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Perfect Fluid: flow measurements are described by ideal hydro

Measuring Viscosity at RHIC Sean Gavin Wayne State University. Perfect Fluid: flow measurements are described by ideal hydro Problem: all fluids have some viscosity -- can we measure it?.

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Perfect Fluid: flow measurements are described by ideal hydro

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  1. Measuring Viscosity at RHIC Sean Gavin Wayne State University Perfect Fluid: flow measurements are described by ideal hydro Problem: all fluids have some viscosity -- can we measure it? I. Radial flow fluctuations: Dissipated by shear viscosity II. Contribution to transverse momentum correlations III. Implications of current fluctuation data S.G., M. Abdel-Aziz, Phys. Rev. Lett. 97, 162302 (2006) IV. Rapidity + Azimuthal Correlation Data -- in progress

  2. Measuring Shear Viscosity Elliptic and radial flow suggest small shear viscosity • Teaney; Kolb & Heinz; Huovinen & Ruuskanen Problem: initial conditions & EOS unknown • CGC  more flow? larger viscosity? Hirano et al.; Kraznitz et al.; Lappi & Venugopalan; Dumitru et al. Small viscosity or strong flow? Additional viscosity probes? What does shear viscosity do? It resists shear flow. flow vx(z) shear viscosity 

  3. Transverse Flow Fluctuations small variations in radial flow in each event neighboring fluid elements flow past one another  viscous friction shear viscosity drives velocity toward the average damping of radial flow fluctuations  viscosity

  4. z Evolution of Fluctuations u momentum current for small fluctuations r u(z,t) ≈ vr  vr  shear stress momentum conservation diffusion equation for momentum current kinematic viscosity shear viscosity  entropy density s, temperature T

  5. Viscosity Broadens Rapidity Distribution viscous diffusion drives fluctuation gt   rapidity broadening random walk in rapidityyvs. proper time V = 2/0 V increase kinematic viscosity Ts formation at0 /0

  6. fluctuations diffuse through volume, drivingrg rg,eq Hydrodynamic Momentum Correlations momentum flux density correlation function rg rg r g,eqsatisfies diffusion equation Gardiner, Handbook of Stochastic Methods, (Springer, 2002) width in relative rapidity grows from initial value 

  7. C()  Transverse Momentum Covariance observable: measures momentum-density correlation function C depends on rapidity interval  propose:measure C() to extract width 2 of rg

  8. Current Data? STAR measures rapidity width of pt fluctuations J.Phys. G32 (2006) L37 find width *increases in central collisions • most peripheral *~ 0.45 • central *~ 0.75 naively identify*with  freezeout  f,p~ 1 fm,  f,c~ 20 fm   ~ 0.09 fm at Tc~ 170 MeV  s ~ 0.08 ~ 1/4

  9. Current Data? STAR measures rapidity width of pt fluctuations J.Phys. G32 (2006) L37 find width *increases in central collisions • most peripheral *~ 0.45 • central *~ 0.75 naively identify*with  (strictly, ) but maybe n  2*STAR, PRC 66, 044904 (2006) uncertainty range *   2*  0.08 < s < 0.3

  10. Part of a   Correlation Landscape near side peak focus:near side peak -- “soft ridge”   behavior: transverse and elliptic flow, momentum conservation plus viscous diffusion S.G. in progress STAR Theory

  11. Soft Ridge: Centrality Dependence STAR, J.Phys. G32 (2006) L37 trends: • rapidity broadening (viscosity) • azimuthal narrowing near side peak • pseudorapidity width   • azimuthal width  centrality dependence: path length   common explanation of trends? find:requires radial and elliptic flow plus viscosity

  12. Flow  Azimuthal Correlations mean flow depends on position blast wave momentum distribution: opening angle for each fluid element depends on r correlations: gaussian spatial r(x1, x2): • t -- width in • t -- width in

  13. radial plus elliptic flow: “eccentric” blast wave constraints: flow velocity, radius from measured v2, pt vs. centrality STAR 200 GeV Au+Au PHENIX 200 GeV Au+Au diffusion + flow for correlations npart npart Measured Flow Constrains Correlations Heinz et al.

  14. Rapidity and Azimuthal Trends rapidity width: • viscous broadening, s ~  • assume local equilibrium for all impact parameters • fixes Fb  STAR data, J.Phys. G32 (2006) L37  azimuthal width: • flow dominates • viscosity effect tiny agreement with data easier if we ignore peripheral region -- nonequilibrium?

  15. Summary: small viscosity or strong flow? need viscosity info to test the perfect liquid • viscosity broadens momentum correlations in rapidity • pt covariance measures these correlations current correlation data compatible with comparable to other observables with different uncertainties azimuthal and rapidity correlations • flow + viscosity works! hydro OK • relation of  structure to the jet-related ridge?

  16. ptFluctuations Energy Independent Au+Au, 5% most central collisions • sources of ptfluctuations: thermalization, flow, jets? • central collisions  thermalized • energy independent bulk quantity  jet contribution small

  17. Azimuthal Correlations from Flow transverse flow: narrows angular correlations • no flow     •  vrel elliptic flow: • v2 contribution • STAR subtracted momentum conservation: •  sin  ; subtracted Borghini, et al viscous diffusion: • increases spatial widths t and t •  t  t-1/2

  18. blast wave: transverse plus elliptic flow: “eccentric” blast wave STAR 200 GeV Au+Au PHENIX 200 GeV Au+Au npart npart Elliptic and Transverse Flow elliptic flow transverse flow flow observables: fix x, y, and R vs. centrality

  19. Blast Wave Azimuthal Correlations gaussian spatial r(x1, x2): • t -- width in • t -- width in azimuthal trend : • t  system size • t constant • roughly: STAR 200 GeV Au+Au data

  20. Uncertainty Range we want: STAR measures: density correlations momentum density correlations density correlation functionrn rn r n,eq may differ from rg maybe n  2* STAR, PRC 66, 044904 (2006) uncertainty range *   2*  0.08  s  0.3

  21. Covariance Momentum Flux covariance unrestricted sum: correlation function: C =0 in equilibrium 

  22. sQGP + Hadronic Corona viscosity in collisions -- Hirano & Gyulassy supersymmetric Yang-Mills: s   pQCD and hadron gas: s~ 1 Broadening from viscosity Abdel-Aziz & S.G, in progress H&G  QGP + mixed phase + hadrons  T()

  23. Part of a   Correlation Landscape soft ridge: near side peak superficially similar to ridge seen with jets J. Putschke, STAR but at soft ptscales -- no jet near side peak STAR, J.Phys. G32 (2006) L37

  24. Flow Contribution dependence on maximumpt, max PHENIX flow added thermalization  2 = pt    pt  explained by blueshift? needed: more realistic hydro + flow fluctuations

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