Au PHENIX: Phys. Rev. Lett 98, (2007)

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 20 FLOW IN  MESONS  mesons: small hadronic cross- section Expected to provide information about the early partonic stages of the system evolution. v 2 (  ) measured using m inv (K + +K - ) Centrality dependence of v 2 consistent with charged hadrons At low p T, v 2 shows hydro mass ordering and follows n q scaling for mesons at intermediate p T s quarks flow as strongly as lighter quarks thermalized hot dense matter with parton collectivity has been formed at RHIC-> STAR: Phys. Rev. Lett., 99, (07), nucl-ex/

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 21 ● PMD measures photons by preshower reconstruction in rapidity range -2.3 to -3.7 for AuAu and CuCu collisions at 200GeV ● Centrality and  dependence similar to charge particles ● v 2 /  {2} scaled with N part for different colliding systems: equilibration? FLOW IN INCLUSIVE PHOTONS MEASURED IN PMD

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 22 ● Large values of Integrated v 2 indicate an early thermalization and is seen to agree with hydro predictions for central collisions ● Elliptic flow at low p T fits ideal hydro-predictions with T c = 165MeV and T freezeout = 100MeV which are close to the values suggested by Blast wave model fits to data ● At intermediate p T : v 2 saturates deviating from ideal hydro predictions ● At intermediate p T, v 2 /n q scales with p T /n q indicating hadron production by quark coalescence model => observed flow orginates in pre-hadronic stage and partonic collectivity is observed ● v 2 /  is seen to increase for small N part and tend to saturate for large N part indicating a possible equilibrium as predicted by hydro. CONCLUSIONS FROM ELLIPTIC FLOW RESULTS

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 23 Extra Slides

Rashmi Raniwala Hot & Dense Matter in RHIC-LHC Era, February 12-14, 2008, TIFR, Mumbai 24 QM’08, Jaipur, India, February 4-10, Anisotropic flow:… page 24 How (in)complete is the thermalization? note that there is a difference of a factor of “2” in the definitions of S Even central Au+Au collisions are about 30-50% away from ideal hydro limit! Note: assumed constant speed of sound - no phase transitions, change in initial conditions with energy, 2d, boost invariance, etc , , 5.7 h=0.46 σ=4.3 h=0.25 σ=5.7